Matchmaking using Fuzzy Analytical Hierarchy ProcessCompatibility Measure and Stable Matching for OnlineMatrimony in India

KEDAR JOSHI and SUSHIL KUMAROperations Management Area Indian Institute of Management Lucknow UP India

ABSTRACT

Use of online matrimony for matchmaking is rapidly growing in India One of the major difficulties faced by the users of suchwebsites is the long time taken to realize the matches We propose an integrated approach to matchmaking in e-matrimonyenvironment using fuzzy analytical hierarchy process considering multiple criteria involved in the process The objective ofthe study is to enable users to search their partners effectively and efficiently and narrow down to the desired matches so thatthe chances of matchmaking through online portal are maximized A compatibility index that is match metric is developed thatenhances the probability of matchmaking with reduction in lead time Furthermore Gale-Shapley stable matching algorithm isused to help customers obtain the desired shortlist of profiles with a suggested stable match An illustrated hypothetical exampleof matchmaking using an Indian matrimony portal is presented and the use of the proposed methodology is demonstratedCopyright copy 2012 John Wiley amp Sons Ltd

KEY WORDS online matrimony fuzzy AHP compatibility index stable matching matchmaking

1 INTRODUCTION

Most of the people in this world if not all would havesome thoughtsexpectations concerning life partnersGiven these expectations finding a perfect partner isnot an easy job In Indian culture marriage means alifetime commitment and it is expected that theperson is wholly committed and dedicated to his orher life partner In the past marriages in India wouldtraditionally be arranged typically by the parents whowith the help of relatives and other persons wouldfinalize the match for their ward In todayrsquos worldhowever with changes in society and family peoplebeing located at different places because of jobs etcmore and more people take the decision themselvesabout their life partners taking their families inconfidence In this process they get good supportfrom the newspaper advertisements and onlinematrimonial websites in lieu of some charges US-basedEmPower Research has published a report that statesthat the online matrimony industry in India may reach21 million registrations with revenues of $63 million

by 2010ndash2011 According to this research thepopularity of online matrimony services in India hasgrownmainly because of convenience and cost-savingsIf e-marital sites can extend the trust gained by identify-ing a spousepartner for a subscriber to many otherlifelong services the e-matrimony industry may attainvery strong Web loyalty among the Indian population

As far as matrimonial agencies and newspaperadvertisements are concerned Indians are comfortablewith that but still the online matrimonial websiteshave a meagre 15 of penetration in total marketshare of matrimonial business Shaadicom andBharatmatrimonycom are two major players today inthe world of online matrimonial business Gordon andGupta (2003) showed that growth acceleration of theservices in the 1990s was mostly because of the fastgrowth in communication services financial servicesbusiness services (IT) and community services

These matchmaking Web portals provide extensivesearch facility to every customer but actual time torealize the match with one of the prospective profilesfor interaction is longer because of few reasons likecertain good profiles getting curtained because of acrisp key-based search process and usually a profileliked by customer might dislike the customerrsquos profilein response Therefore further contacting them is awaste of time that is lead time of whole matchmakingprocess is prolonged

Correspondence to Operations Management Area IndianInstitute of Management Off Sitapur Road Lucknow-226013 UP India E-mail kedarjoshiiimlorg

Copyright copy 2012 John Wiley amp Sons LtdReceived 31 December 2010

Accepted 7 October 2011

JOURNAL OF MULTI-CRITERIA DECISION ANALYSISJ Multi-Crit Decis Anal 19 57ndash66 (2012)Published online in Wiley Online Library(wileyonlinelibrarycom) DOI 101002mcda487

We propose an integrated fuzzy analytical hierarchyprocess (FAHP) compatibility measure and stablematching-based technique to address these issuesDifferent criteria are fuzzily defined in terms of satisfac-tion level Typical AHP procedure is employed forcalculating profile scores Compatibility measure isdeveloped to reduce the efforts of the customer insearching and sorting the profile from mutual point ofview Gale-Shapley algorithm suggests a stable matchthat specifies the higher probability of getting positiveresponse from the contacted profile

Section 2 explains the findings from the literatureconcerning the online matrimony business in Indiaand the techniques used in helping the process ofmatchmaking Section 3 is devoted towards currentprofile search process in Web portals and the proposedsearch process with AHP compatibility index (CI)and stable matching algorithm Section 4 describesan illustrated example of matchmaking throughInternet portal in India The last section concludesthe findings and highlights the possible improvementsin the matchmaking process

2 ONLINE MATRIMONY BUSINESS IN INDIA

Arranged marriages have been the tradition in Indiansociety for centuries Even today an overwhelmingmajority of Indians have their marriages planned bytheir parents and other respected family membersAlthough most marriages are arranged some couplesin India are opting for love marriage in urban areasAn arranged marriage is effectively the result of awide search by both the girlrsquos family and the boyrsquosfamily Banerjee et al (20009) studied the role playedby caste education and other social and economicattributes in arranged marriages among middle-classIndians Even in modern India there is a strongpreference towards within-caste marriage Parentsgenerally discuss expectations with their sondaughterbefore starting searching for a match These expecta-tions are shared with relatives and family friends whooften bring in valuable suggestions Indian matrimonialsites attempt to provide databases that can be queried tofind matches using similar attributes

Acceptance of online matchmaking as a culturallylegitimate approach to mate selection and consumerspending on these services continues to rise Theonline dating industry is clearly growing in impor-tance as an industry not only because it is becominga popular and efficient way for busy singles to findlove interests but also because of the rich and valuableinformation that it provides for potentially reducing

the rising divorce rate and other types of unsuccessfulrelationships Therefore it is crucial that onlinematching services purporting to use empiricallyvalidated matching systems actually do validatetheir systems and release their findings to the public(Chang et al 2006)

Given the varied and complex matchmakingprocess followed in India that is based on diverseaspects such as caste religion economic standardjob status age height complexion family background etc online matrimony services have becomequite successful Pathak (2005) stated an importanceof the role of computers in future matchmaking atthe hands of marriage bureaus or when independentlyused by the interested parties Online matrimony is anorganized Web-based matrimonial service facilitatingwishful young men and women to find their suitablelife partners In India organized marriage servicesbusiness is worth 10 billion Online matrimony catersto people spread across the globe to find their suitablepartner living in a remote place by matching his or herspecific interests and requirements Dugar et al (2010)indicated that affirmative action policies in India whichseek to enhance the income of the lower-caste popula-tion are not likely to produce any significant changein intercaste marriage

To deal with the behaviour of the clients of amarriage bureau Vaillant (2004) provided roughestimates of the lengths of the personal partnersearches of individuals who seek remarriage using amarriage bureau Few studies related to personslooking for partnership based on multiple attributesin other domains are carried out Chang et al (2006)proposed a fuzzy multiple attribute decision-makingmethod based on the fuzzy linguistic quantifier toselect supply chain partners at different phases ofproduct life cycle Li and Murata (2009) proposed anovel method to match buyers and suppliers in B2Be-marketplace based on priority and multi-objectiveoptimization They analysed matchmaking in a stablebilateral market where each buyer or supplier ismatched with trade partners Batabyal and DeAngelo(2008) studied matchmaking from the perspective ofa matchmaker They analysed the circumstances underwhich a matchmaker optimally accepts or rejectsindividual matching assignments AHP for decisionmaking uses objective mathematics to process theinescapably subjective and personal preferences of anindividual or a group in making a decision With AHPand its generalization one constructs hierarchies thenmakes judgments or performs measurements on pairsof elements with respect to a controlling element toderive ratio scales that are then synthesized throughout

K JOSHI AND S KUMAR58

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

the structure to select the best alternative (Saaty 1980Salo and Hamalainen 1997 Triantaphyllou 2001)Few review papers described the application area inwhich AHP has been successfully used either viastand-alone tool or in combination with other tech-niques (Vaidya and Kumar 2006 Sipahi and Timor2010) Hajeeh and Lairi (2009) employed the AHPbecause of the multiplicity of objectives and surveyedwomen from different ethnic religious and residentialbackgrounds to explore the most preferred criteriaThomaidis and Mavrakis (2006) applied AHP methodwith geopolitical economic and technical criteria todefine the most preferred route of the transcontinentalgas pipeline that branches in SE Europe to transportCaspian gas further into the targeted markets ofEurope Korkmaz (2008) proposed AHP and two-sidedmatching-based decision support system to assistdetailers in the context of assignment of militarypersonnel to positions Matchmaking business hasrecently caught great attention in business schools tooHarvard Business Review published eHarmony (Prodno 709424-HCB-ENG) a case on such business witha successful differentiation strategy It offers a uniqueproduct which combines an extensive relationshipquestionnaire a patented matching system and a guidedcommunication system Vi et al (2010) proposed amathematical approach to optimizing marriage byallocating spouses in such a way that would reduce thelikelihood of divorce or separation Hitsch et al(2010) used a novel data set obtained from an onlinedating service to draw inferences on mate preferencesand to investigate the role played by these preferencesin determining match outcomes and sorting patterns

Various researchers have been looking into economicempirical modeling aspects of this matchmaking Wehave not come across any work that focuses on thematchmaking process in e-matrimony environment

3 PROCESS OF ONLINE MATCHMAKING

In India marriage is viewed as lsquoStrategic decisionrsquo inthe life of humankind because of its non-repetitivenature (in normal conditions) and having long-termeffect on the life of an individual and the followinggenerations It is not an easy decision to make and tolay the proper foundation for any marriage carefuland studied steps that require wisdom and thoroughplanning are necessary Therefore matchmaking isindeed a multi-criterion decision-making processThrough any website portal a customer provides hisor her details as input and expects prospective profilesas a result of search he or she makes using keywords

like height range complexion age difference eatinghabits profession educational qualification etc Eachuser provides his or her authentic information throughonline registration Most of the online matrimony por-tals have person verification requirements as a part oftheir registration process that can be briefed in Figure 1

Although the website provides extensive search facil-ity to the member of the portal the actual time to realizethe match with one of the prospective profiles forinteraction is longer because of the following reasons

bull It is a keyword-based search (0 or 1 type)bull All factors may not be considered by a customerbull Few good profiles might get curtained because ofa specific (crisp) key-based search process

bull Many times person liked by customer might bedisliked by prospective partner therefore proposingto such profiles is waste of time

To overcome the problems faced in the current searchand proposal process we propose a new integratedmethod as depicted in Figure 2 This integrated approachbased on FAHP CI and stable matching algorithm-basedprocess is elaborated stepwise in the following

Step 1 Defining attributes in terms of fuzzy setsUser would like to describe his or her own requirements(attributes) like complexion and salary in terms ofmore fair around 50 000 etc Such linguistic expres-sions need to be converted into fuzzy sets as describedin the example The classical AHP also performspairwise comparison of candidates attribute-wise It iscumbersome here to ask and gather each userrsquos needsattributewise Belot and Francesconi (2010) found thatboth women and men value physical attributes suchas age and weight and those choices are assortativealong age height and education

Let us assume that m men and n women areregistered to the website with their details related to t attri-butes (eg educationoccupation wealth personality)Let D1 D2 D3 Dt represent the customerrsquosattribute-wise requirements in the form of fuzzy sets as(D1 mD1) (D2 mD2) (Dt mDt) where mDt8D=12 3 t represents the membership values of thecustomerrsquos specifications on attribute t

Step 2 Pairwise comparison and calculating scoreof each profileA typical AHP procedure is conducted which consistsof pairwise comparison of attributes at respectivehierarchy to calculate weights for respective criteriaIt leads to calculate the aggregated profile score where

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 59

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

weight of each attribute is multiplied by its respectivefuzzy membership function and then added

Ranking using this profile score will not sufficethe purpose of online matchmaking because of the fol-lowing reasons

bull Matchmaking is a two-sided utility maximizationprocess

bull Every member of the website does rate his or herprospective spousersquos profile

bull It may happen that a person rates the prospectivespouse as the best match on the contrary thatprospective spouse may rate the person as theworst match and vice versa

Step 3 Two-sided matching and sortingMarriage matching on Internet-based system is a typicaltwo-way preferential matching problem Authors ofexperimental empirical theoretical and computationalstudies of two-sided matching markets have recognizedthe importance of correlated preferences Celik andKnoblauch (2007) developed a general method for thestudy of the effect of correlation of preferences on theoutcomes generated by two-sided matching mechan-isms Preferences of both sides are important in two-sided matching Every member of the website has hisor her own attribute requirements and priorities tochoose a life partner Simultaneously a male memberrsquosprofile is rated by respective prospective partnermemberrsquos set factors and subsequent priorities

Here we propose a CI-based method of two-sided matching to emphasize a both-ways matchingintent There are two objectives in this compositionFirst the sum of these two scores in a pair has to bemaximized Second the difference of the opinion abouteach other in terms of aggregate score should be atminimum To meet these objectives a CI is definedas follows

CI frac14 13

Amn thorn Bnm

1thorn 0

5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiAmn Bnm

2 thorn 1q

8gtltgt

9gt=gt

where

Amn = aggregated score of nth female profile as permth malersquos preferencesBnm= aggregated score of mth male profile as per nthfemalersquos preferences

Final sorting in descending order has to be carriedout based on this index CI

Step 4 Stable matching based on Gale-ShapleyalgorithmStable matching problems consist of a set of agentseach of whom submits a preference list ranking asubset of the other agents in order of preference Theproblem is to form a matching M of the agents suchthat no two agents would prefer each other to theirassignment inM (Abraham 2003) The stable matchingproblem is to find such a match between pair of agentsso that neither of the pair finds any other match betterthan the allocated match

An instance of the stable marriage problem consistsof N men N women and each personrsquos preference listA preference list is a totally ordered list including allmembers of the opposite sex depending on his or herpreference For a matchingM betweenmen and womena pair of a man m and a woman w is called a blockingpair if both prefer each other to their current partnersA matching with no blocking pair is called stable Galeand Shapley showed that every instance admits at leastone stable matching and proposed a polynomial timealgorithm to find one which is known as the Gale-Shapley algorithm (Gale amp Shapley 1962) Teo et al(2001) studied the matching mechanism used by theMinistry of Education in the placement of primary sixstudents in secondary schools and discussed why thecurrent method has limited success in accommodatingthe preferences of the students and the specific needsof the schools (in terms of the lsquomixrsquo of admittedstudents) They showed that stable matching mechan-isms are more appropriate in this matching market andexplained why the strategic behaviour of the students

Figure 1 Current search and matchmaking process

K JOSHI AND S KUMAR60

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

need not be a major concern The final outcome of theprocess is a stable match profile and the list of mostrelevant profiles The Gale-Shapley framework is notjust a seminal theoretical benchmark in the economicanalysis of marriage markets it also provides anapproximation to the match outcomes from a realisticsearch and matching model that resembles the environ-ment of an online dating site (Adachi 2003)

An instance of a stable marriage problem may bespecified by the male and female ranking matricesRelative to arbitrary but fixed numberings of menand women these are defined by mr(i k) = j if womank is the jth choice of man i wr(i k) = j if man k is the jth

choice of woman i The problem of how to find a

stable marriage maximizing total satisfaction wasunsolved until Irving et al (1987) used theegalitarian measure of optimality under which totalsatisfaction is maximized

Suppose that for a given stable marriage instanceS = (m1 wl) (mn wn) is a stable matching Theydefined the value c(S) of S by

c Seth THORN frac14 Σn1mr miwieth THORNthornΣn

1wr wimieth THORN

and they said that a stable matching S is optimal if it hasminimum possible value c(S) In real online systemthere are m male and n female profiles as mentioned

Figure 2 Search process with fuzzy analytical hierarchy process and stable matching

Figure 3 Analytical hierarchy process

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 61

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Figure 4 Customerrsquos attribute-wise requirements in the form of fuzzy sets Please see Table VI for abbreviations used

K JOSHI AND S KUMAR62

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

earlier Every customer will receive a suggested stablematched profile and also his or her own preference listbased on lsquocompatibility indexrsquo This enhances the prob-ability of getting a positive response from recipient person

4 ILLUSTRATED EXAMPLE

To validate the proposed method we chose an advancedsearch process from a Web portal known as Jeevansathicom In this illustration we have assumed case of a manwho is looking for a woman as prospective partner formarriage The customer is interested in various profileswith following requirements that are arranged inhierarchical manner as shown in Figure 3

Usually in India partner search is based upon threebroad criteria of prospective partner viz educationoccupation wealth personality An education criterionis related to qualification like Undergraduate Mastersor PhD etc in diverse disciplines like arts commerceengineering and medicine etc Occupation criteriameans a person is an engineer a doctor a charteredaccountant or a professor etc A Wealth criterion con-sists of family status (low class middle class upperclass) earnings (annual income) and location (semi-urban urban metro city) A personality criterion con-sists of age (years) height (cm) complexion (darkwhitish brown brown fair) diet (vegetarian eggitariannon-vegetarian) and body type (slim athletic heavy)

Step 1 Defining attributes in terms of fuzzy setsThe male customer who is looking for a spouse ie awoman with various attributes with hierarchy as statedin Figure 3 Assume that the customer is looking for alsquovery fairrsquo girl in case of attribute type lsquocomplexionrsquoThe customer can define the acceptability with respectto complexion as fuzzy set for example 08 Thismeans that his satisfaction level with that particularattribute is 80 Similarly for every attribute underconsideration he defines his acceptability level iemembership level is asked and fuzzily definedrequirement is generated as shown in Figure 4

Step 2 Pairwise comparison and calculatingaggregate score of each profileA classic AHP procedure is conducted which consistsof a pairwise comparison of attributes at respective

Table I Pairwise comparison of education and occupation

Education Occupation

Education 1 4Occupation 14 1

Table II Pairwise comparison of family status earning andlocation

Family status Earning Location

Family status 1 14 17Earning 4 1 12Location 7 2 1

Table III Pairwise comparison of height age complexiondiet and body type

Height Age Complexion Diet Bodytype

Height 1 6 8 9 5Age 16 1 7 15 110Complexion 18 17 1 7 2Diet 19 5 17 1 5Body type 15 10 12 15 1

Table IV Pairwise comparison of education wealth andpersonality

Education Wealth Personality

Education 1 3 3Wealth 13 1 12Personality 13 3 1

Table V The weight of attributes

Attribute Education Height Occupation Location Body type

Weight () 3945 1513 986 811 621Rank 1 2 3 4 5Attribute Diet Complexion Earning Age Family statusWeight () 587 536 446 442 113Rank 6 7 8 9 10

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 63

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

hierarchy to calculate respective weight for each attri-bute (Tables IndashIV) In this case customer rates eachattribute with respect to other attribute at the samelevel and under the same group From the pairwisecomparisons we get relative weights of attributes asshown in Table V

In our example we consider 10 female memberrsquosdata with different attributes as shown in Table VIThere can be thousands of the profiles in the databaseof any website available Let us calculate profile scorefor profile no 2 This profile has attributes like 27years old 134 cm height complexion as whitishbrown qualification as chartered accountant (CA)belongs to Rich class annual income 22 lac livingin Metro Eating habit as Vegetarian and body typeis Athletic etc

For every profile according to fuzzily definedrequirements membership value can be calculatedComparing the membership values from respectivefuzzy sets and attributes of the profile we get variousmembership values as Education is CA and respectivesatisfaction level is 1 therefore Education=1 Likewiseremaining membership values are Occupation= 044Family status = 0 Earning=1 Location=07 Height =0 Age=06 Complexion=07 Diet = 1 and Bodytype=09

A profile score is calculated by multiplying thismembership value with respective weight fromTable V and aggregating for all attributes For exam-ple for education the weight is 0394

Profile score (A12) = 03945(1) + 00986(044) + 00113(0) + 00446(1) + 00811 (07) + 01513(0) + 00442(06) + 00536(07) + 00587(1) + 00621(09) = 07179

Thus the profile score is 07179 Similarlyprofile scores as per nomenclature describedearlier are as shown in Tables VII and VIII As men-tioned earlier in this mutual matching problem wemust consider what each woman is looking for Everywoman also has defined her requirements in termsof fuzzy sets and done pairwise comparisonThus profile score of this male customer who islooking for female partner can be calculated Tocalculate the compatibility score we use formuladefined in step 3

For example in case of pair male1 and female5ie A15 and B51

CI = 13 [(08372 + 05839) + (08372 + 05839)(2radic[(08372 05839)2 + 1])] = 06963

Thus CI based on male no1rsquos preference witheach female are listed in Table VIII Similarly forevery possible matching pair CI is calculated asrecorded in Table IX T

able

VI

Detailsof

femalemem

bers

No

Educatio

nOccupation

Fam

ilystatus

Earning

Location

Height

Age

Com

plexion

Diet

Bodytype

1BEBTech

Not

working

Upper

middleclass

0Urban

160

26Whitish

Eggitarian

Athletic

2Chartered

accountant

Businessm

anRichclass

22Metro

134

27Whitishbrow

nVegetarian

Athletic

3MCom

Banking

Middleclass

4Rural

137

24Fair

Eggitarian

Slim

4MEM

Tech

EngineeringRampD

Upper

middleclass

14Urban

139

27Fair

Eggitarian

Athletic

5MBAPGDM

LogisticsSCM

Richclass

16Urban

139

27Veryfair

Eggitarian

Heavy

6MCAPGDCA

Software

Middleclass

12Sem

iUrban

162

26Whitishbrow

nVegetarian

Slim

7MDM

S(M

edical)

Teaching

Middleclass

7Sem

iUrban

167

29Dark

Eggitarian

Athletic

8BAMS

Looking

forajob

Middleclass

0Rural

170

25Veryfair

Vegetarian

Slim

9MLLLM

Governm

entservices

Upper

middleclass

8Metro

144

27Whitish

Vegetarian

Athletic

10MBBSBDS

Governm

entservices

Richclass

8Metro

144

27Whitish

Vegetarian

Heavy

Bachelorrsquosof

Engineering

(BE)Masterrsquosof

EngineeringTechnology(M

EM

Tech)Chartered

Accountant(CA)Masterof

Com

merce

(MCom

)Masterof

BusinessAdm

inis-

tration(M

BA)PostG

raduateDiplomain

Managem

ent(PGDM)Masterof

Com

puterApplications

(MCA)PostGraduateDiplomain

Com

puterApplications

(PGDCA)Doctorof

Medicine(M

D)Masters

ofSurgery

(MS)Masterof

Law

(MLLLM)Bachelorof

Ayurveda

MedicineandSurgery

(BAMS)Bachelorof

DentalSurgery

(BDS)

Bachelorof

MedicineBachelorof

Surgery

(MBBS)ResearchandDevelopment(R

ampD)SupplyChain

Managem

ent(SCM)Governm

ent(G

ovt)

K JOSHI AND S KUMAR64

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Based on compatibility scores profiles getshortlisted and ranked in descending order Fur-thermore the customer has liberty to re-rank theprofiles after looking at each of the top 10 profilesSubsequently if the customer re-ranks the profiles thepreferences are taken as input for Gale-Shapleyalgorithm Otherwise profiles ranked based on CI aretreated with respect to their rank To demonstrateGale-Shapley algorithm in this context we assume thatthere are five male and five female profiles with theirpreferences as mentioned in the following table

M1=gtF1-F3-F2-F4-F5 F1 =gtM5-M2-M4-M3-M1M2=gtF2-F1-F3-F5-F4 F2 =gtM2-M4-M5-M1-M3M3=gtF2-F4-F5-F1-F3 F3 =gtM3-M1-M4-M5-M2M4=gtF3-F1-F4-F5-F2 F4 =gtM1-M3-M2-M4-M5M5=gtF5-F2-F4-F3-F1 F5 =gtM2-M1-M3-M5-M4

Gale-Shapley algorithm generates the followingmatches

Male1 is paired with female5 male2 is paired withfemale3 male3 is paired with female4 male4 is pairedwith female2 and male5 is paired with female1

This is an add-on facility for a customer where heor she will receive a suggested stable matched profileIf they contact this suggested profile as well as a few

profiles listed based on their CI then the probabilityof getting positive response increases

5 CONCLUSIONS

In todayrsquos Internet era services seeking efficiency isof paramount importance The approach presented inthis paper attempts to exploit current IT-enabledpartner search for marriage through Web portals

Salient features of this proposed method are asfollows

bull Integrated way to quantify the online profiles withimplicit needs

bull Two-phase short listing ie FAHP and stablematching algorithm

bull Reducing customerrsquos effort to find their mateonline according to their implicit needs (definedfuzzily)

bull Enhancing the probability of getting positiveresponse and matchmaking

A sorting based on CI in descending orderenhances the probability of matchmaking It thus leadsto reduction in lead time of waiting of the positive ornegative reply from the opposite party This opera-tional viewpoint has been presented in this paper with

Table IX Ranking based on compatibility index

A16 A17 A19 A11 A14 A18 A12 A15 A13 A110

Score 09684 08954 07958 08756 08974 08009 07179 08372 04858 08317B61 B71 B91 B11 B41 B81 B21 B51 B31 B101

Score 08517 08692 09306 08142 06982 07576 07743 05839 08824 05079CI 09059 08821 08580 08438 07876 07787 07453 06963 06531 06486Rank 1 2 3 4 5 6 7 8 9 10

CI compatibility index

Table VII Profile scores when female rated by male no 1

A11 A12 A13 A14 A15 A16 A17 A18 A19 A110

Score 08756 07179 04858 08974 08372 09684 08954 08009 07958 08317

Table VIII Profile scores of male no 1 rated by each female

B11 B21 B31 B41 B51 B61 B71 B81 B91 B101

Score 08142 07743 08824 06982 05839 08517 08692 07576 09306 05079

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 65

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

introduction of a CI This index helps user to maxi-mize their requirements while mutual matching

Future studies might cover an enhancement inrating parameters Few Web portals have incorporatedmatchmaking based on personality behaviour Morequalitative and quantitative factors can be includedwith involvement of ratings by parents and relativesSuch study will lead to multi-criteria group decision-making kind of problem

REFERENCES

Abraham DJ 2003 Algorithmics of two-sided matchingproblems Masterrsquos thesis University of GlasgowDepartment of Computing Science Accessed September2010

Adachi H 2003 A search model of two-sided matchingunder nontransferable utility Journal of Economic Theory113(2) 182ndash198

Banerjee Abhijit V Duflo Esther Ghatak MaitreeshLafortune J 20009 Marry for What Caste and MateSelection in Modern India NBER Working Paper Seriesw14958 Available at SSRN httpssrncomabstract=1405966 accessed July 2010

Batabyal A DeAngelo G 2008 To match or not to matchaspects of marital matchmaking under uncertainty Opera-tions Research Letters 36(1) 94ndash98

Belot M Francesconi M 2010 Meeting opportunities and part-ner selection a field study 1ndash40 Available at httpwwwtauacil~weissfam_econRESTAT-13763-1-manuscriptpdf(accessed on 18 December 2010)

Celik O Knoblauch V 2007 Marriage matching withcorrelated preferences Working Paper 1ndash10 Universityof Connecticut

Chang S Wang R Wang S 2006 Applying fuzzy linguisticquantifier to select supply chain partners at differentphases of product life cycle International Journal ofProduction Economics 100 348ndash359

Dugar S Bhattacharya H Reiley DH 2010 Canrsquot buy melove a field experiment exploring the trade-off betweenincome and caste status in an Indian matrimonial marketAvailable at SSRN httpssrncomabstract=1288987Accessed July 2010

Gale D Shapley LS 1962 College admissions and the stabilityof marriage American Mathematical Monthly 69(1) 9ndash15

Gordon J Gupta P 2003 Understanding Indiarsquos servicesevolution httpimforgexternalnpapdseminars2003newdelhigordonpdf Accessed August 2010

Hajeeh M Lairi S 2009 Marriage partner selection inKuwait an analytical hierarchy process approach Journalof Mathematical Sociology 33 222ndash240

Hitsch GJ Hortaccedilsu A Ariely D 2010 What makes youclick mdash mate preferences in online dating QuantitativeMarketing and Economics 8(4) 393ndash427

Irving RW Leather P Gusfield D 1987 An efficientalgorithm for the ldquooptimalrdquo stable marriage Journal ofthe ACM 34(3) 532ndash543

Korkmaz I 2008 An analytic hierarchy process and two-sided matching based decision support system formilitary personnel assignment Information Sciences 1782915ndash2927

Li X Murata T 2009 Priority based matchmaking method ofbuyers and suppliers in B2B e-marketplace using multi-objective optimization Proceedings of the InternationalMulti Conference of Engineers and Computer Scientists1 18ndash20

Pathak RS 2005 Matrimonial advertisements in India asociolinguistic profile South Asian Language Review 15(2)1ndash18

Saaty TL 1980 The Analytic Hierarchy Process PlanningPriority Setting Resource Allocation McGraw-HillNew York

Salo AA Hamalainen RP 1997 On the measurement ofpreferences in the AHP Journal of Multi-criteriaDecision Analysis 6 303ndash319

Sipahi S Timor M 2010 The analytic hierarchy process andanalytic network process an overview of applicationsManagement Decision 48(5) 775ndash808

Teo CP Sethuraman J Tan WP 2001 Gale-Shapley stablemarriage problem revisited strategic issues and applica-tions Management Science 47(9) 1252ndash1267

Thomaidis F Mavrakis D 2006 Optimum route of the southtranscontinental gas pipeline in SE Europe using AHPJournal of Multi-CriteriaDecision Analysis 14(1ndash3) 77ndash88

Triantaphyllou E 2001 Two new cases of rank reversalswhen the AHP and some of its additive variants are usedthat do not occur with the multiplicative AHP Journal ofMulti-Criteria Decision Analysis 10(1) 11ndash25

Vaidya OS Kumar S 2006 Analytic hierarchy process anoverview of applications European Journal of OperationalResearch 169(1) 1ndash29

Vaillant N 2004 Estimating the time elapsed betweenending a relationship and joining a matchmaking agencyevidence from a French marriage bureau Journal ofEconomic Psychology 25(6) 789ndash802

Vi N Fragniegravere E Gauthier J Sapin M Widmer ED 2010Optimizing the marriage market an application of thelinear assignment model European Journal of OperationalResearch 202(2) 547ndash553

K JOSHI AND S KUMAR66

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

We propose an integrated fuzzy analytical hierarchyprocess (FAHP) compatibility measure and stablematching-based technique to address these issuesDifferent criteria are fuzzily defined in terms of satisfac-tion level Typical AHP procedure is employed forcalculating profile scores Compatibility measure isdeveloped to reduce the efforts of the customer insearching and sorting the profile from mutual point ofview Gale-Shapley algorithm suggests a stable matchthat specifies the higher probability of getting positiveresponse from the contacted profile

Section 2 explains the findings from the literatureconcerning the online matrimony business in Indiaand the techniques used in helping the process ofmatchmaking Section 3 is devoted towards currentprofile search process in Web portals and the proposedsearch process with AHP compatibility index (CI)and stable matching algorithm Section 4 describesan illustrated example of matchmaking throughInternet portal in India The last section concludesthe findings and highlights the possible improvementsin the matchmaking process

2 ONLINE MATRIMONY BUSINESS IN INDIA

Arranged marriages have been the tradition in Indiansociety for centuries Even today an overwhelmingmajority of Indians have their marriages planned bytheir parents and other respected family membersAlthough most marriages are arranged some couplesin India are opting for love marriage in urban areasAn arranged marriage is effectively the result of awide search by both the girlrsquos family and the boyrsquosfamily Banerjee et al (20009) studied the role playedby caste education and other social and economicattributes in arranged marriages among middle-classIndians Even in modern India there is a strongpreference towards within-caste marriage Parentsgenerally discuss expectations with their sondaughterbefore starting searching for a match These expecta-tions are shared with relatives and family friends whooften bring in valuable suggestions Indian matrimonialsites attempt to provide databases that can be queried tofind matches using similar attributes

Acceptance of online matchmaking as a culturallylegitimate approach to mate selection and consumerspending on these services continues to rise Theonline dating industry is clearly growing in impor-tance as an industry not only because it is becominga popular and efficient way for busy singles to findlove interests but also because of the rich and valuableinformation that it provides for potentially reducing

the rising divorce rate and other types of unsuccessfulrelationships Therefore it is crucial that onlinematching services purporting to use empiricallyvalidated matching systems actually do validatetheir systems and release their findings to the public(Chang et al 2006)

Given the varied and complex matchmakingprocess followed in India that is based on diverseaspects such as caste religion economic standardjob status age height complexion family background etc online matrimony services have becomequite successful Pathak (2005) stated an importanceof the role of computers in future matchmaking atthe hands of marriage bureaus or when independentlyused by the interested parties Online matrimony is anorganized Web-based matrimonial service facilitatingwishful young men and women to find their suitablelife partners In India organized marriage servicesbusiness is worth 10 billion Online matrimony catersto people spread across the globe to find their suitablepartner living in a remote place by matching his or herspecific interests and requirements Dugar et al (2010)indicated that affirmative action policies in India whichseek to enhance the income of the lower-caste popula-tion are not likely to produce any significant changein intercaste marriage

To deal with the behaviour of the clients of amarriage bureau Vaillant (2004) provided roughestimates of the lengths of the personal partnersearches of individuals who seek remarriage using amarriage bureau Few studies related to personslooking for partnership based on multiple attributesin other domains are carried out Chang et al (2006)proposed a fuzzy multiple attribute decision-makingmethod based on the fuzzy linguistic quantifier toselect supply chain partners at different phases ofproduct life cycle Li and Murata (2009) proposed anovel method to match buyers and suppliers in B2Be-marketplace based on priority and multi-objectiveoptimization They analysed matchmaking in a stablebilateral market where each buyer or supplier ismatched with trade partners Batabyal and DeAngelo(2008) studied matchmaking from the perspective ofa matchmaker They analysed the circumstances underwhich a matchmaker optimally accepts or rejectsindividual matching assignments AHP for decisionmaking uses objective mathematics to process theinescapably subjective and personal preferences of anindividual or a group in making a decision With AHPand its generalization one constructs hierarchies thenmakes judgments or performs measurements on pairsof elements with respect to a controlling element toderive ratio scales that are then synthesized throughout

K JOSHI AND S KUMAR58

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

the structure to select the best alternative (Saaty 1980Salo and Hamalainen 1997 Triantaphyllou 2001)Few review papers described the application area inwhich AHP has been successfully used either viastand-alone tool or in combination with other tech-niques (Vaidya and Kumar 2006 Sipahi and Timor2010) Hajeeh and Lairi (2009) employed the AHPbecause of the multiplicity of objectives and surveyedwomen from different ethnic religious and residentialbackgrounds to explore the most preferred criteriaThomaidis and Mavrakis (2006) applied AHP methodwith geopolitical economic and technical criteria todefine the most preferred route of the transcontinentalgas pipeline that branches in SE Europe to transportCaspian gas further into the targeted markets ofEurope Korkmaz (2008) proposed AHP and two-sidedmatching-based decision support system to assistdetailers in the context of assignment of militarypersonnel to positions Matchmaking business hasrecently caught great attention in business schools tooHarvard Business Review published eHarmony (Prodno 709424-HCB-ENG) a case on such business witha successful differentiation strategy It offers a uniqueproduct which combines an extensive relationshipquestionnaire a patented matching system and a guidedcommunication system Vi et al (2010) proposed amathematical approach to optimizing marriage byallocating spouses in such a way that would reduce thelikelihood of divorce or separation Hitsch et al(2010) used a novel data set obtained from an onlinedating service to draw inferences on mate preferencesand to investigate the role played by these preferencesin determining match outcomes and sorting patterns

Various researchers have been looking into economicempirical modeling aspects of this matchmaking Wehave not come across any work that focuses on thematchmaking process in e-matrimony environment

3 PROCESS OF ONLINE MATCHMAKING

In India marriage is viewed as lsquoStrategic decisionrsquo inthe life of humankind because of its non-repetitivenature (in normal conditions) and having long-termeffect on the life of an individual and the followinggenerations It is not an easy decision to make and tolay the proper foundation for any marriage carefuland studied steps that require wisdom and thoroughplanning are necessary Therefore matchmaking isindeed a multi-criterion decision-making processThrough any website portal a customer provides hisor her details as input and expects prospective profilesas a result of search he or she makes using keywords

like height range complexion age difference eatinghabits profession educational qualification etc Eachuser provides his or her authentic information throughonline registration Most of the online matrimony por-tals have person verification requirements as a part oftheir registration process that can be briefed in Figure 1

Although the website provides extensive search facil-ity to the member of the portal the actual time to realizethe match with one of the prospective profiles forinteraction is longer because of the following reasons

bull It is a keyword-based search (0 or 1 type)bull All factors may not be considered by a customerbull Few good profiles might get curtained because ofa specific (crisp) key-based search process

bull Many times person liked by customer might bedisliked by prospective partner therefore proposingto such profiles is waste of time

To overcome the problems faced in the current searchand proposal process we propose a new integratedmethod as depicted in Figure 2 This integrated approachbased on FAHP CI and stable matching algorithm-basedprocess is elaborated stepwise in the following

Step 1 Defining attributes in terms of fuzzy setsUser would like to describe his or her own requirements(attributes) like complexion and salary in terms ofmore fair around 50 000 etc Such linguistic expres-sions need to be converted into fuzzy sets as describedin the example The classical AHP also performspairwise comparison of candidates attribute-wise It iscumbersome here to ask and gather each userrsquos needsattributewise Belot and Francesconi (2010) found thatboth women and men value physical attributes suchas age and weight and those choices are assortativealong age height and education

Let us assume that m men and n women areregistered to the website with their details related to t attri-butes (eg educationoccupation wealth personality)Let D1 D2 D3 Dt represent the customerrsquosattribute-wise requirements in the form of fuzzy sets as(D1 mD1) (D2 mD2) (Dt mDt) where mDt8D=12 3 t represents the membership values of thecustomerrsquos specifications on attribute t

Step 2 Pairwise comparison and calculating scoreof each profileA typical AHP procedure is conducted which consistsof pairwise comparison of attributes at respectivehierarchy to calculate weights for respective criteriaIt leads to calculate the aggregated profile score where

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 59

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

weight of each attribute is multiplied by its respectivefuzzy membership function and then added

Ranking using this profile score will not sufficethe purpose of online matchmaking because of the fol-lowing reasons

bull Matchmaking is a two-sided utility maximizationprocess

bull Every member of the website does rate his or herprospective spousersquos profile

bull It may happen that a person rates the prospectivespouse as the best match on the contrary thatprospective spouse may rate the person as theworst match and vice versa

Step 3 Two-sided matching and sortingMarriage matching on Internet-based system is a typicaltwo-way preferential matching problem Authors ofexperimental empirical theoretical and computationalstudies of two-sided matching markets have recognizedthe importance of correlated preferences Celik andKnoblauch (2007) developed a general method for thestudy of the effect of correlation of preferences on theoutcomes generated by two-sided matching mechan-isms Preferences of both sides are important in two-sided matching Every member of the website has hisor her own attribute requirements and priorities tochoose a life partner Simultaneously a male memberrsquosprofile is rated by respective prospective partnermemberrsquos set factors and subsequent priorities

Here we propose a CI-based method of two-sided matching to emphasize a both-ways matchingintent There are two objectives in this compositionFirst the sum of these two scores in a pair has to bemaximized Second the difference of the opinion abouteach other in terms of aggregate score should be atminimum To meet these objectives a CI is definedas follows

CI frac14 13

Amn thorn Bnm

1thorn 0

5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiAmn Bnm

2 thorn 1q

8gtltgt

9gt=gt

where

Amn = aggregated score of nth female profile as permth malersquos preferencesBnm= aggregated score of mth male profile as per nthfemalersquos preferences

Final sorting in descending order has to be carriedout based on this index CI

Step 4 Stable matching based on Gale-ShapleyalgorithmStable matching problems consist of a set of agentseach of whom submits a preference list ranking asubset of the other agents in order of preference Theproblem is to form a matching M of the agents suchthat no two agents would prefer each other to theirassignment inM (Abraham 2003) The stable matchingproblem is to find such a match between pair of agentsso that neither of the pair finds any other match betterthan the allocated match

An instance of the stable marriage problem consistsof N men N women and each personrsquos preference listA preference list is a totally ordered list including allmembers of the opposite sex depending on his or herpreference For a matchingM betweenmen and womena pair of a man m and a woman w is called a blockingpair if both prefer each other to their current partnersA matching with no blocking pair is called stable Galeand Shapley showed that every instance admits at leastone stable matching and proposed a polynomial timealgorithm to find one which is known as the Gale-Shapley algorithm (Gale amp Shapley 1962) Teo et al(2001) studied the matching mechanism used by theMinistry of Education in the placement of primary sixstudents in secondary schools and discussed why thecurrent method has limited success in accommodatingthe preferences of the students and the specific needsof the schools (in terms of the lsquomixrsquo of admittedstudents) They showed that stable matching mechan-isms are more appropriate in this matching market andexplained why the strategic behaviour of the students

Figure 1 Current search and matchmaking process

K JOSHI AND S KUMAR60

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

need not be a major concern The final outcome of theprocess is a stable match profile and the list of mostrelevant profiles The Gale-Shapley framework is notjust a seminal theoretical benchmark in the economicanalysis of marriage markets it also provides anapproximation to the match outcomes from a realisticsearch and matching model that resembles the environ-ment of an online dating site (Adachi 2003)

An instance of a stable marriage problem may bespecified by the male and female ranking matricesRelative to arbitrary but fixed numberings of menand women these are defined by mr(i k) = j if womank is the jth choice of man i wr(i k) = j if man k is the jth

choice of woman i The problem of how to find a

stable marriage maximizing total satisfaction wasunsolved until Irving et al (1987) used theegalitarian measure of optimality under which totalsatisfaction is maximized

Suppose that for a given stable marriage instanceS = (m1 wl) (mn wn) is a stable matching Theydefined the value c(S) of S by

c Seth THORN frac14 Σn1mr miwieth THORNthornΣn

1wr wimieth THORN

and they said that a stable matching S is optimal if it hasminimum possible value c(S) In real online systemthere are m male and n female profiles as mentioned

Figure 2 Search process with fuzzy analytical hierarchy process and stable matching

Figure 3 Analytical hierarchy process

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 61

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Figure 4 Customerrsquos attribute-wise requirements in the form of fuzzy sets Please see Table VI for abbreviations used

K JOSHI AND S KUMAR62

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

earlier Every customer will receive a suggested stablematched profile and also his or her own preference listbased on lsquocompatibility indexrsquo This enhances the prob-ability of getting a positive response from recipient person

4 ILLUSTRATED EXAMPLE

To validate the proposed method we chose an advancedsearch process from a Web portal known as Jeevansathicom In this illustration we have assumed case of a manwho is looking for a woman as prospective partner formarriage The customer is interested in various profileswith following requirements that are arranged inhierarchical manner as shown in Figure 3

Usually in India partner search is based upon threebroad criteria of prospective partner viz educationoccupation wealth personality An education criterionis related to qualification like Undergraduate Mastersor PhD etc in diverse disciplines like arts commerceengineering and medicine etc Occupation criteriameans a person is an engineer a doctor a charteredaccountant or a professor etc A Wealth criterion con-sists of family status (low class middle class upperclass) earnings (annual income) and location (semi-urban urban metro city) A personality criterion con-sists of age (years) height (cm) complexion (darkwhitish brown brown fair) diet (vegetarian eggitariannon-vegetarian) and body type (slim athletic heavy)

Step 1 Defining attributes in terms of fuzzy setsThe male customer who is looking for a spouse ie awoman with various attributes with hierarchy as statedin Figure 3 Assume that the customer is looking for alsquovery fairrsquo girl in case of attribute type lsquocomplexionrsquoThe customer can define the acceptability with respectto complexion as fuzzy set for example 08 Thismeans that his satisfaction level with that particularattribute is 80 Similarly for every attribute underconsideration he defines his acceptability level iemembership level is asked and fuzzily definedrequirement is generated as shown in Figure 4

Step 2 Pairwise comparison and calculatingaggregate score of each profileA classic AHP procedure is conducted which consistsof a pairwise comparison of attributes at respective

Table I Pairwise comparison of education and occupation

Education Occupation

Education 1 4Occupation 14 1

Table II Pairwise comparison of family status earning andlocation

Family status Earning Location

Family status 1 14 17Earning 4 1 12Location 7 2 1

Table III Pairwise comparison of height age complexiondiet and body type

Height Age Complexion Diet Bodytype

Height 1 6 8 9 5Age 16 1 7 15 110Complexion 18 17 1 7 2Diet 19 5 17 1 5Body type 15 10 12 15 1

Table IV Pairwise comparison of education wealth andpersonality

Education Wealth Personality

Education 1 3 3Wealth 13 1 12Personality 13 3 1

Table V The weight of attributes

Attribute Education Height Occupation Location Body type

Weight () 3945 1513 986 811 621Rank 1 2 3 4 5Attribute Diet Complexion Earning Age Family statusWeight () 587 536 446 442 113Rank 6 7 8 9 10

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 63

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

hierarchy to calculate respective weight for each attri-bute (Tables IndashIV) In this case customer rates eachattribute with respect to other attribute at the samelevel and under the same group From the pairwisecomparisons we get relative weights of attributes asshown in Table V

In our example we consider 10 female memberrsquosdata with different attributes as shown in Table VIThere can be thousands of the profiles in the databaseof any website available Let us calculate profile scorefor profile no 2 This profile has attributes like 27years old 134 cm height complexion as whitishbrown qualification as chartered accountant (CA)belongs to Rich class annual income 22 lac livingin Metro Eating habit as Vegetarian and body typeis Athletic etc

For every profile according to fuzzily definedrequirements membership value can be calculatedComparing the membership values from respectivefuzzy sets and attributes of the profile we get variousmembership values as Education is CA and respectivesatisfaction level is 1 therefore Education=1 Likewiseremaining membership values are Occupation= 044Family status = 0 Earning=1 Location=07 Height =0 Age=06 Complexion=07 Diet = 1 and Bodytype=09

A profile score is calculated by multiplying thismembership value with respective weight fromTable V and aggregating for all attributes For exam-ple for education the weight is 0394

Profile score (A12) = 03945(1) + 00986(044) + 00113(0) + 00446(1) + 00811 (07) + 01513(0) + 00442(06) + 00536(07) + 00587(1) + 00621(09) = 07179

Thus the profile score is 07179 Similarlyprofile scores as per nomenclature describedearlier are as shown in Tables VII and VIII As men-tioned earlier in this mutual matching problem wemust consider what each woman is looking for Everywoman also has defined her requirements in termsof fuzzy sets and done pairwise comparisonThus profile score of this male customer who islooking for female partner can be calculated Tocalculate the compatibility score we use formuladefined in step 3

For example in case of pair male1 and female5ie A15 and B51

CI = 13 [(08372 + 05839) + (08372 + 05839)(2radic[(08372 05839)2 + 1])] = 06963

Thus CI based on male no1rsquos preference witheach female are listed in Table VIII Similarly forevery possible matching pair CI is calculated asrecorded in Table IX T

able

VI

Detailsof

femalemem

bers

No

Educatio

nOccupation

Fam

ilystatus

Earning

Location

Height

Age

Com

plexion

Diet

Bodytype

1BEBTech

Not

working

Upper

middleclass

0Urban

160

26Whitish

Eggitarian

Athletic

2Chartered

accountant

Businessm

anRichclass

22Metro

134

27Whitishbrow

nVegetarian

Athletic

3MCom

Banking

Middleclass

4Rural

137

24Fair

Eggitarian

Slim

4MEM

Tech

EngineeringRampD

Upper

middleclass

14Urban

139

27Fair

Eggitarian

Athletic

5MBAPGDM

LogisticsSCM

Richclass

16Urban

139

27Veryfair

Eggitarian

Heavy

6MCAPGDCA

Software

Middleclass

12Sem

iUrban

162

26Whitishbrow

nVegetarian

Slim

7MDM

S(M

edical)

Teaching

Middleclass

7Sem

iUrban

167

29Dark

Eggitarian

Athletic

8BAMS

Looking

forajob

Middleclass

0Rural

170

25Veryfair

Vegetarian

Slim

9MLLLM

Governm

entservices

Upper

middleclass

8Metro

144

27Whitish

Vegetarian

Athletic

10MBBSBDS

Governm

entservices

Richclass

8Metro

144

27Whitish

Vegetarian

Heavy

Bachelorrsquosof

Engineering

(BE)Masterrsquosof

EngineeringTechnology(M

EM

Tech)Chartered

Accountant(CA)Masterof

Com

merce

(MCom

)Masterof

BusinessAdm

inis-

tration(M

BA)PostG

raduateDiplomain

Managem

ent(PGDM)Masterof

Com

puterApplications

(MCA)PostGraduateDiplomain

Com

puterApplications

(PGDCA)Doctorof

Medicine(M

D)Masters

ofSurgery

(MS)Masterof

Law

(MLLLM)Bachelorof

Ayurveda

MedicineandSurgery

(BAMS)Bachelorof

DentalSurgery

(BDS)

Bachelorof

MedicineBachelorof

Surgery

(MBBS)ResearchandDevelopment(R

ampD)SupplyChain

Managem

ent(SCM)Governm

ent(G

ovt)

K JOSHI AND S KUMAR64

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Based on compatibility scores profiles getshortlisted and ranked in descending order Fur-thermore the customer has liberty to re-rank theprofiles after looking at each of the top 10 profilesSubsequently if the customer re-ranks the profiles thepreferences are taken as input for Gale-Shapleyalgorithm Otherwise profiles ranked based on CI aretreated with respect to their rank To demonstrateGale-Shapley algorithm in this context we assume thatthere are five male and five female profiles with theirpreferences as mentioned in the following table

M1=gtF1-F3-F2-F4-F5 F1 =gtM5-M2-M4-M3-M1M2=gtF2-F1-F3-F5-F4 F2 =gtM2-M4-M5-M1-M3M3=gtF2-F4-F5-F1-F3 F3 =gtM3-M1-M4-M5-M2M4=gtF3-F1-F4-F5-F2 F4 =gtM1-M3-M2-M4-M5M5=gtF5-F2-F4-F3-F1 F5 =gtM2-M1-M3-M5-M4

Gale-Shapley algorithm generates the followingmatches

Male1 is paired with female5 male2 is paired withfemale3 male3 is paired with female4 male4 is pairedwith female2 and male5 is paired with female1

This is an add-on facility for a customer where heor she will receive a suggested stable matched profileIf they contact this suggested profile as well as a few

profiles listed based on their CI then the probabilityof getting positive response increases

5 CONCLUSIONS

In todayrsquos Internet era services seeking efficiency isof paramount importance The approach presented inthis paper attempts to exploit current IT-enabledpartner search for marriage through Web portals

Salient features of this proposed method are asfollows

bull Integrated way to quantify the online profiles withimplicit needs

bull Two-phase short listing ie FAHP and stablematching algorithm

bull Reducing customerrsquos effort to find their mateonline according to their implicit needs (definedfuzzily)

bull Enhancing the probability of getting positiveresponse and matchmaking

A sorting based on CI in descending orderenhances the probability of matchmaking It thus leadsto reduction in lead time of waiting of the positive ornegative reply from the opposite party This opera-tional viewpoint has been presented in this paper with

Table IX Ranking based on compatibility index

A16 A17 A19 A11 A14 A18 A12 A15 A13 A110

Score 09684 08954 07958 08756 08974 08009 07179 08372 04858 08317B61 B71 B91 B11 B41 B81 B21 B51 B31 B101

Score 08517 08692 09306 08142 06982 07576 07743 05839 08824 05079CI 09059 08821 08580 08438 07876 07787 07453 06963 06531 06486Rank 1 2 3 4 5 6 7 8 9 10

CI compatibility index

Table VII Profile scores when female rated by male no 1

A11 A12 A13 A14 A15 A16 A17 A18 A19 A110

Score 08756 07179 04858 08974 08372 09684 08954 08009 07958 08317

Table VIII Profile scores of male no 1 rated by each female

B11 B21 B31 B41 B51 B61 B71 B81 B91 B101

Score 08142 07743 08824 06982 05839 08517 08692 07576 09306 05079

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 65

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

introduction of a CI This index helps user to maxi-mize their requirements while mutual matching

Future studies might cover an enhancement inrating parameters Few Web portals have incorporatedmatchmaking based on personality behaviour Morequalitative and quantitative factors can be includedwith involvement of ratings by parents and relativesSuch study will lead to multi-criteria group decision-making kind of problem

REFERENCES

Abraham DJ 2003 Algorithmics of two-sided matchingproblems Masterrsquos thesis University of GlasgowDepartment of Computing Science Accessed September2010

Adachi H 2003 A search model of two-sided matchingunder nontransferable utility Journal of Economic Theory113(2) 182ndash198

Banerjee Abhijit V Duflo Esther Ghatak MaitreeshLafortune J 20009 Marry for What Caste and MateSelection in Modern India NBER Working Paper Seriesw14958 Available at SSRN httpssrncomabstract=1405966 accessed July 2010

Batabyal A DeAngelo G 2008 To match or not to matchaspects of marital matchmaking under uncertainty Opera-tions Research Letters 36(1) 94ndash98

Belot M Francesconi M 2010 Meeting opportunities and part-ner selection a field study 1ndash40 Available at httpwwwtauacil~weissfam_econRESTAT-13763-1-manuscriptpdf(accessed on 18 December 2010)

Celik O Knoblauch V 2007 Marriage matching withcorrelated preferences Working Paper 1ndash10 Universityof Connecticut

Chang S Wang R Wang S 2006 Applying fuzzy linguisticquantifier to select supply chain partners at differentphases of product life cycle International Journal ofProduction Economics 100 348ndash359

Dugar S Bhattacharya H Reiley DH 2010 Canrsquot buy melove a field experiment exploring the trade-off betweenincome and caste status in an Indian matrimonial marketAvailable at SSRN httpssrncomabstract=1288987Accessed July 2010

Gale D Shapley LS 1962 College admissions and the stabilityof marriage American Mathematical Monthly 69(1) 9ndash15

Gordon J Gupta P 2003 Understanding Indiarsquos servicesevolution httpimforgexternalnpapdseminars2003newdelhigordonpdf Accessed August 2010

Hajeeh M Lairi S 2009 Marriage partner selection inKuwait an analytical hierarchy process approach Journalof Mathematical Sociology 33 222ndash240

Hitsch GJ Hortaccedilsu A Ariely D 2010 What makes youclick mdash mate preferences in online dating QuantitativeMarketing and Economics 8(4) 393ndash427

Irving RW Leather P Gusfield D 1987 An efficientalgorithm for the ldquooptimalrdquo stable marriage Journal ofthe ACM 34(3) 532ndash543

Korkmaz I 2008 An analytic hierarchy process and two-sided matching based decision support system formilitary personnel assignment Information Sciences 1782915ndash2927

Li X Murata T 2009 Priority based matchmaking method ofbuyers and suppliers in B2B e-marketplace using multi-objective optimization Proceedings of the InternationalMulti Conference of Engineers and Computer Scientists1 18ndash20

Pathak RS 2005 Matrimonial advertisements in India asociolinguistic profile South Asian Language Review 15(2)1ndash18

Saaty TL 1980 The Analytic Hierarchy Process PlanningPriority Setting Resource Allocation McGraw-HillNew York

Salo AA Hamalainen RP 1997 On the measurement ofpreferences in the AHP Journal of Multi-criteriaDecision Analysis 6 303ndash319

Sipahi S Timor M 2010 The analytic hierarchy process andanalytic network process an overview of applicationsManagement Decision 48(5) 775ndash808

Teo CP Sethuraman J Tan WP 2001 Gale-Shapley stablemarriage problem revisited strategic issues and applica-tions Management Science 47(9) 1252ndash1267

Thomaidis F Mavrakis D 2006 Optimum route of the southtranscontinental gas pipeline in SE Europe using AHPJournal of Multi-CriteriaDecision Analysis 14(1ndash3) 77ndash88

Triantaphyllou E 2001 Two new cases of rank reversalswhen the AHP and some of its additive variants are usedthat do not occur with the multiplicative AHP Journal ofMulti-Criteria Decision Analysis 10(1) 11ndash25

Vaidya OS Kumar S 2006 Analytic hierarchy process anoverview of applications European Journal of OperationalResearch 169(1) 1ndash29

Vaillant N 2004 Estimating the time elapsed betweenending a relationship and joining a matchmaking agencyevidence from a French marriage bureau Journal ofEconomic Psychology 25(6) 789ndash802

Vi N Fragniegravere E Gauthier J Sapin M Widmer ED 2010Optimizing the marriage market an application of thelinear assignment model European Journal of OperationalResearch 202(2) 547ndash553

K JOSHI AND S KUMAR66

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

the structure to select the best alternative (Saaty 1980Salo and Hamalainen 1997 Triantaphyllou 2001)Few review papers described the application area inwhich AHP has been successfully used either viastand-alone tool or in combination with other tech-niques (Vaidya and Kumar 2006 Sipahi and Timor2010) Hajeeh and Lairi (2009) employed the AHPbecause of the multiplicity of objectives and surveyedwomen from different ethnic religious and residentialbackgrounds to explore the most preferred criteriaThomaidis and Mavrakis (2006) applied AHP methodwith geopolitical economic and technical criteria todefine the most preferred route of the transcontinentalgas pipeline that branches in SE Europe to transportCaspian gas further into the targeted markets ofEurope Korkmaz (2008) proposed AHP and two-sidedmatching-based decision support system to assistdetailers in the context of assignment of militarypersonnel to positions Matchmaking business hasrecently caught great attention in business schools tooHarvard Business Review published eHarmony (Prodno 709424-HCB-ENG) a case on such business witha successful differentiation strategy It offers a uniqueproduct which combines an extensive relationshipquestionnaire a patented matching system and a guidedcommunication system Vi et al (2010) proposed amathematical approach to optimizing marriage byallocating spouses in such a way that would reduce thelikelihood of divorce or separation Hitsch et al(2010) used a novel data set obtained from an onlinedating service to draw inferences on mate preferencesand to investigate the role played by these preferencesin determining match outcomes and sorting patterns

Various researchers have been looking into economicempirical modeling aspects of this matchmaking Wehave not come across any work that focuses on thematchmaking process in e-matrimony environment

3 PROCESS OF ONLINE MATCHMAKING

In India marriage is viewed as lsquoStrategic decisionrsquo inthe life of humankind because of its non-repetitivenature (in normal conditions) and having long-termeffect on the life of an individual and the followinggenerations It is not an easy decision to make and tolay the proper foundation for any marriage carefuland studied steps that require wisdom and thoroughplanning are necessary Therefore matchmaking isindeed a multi-criterion decision-making processThrough any website portal a customer provides hisor her details as input and expects prospective profilesas a result of search he or she makes using keywords

like height range complexion age difference eatinghabits profession educational qualification etc Eachuser provides his or her authentic information throughonline registration Most of the online matrimony por-tals have person verification requirements as a part oftheir registration process that can be briefed in Figure 1

Although the website provides extensive search facil-ity to the member of the portal the actual time to realizethe match with one of the prospective profiles forinteraction is longer because of the following reasons

bull It is a keyword-based search (0 or 1 type)bull All factors may not be considered by a customerbull Few good profiles might get curtained because ofa specific (crisp) key-based search process

bull Many times person liked by customer might bedisliked by prospective partner therefore proposingto such profiles is waste of time

To overcome the problems faced in the current searchand proposal process we propose a new integratedmethod as depicted in Figure 2 This integrated approachbased on FAHP CI and stable matching algorithm-basedprocess is elaborated stepwise in the following

Step 1 Defining attributes in terms of fuzzy setsUser would like to describe his or her own requirements(attributes) like complexion and salary in terms ofmore fair around 50 000 etc Such linguistic expres-sions need to be converted into fuzzy sets as describedin the example The classical AHP also performspairwise comparison of candidates attribute-wise It iscumbersome here to ask and gather each userrsquos needsattributewise Belot and Francesconi (2010) found thatboth women and men value physical attributes suchas age and weight and those choices are assortativealong age height and education

Let us assume that m men and n women areregistered to the website with their details related to t attri-butes (eg educationoccupation wealth personality)Let D1 D2 D3 Dt represent the customerrsquosattribute-wise requirements in the form of fuzzy sets as(D1 mD1) (D2 mD2) (Dt mDt) where mDt8D=12 3 t represents the membership values of thecustomerrsquos specifications on attribute t

Step 2 Pairwise comparison and calculating scoreof each profileA typical AHP procedure is conducted which consistsof pairwise comparison of attributes at respectivehierarchy to calculate weights for respective criteriaIt leads to calculate the aggregated profile score where

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 59

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

weight of each attribute is multiplied by its respectivefuzzy membership function and then added

Ranking using this profile score will not sufficethe purpose of online matchmaking because of the fol-lowing reasons

bull Matchmaking is a two-sided utility maximizationprocess

bull Every member of the website does rate his or herprospective spousersquos profile

bull It may happen that a person rates the prospectivespouse as the best match on the contrary thatprospective spouse may rate the person as theworst match and vice versa

Step 3 Two-sided matching and sortingMarriage matching on Internet-based system is a typicaltwo-way preferential matching problem Authors ofexperimental empirical theoretical and computationalstudies of two-sided matching markets have recognizedthe importance of correlated preferences Celik andKnoblauch (2007) developed a general method for thestudy of the effect of correlation of preferences on theoutcomes generated by two-sided matching mechan-isms Preferences of both sides are important in two-sided matching Every member of the website has hisor her own attribute requirements and priorities tochoose a life partner Simultaneously a male memberrsquosprofile is rated by respective prospective partnermemberrsquos set factors and subsequent priorities

Here we propose a CI-based method of two-sided matching to emphasize a both-ways matchingintent There are two objectives in this compositionFirst the sum of these two scores in a pair has to bemaximized Second the difference of the opinion abouteach other in terms of aggregate score should be atminimum To meet these objectives a CI is definedas follows

CI frac14 13

Amn thorn Bnm

1thorn 0

5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiAmn Bnm

2 thorn 1q

8gtltgt

9gt=gt

where

Amn = aggregated score of nth female profile as permth malersquos preferencesBnm= aggregated score of mth male profile as per nthfemalersquos preferences

Final sorting in descending order has to be carriedout based on this index CI

Step 4 Stable matching based on Gale-ShapleyalgorithmStable matching problems consist of a set of agentseach of whom submits a preference list ranking asubset of the other agents in order of preference Theproblem is to form a matching M of the agents suchthat no two agents would prefer each other to theirassignment inM (Abraham 2003) The stable matchingproblem is to find such a match between pair of agentsso that neither of the pair finds any other match betterthan the allocated match

An instance of the stable marriage problem consistsof N men N women and each personrsquos preference listA preference list is a totally ordered list including allmembers of the opposite sex depending on his or herpreference For a matchingM betweenmen and womena pair of a man m and a woman w is called a blockingpair if both prefer each other to their current partnersA matching with no blocking pair is called stable Galeand Shapley showed that every instance admits at leastone stable matching and proposed a polynomial timealgorithm to find one which is known as the Gale-Shapley algorithm (Gale amp Shapley 1962) Teo et al(2001) studied the matching mechanism used by theMinistry of Education in the placement of primary sixstudents in secondary schools and discussed why thecurrent method has limited success in accommodatingthe preferences of the students and the specific needsof the schools (in terms of the lsquomixrsquo of admittedstudents) They showed that stable matching mechan-isms are more appropriate in this matching market andexplained why the strategic behaviour of the students

Figure 1 Current search and matchmaking process

K JOSHI AND S KUMAR60

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

need not be a major concern The final outcome of theprocess is a stable match profile and the list of mostrelevant profiles The Gale-Shapley framework is notjust a seminal theoretical benchmark in the economicanalysis of marriage markets it also provides anapproximation to the match outcomes from a realisticsearch and matching model that resembles the environ-ment of an online dating site (Adachi 2003)

An instance of a stable marriage problem may bespecified by the male and female ranking matricesRelative to arbitrary but fixed numberings of menand women these are defined by mr(i k) = j if womank is the jth choice of man i wr(i k) = j if man k is the jth

choice of woman i The problem of how to find a

stable marriage maximizing total satisfaction wasunsolved until Irving et al (1987) used theegalitarian measure of optimality under which totalsatisfaction is maximized

Suppose that for a given stable marriage instanceS = (m1 wl) (mn wn) is a stable matching Theydefined the value c(S) of S by

c Seth THORN frac14 Σn1mr miwieth THORNthornΣn

1wr wimieth THORN

and they said that a stable matching S is optimal if it hasminimum possible value c(S) In real online systemthere are m male and n female profiles as mentioned

Figure 2 Search process with fuzzy analytical hierarchy process and stable matching

Figure 3 Analytical hierarchy process

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 61

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Figure 4 Customerrsquos attribute-wise requirements in the form of fuzzy sets Please see Table VI for abbreviations used

K JOSHI AND S KUMAR62

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

earlier Every customer will receive a suggested stablematched profile and also his or her own preference listbased on lsquocompatibility indexrsquo This enhances the prob-ability of getting a positive response from recipient person

4 ILLUSTRATED EXAMPLE

To validate the proposed method we chose an advancedsearch process from a Web portal known as Jeevansathicom In this illustration we have assumed case of a manwho is looking for a woman as prospective partner formarriage The customer is interested in various profileswith following requirements that are arranged inhierarchical manner as shown in Figure 3

Usually in India partner search is based upon threebroad criteria of prospective partner viz educationoccupation wealth personality An education criterionis related to qualification like Undergraduate Mastersor PhD etc in diverse disciplines like arts commerceengineering and medicine etc Occupation criteriameans a person is an engineer a doctor a charteredaccountant or a professor etc A Wealth criterion con-sists of family status (low class middle class upperclass) earnings (annual income) and location (semi-urban urban metro city) A personality criterion con-sists of age (years) height (cm) complexion (darkwhitish brown brown fair) diet (vegetarian eggitariannon-vegetarian) and body type (slim athletic heavy)

Step 1 Defining attributes in terms of fuzzy setsThe male customer who is looking for a spouse ie awoman with various attributes with hierarchy as statedin Figure 3 Assume that the customer is looking for alsquovery fairrsquo girl in case of attribute type lsquocomplexionrsquoThe customer can define the acceptability with respectto complexion as fuzzy set for example 08 Thismeans that his satisfaction level with that particularattribute is 80 Similarly for every attribute underconsideration he defines his acceptability level iemembership level is asked and fuzzily definedrequirement is generated as shown in Figure 4

Step 2 Pairwise comparison and calculatingaggregate score of each profileA classic AHP procedure is conducted which consistsof a pairwise comparison of attributes at respective

Table I Pairwise comparison of education and occupation

Education Occupation

Education 1 4Occupation 14 1

Table II Pairwise comparison of family status earning andlocation

Family status Earning Location

Family status 1 14 17Earning 4 1 12Location 7 2 1

Table III Pairwise comparison of height age complexiondiet and body type

Height Age Complexion Diet Bodytype

Height 1 6 8 9 5Age 16 1 7 15 110Complexion 18 17 1 7 2Diet 19 5 17 1 5Body type 15 10 12 15 1

Table IV Pairwise comparison of education wealth andpersonality

Education Wealth Personality

Education 1 3 3Wealth 13 1 12Personality 13 3 1

Table V The weight of attributes

Attribute Education Height Occupation Location Body type

Weight () 3945 1513 986 811 621Rank 1 2 3 4 5Attribute Diet Complexion Earning Age Family statusWeight () 587 536 446 442 113Rank 6 7 8 9 10

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 63

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

hierarchy to calculate respective weight for each attri-bute (Tables IndashIV) In this case customer rates eachattribute with respect to other attribute at the samelevel and under the same group From the pairwisecomparisons we get relative weights of attributes asshown in Table V

In our example we consider 10 female memberrsquosdata with different attributes as shown in Table VIThere can be thousands of the profiles in the databaseof any website available Let us calculate profile scorefor profile no 2 This profile has attributes like 27years old 134 cm height complexion as whitishbrown qualification as chartered accountant (CA)belongs to Rich class annual income 22 lac livingin Metro Eating habit as Vegetarian and body typeis Athletic etc

For every profile according to fuzzily definedrequirements membership value can be calculatedComparing the membership values from respectivefuzzy sets and attributes of the profile we get variousmembership values as Education is CA and respectivesatisfaction level is 1 therefore Education=1 Likewiseremaining membership values are Occupation= 044Family status = 0 Earning=1 Location=07 Height =0 Age=06 Complexion=07 Diet = 1 and Bodytype=09

A profile score is calculated by multiplying thismembership value with respective weight fromTable V and aggregating for all attributes For exam-ple for education the weight is 0394

Profile score (A12) = 03945(1) + 00986(044) + 00113(0) + 00446(1) + 00811 (07) + 01513(0) + 00442(06) + 00536(07) + 00587(1) + 00621(09) = 07179

Thus the profile score is 07179 Similarlyprofile scores as per nomenclature describedearlier are as shown in Tables VII and VIII As men-tioned earlier in this mutual matching problem wemust consider what each woman is looking for Everywoman also has defined her requirements in termsof fuzzy sets and done pairwise comparisonThus profile score of this male customer who islooking for female partner can be calculated Tocalculate the compatibility score we use formuladefined in step 3

For example in case of pair male1 and female5ie A15 and B51

CI = 13 [(08372 + 05839) + (08372 + 05839)(2radic[(08372 05839)2 + 1])] = 06963

Thus CI based on male no1rsquos preference witheach female are listed in Table VIII Similarly forevery possible matching pair CI is calculated asrecorded in Table IX T

able

VI

Detailsof

femalemem

bers

No

Educatio

nOccupation

Fam

ilystatus

Earning

Location

Height

Age

Com

plexion

Diet

Bodytype

1BEBTech

Not

working

Upper

middleclass

0Urban

160

26Whitish

Eggitarian

Athletic

2Chartered

accountant

Businessm

anRichclass

22Metro

134

27Whitishbrow

nVegetarian

Athletic

3MCom

Banking

Middleclass

4Rural

137

24Fair

Eggitarian

Slim

4MEM

Tech

EngineeringRampD

Upper

middleclass

14Urban

139

27Fair

Eggitarian

Athletic

5MBAPGDM

LogisticsSCM

Richclass

16Urban

139

27Veryfair

Eggitarian

Heavy

6MCAPGDCA

Software

Middleclass

12Sem

iUrban

162

26Whitishbrow

nVegetarian

Slim

7MDM

S(M

edical)

Teaching

Middleclass

7Sem

iUrban

167

29Dark

Eggitarian

Athletic

8BAMS

Looking

forajob

Middleclass

0Rural

170

25Veryfair

Vegetarian

Slim

9MLLLM

Governm

entservices

Upper

middleclass

8Metro

144

27Whitish

Vegetarian

Athletic

10MBBSBDS

Governm

entservices

Richclass

8Metro

144

27Whitish

Vegetarian

Heavy

Bachelorrsquosof

Engineering

(BE)Masterrsquosof

EngineeringTechnology(M

EM

Tech)Chartered

Accountant(CA)Masterof

Com

merce

(MCom

)Masterof

BusinessAdm

inis-

tration(M

BA)PostG

raduateDiplomain

Managem

ent(PGDM)Masterof

Com

puterApplications

(MCA)PostGraduateDiplomain

Com

puterApplications

(PGDCA)Doctorof

Medicine(M

D)Masters

ofSurgery

(MS)Masterof

Law

(MLLLM)Bachelorof

Ayurveda

MedicineandSurgery

(BAMS)Bachelorof

DentalSurgery

(BDS)

Bachelorof

MedicineBachelorof

Surgery

(MBBS)ResearchandDevelopment(R

ampD)SupplyChain

Managem

ent(SCM)Governm

ent(G

ovt)

K JOSHI AND S KUMAR64

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Based on compatibility scores profiles getshortlisted and ranked in descending order Fur-thermore the customer has liberty to re-rank theprofiles after looking at each of the top 10 profilesSubsequently if the customer re-ranks the profiles thepreferences are taken as input for Gale-Shapleyalgorithm Otherwise profiles ranked based on CI aretreated with respect to their rank To demonstrateGale-Shapley algorithm in this context we assume thatthere are five male and five female profiles with theirpreferences as mentioned in the following table

M1=gtF1-F3-F2-F4-F5 F1 =gtM5-M2-M4-M3-M1M2=gtF2-F1-F3-F5-F4 F2 =gtM2-M4-M5-M1-M3M3=gtF2-F4-F5-F1-F3 F3 =gtM3-M1-M4-M5-M2M4=gtF3-F1-F4-F5-F2 F4 =gtM1-M3-M2-M4-M5M5=gtF5-F2-F4-F3-F1 F5 =gtM2-M1-M3-M5-M4

Gale-Shapley algorithm generates the followingmatches

Male1 is paired with female5 male2 is paired withfemale3 male3 is paired with female4 male4 is pairedwith female2 and male5 is paired with female1

This is an add-on facility for a customer where heor she will receive a suggested stable matched profileIf they contact this suggested profile as well as a few

profiles listed based on their CI then the probabilityof getting positive response increases

5 CONCLUSIONS

In todayrsquos Internet era services seeking efficiency isof paramount importance The approach presented inthis paper attempts to exploit current IT-enabledpartner search for marriage through Web portals

Salient features of this proposed method are asfollows

bull Integrated way to quantify the online profiles withimplicit needs

bull Two-phase short listing ie FAHP and stablematching algorithm

bull Reducing customerrsquos effort to find their mateonline according to their implicit needs (definedfuzzily)

bull Enhancing the probability of getting positiveresponse and matchmaking

A sorting based on CI in descending orderenhances the probability of matchmaking It thus leadsto reduction in lead time of waiting of the positive ornegative reply from the opposite party This opera-tional viewpoint has been presented in this paper with

Table IX Ranking based on compatibility index

A16 A17 A19 A11 A14 A18 A12 A15 A13 A110

Score 09684 08954 07958 08756 08974 08009 07179 08372 04858 08317B61 B71 B91 B11 B41 B81 B21 B51 B31 B101

Score 08517 08692 09306 08142 06982 07576 07743 05839 08824 05079CI 09059 08821 08580 08438 07876 07787 07453 06963 06531 06486Rank 1 2 3 4 5 6 7 8 9 10

CI compatibility index

Table VII Profile scores when female rated by male no 1

A11 A12 A13 A14 A15 A16 A17 A18 A19 A110

Score 08756 07179 04858 08974 08372 09684 08954 08009 07958 08317

Table VIII Profile scores of male no 1 rated by each female

B11 B21 B31 B41 B51 B61 B71 B81 B91 B101

Score 08142 07743 08824 06982 05839 08517 08692 07576 09306 05079

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 65

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

introduction of a CI This index helps user to maxi-mize their requirements while mutual matching

Future studies might cover an enhancement inrating parameters Few Web portals have incorporatedmatchmaking based on personality behaviour Morequalitative and quantitative factors can be includedwith involvement of ratings by parents and relativesSuch study will lead to multi-criteria group decision-making kind of problem

REFERENCES

Abraham DJ 2003 Algorithmics of two-sided matchingproblems Masterrsquos thesis University of GlasgowDepartment of Computing Science Accessed September2010

Adachi H 2003 A search model of two-sided matchingunder nontransferable utility Journal of Economic Theory113(2) 182ndash198

Banerjee Abhijit V Duflo Esther Ghatak MaitreeshLafortune J 20009 Marry for What Caste and MateSelection in Modern India NBER Working Paper Seriesw14958 Available at SSRN httpssrncomabstract=1405966 accessed July 2010

Batabyal A DeAngelo G 2008 To match or not to matchaspects of marital matchmaking under uncertainty Opera-tions Research Letters 36(1) 94ndash98

Belot M Francesconi M 2010 Meeting opportunities and part-ner selection a field study 1ndash40 Available at httpwwwtauacil~weissfam_econRESTAT-13763-1-manuscriptpdf(accessed on 18 December 2010)

Celik O Knoblauch V 2007 Marriage matching withcorrelated preferences Working Paper 1ndash10 Universityof Connecticut

Chang S Wang R Wang S 2006 Applying fuzzy linguisticquantifier to select supply chain partners at differentphases of product life cycle International Journal ofProduction Economics 100 348ndash359

Dugar S Bhattacharya H Reiley DH 2010 Canrsquot buy melove a field experiment exploring the trade-off betweenincome and caste status in an Indian matrimonial marketAvailable at SSRN httpssrncomabstract=1288987Accessed July 2010

Gale D Shapley LS 1962 College admissions and the stabilityof marriage American Mathematical Monthly 69(1) 9ndash15

Gordon J Gupta P 2003 Understanding Indiarsquos servicesevolution httpimforgexternalnpapdseminars2003newdelhigordonpdf Accessed August 2010

Hajeeh M Lairi S 2009 Marriage partner selection inKuwait an analytical hierarchy process approach Journalof Mathematical Sociology 33 222ndash240

Hitsch GJ Hortaccedilsu A Ariely D 2010 What makes youclick mdash mate preferences in online dating QuantitativeMarketing and Economics 8(4) 393ndash427

Irving RW Leather P Gusfield D 1987 An efficientalgorithm for the ldquooptimalrdquo stable marriage Journal ofthe ACM 34(3) 532ndash543

Korkmaz I 2008 An analytic hierarchy process and two-sided matching based decision support system formilitary personnel assignment Information Sciences 1782915ndash2927

Li X Murata T 2009 Priority based matchmaking method ofbuyers and suppliers in B2B e-marketplace using multi-objective optimization Proceedings of the InternationalMulti Conference of Engineers and Computer Scientists1 18ndash20

Pathak RS 2005 Matrimonial advertisements in India asociolinguistic profile South Asian Language Review 15(2)1ndash18

Saaty TL 1980 The Analytic Hierarchy Process PlanningPriority Setting Resource Allocation McGraw-HillNew York

Salo AA Hamalainen RP 1997 On the measurement ofpreferences in the AHP Journal of Multi-criteriaDecision Analysis 6 303ndash319

Sipahi S Timor M 2010 The analytic hierarchy process andanalytic network process an overview of applicationsManagement Decision 48(5) 775ndash808

Teo CP Sethuraman J Tan WP 2001 Gale-Shapley stablemarriage problem revisited strategic issues and applica-tions Management Science 47(9) 1252ndash1267

Thomaidis F Mavrakis D 2006 Optimum route of the southtranscontinental gas pipeline in SE Europe using AHPJournal of Multi-CriteriaDecision Analysis 14(1ndash3) 77ndash88

Triantaphyllou E 2001 Two new cases of rank reversalswhen the AHP and some of its additive variants are usedthat do not occur with the multiplicative AHP Journal ofMulti-Criteria Decision Analysis 10(1) 11ndash25

Vaidya OS Kumar S 2006 Analytic hierarchy process anoverview of applications European Journal of OperationalResearch 169(1) 1ndash29

Vaillant N 2004 Estimating the time elapsed betweenending a relationship and joining a matchmaking agencyevidence from a French marriage bureau Journal ofEconomic Psychology 25(6) 789ndash802

Vi N Fragniegravere E Gauthier J Sapin M Widmer ED 2010Optimizing the marriage market an application of thelinear assignment model European Journal of OperationalResearch 202(2) 547ndash553

K JOSHI AND S KUMAR66

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

weight of each attribute is multiplied by its respectivefuzzy membership function and then added

Ranking using this profile score will not sufficethe purpose of online matchmaking because of the fol-lowing reasons

bull Matchmaking is a two-sided utility maximizationprocess

bull Every member of the website does rate his or herprospective spousersquos profile

bull It may happen that a person rates the prospectivespouse as the best match on the contrary thatprospective spouse may rate the person as theworst match and vice versa

Step 3 Two-sided matching and sortingMarriage matching on Internet-based system is a typicaltwo-way preferential matching problem Authors ofexperimental empirical theoretical and computationalstudies of two-sided matching markets have recognizedthe importance of correlated preferences Celik andKnoblauch (2007) developed a general method for thestudy of the effect of correlation of preferences on theoutcomes generated by two-sided matching mechan-isms Preferences of both sides are important in two-sided matching Every member of the website has hisor her own attribute requirements and priorities tochoose a life partner Simultaneously a male memberrsquosprofile is rated by respective prospective partnermemberrsquos set factors and subsequent priorities

Here we propose a CI-based method of two-sided matching to emphasize a both-ways matchingintent There are two objectives in this compositionFirst the sum of these two scores in a pair has to bemaximized Second the difference of the opinion abouteach other in terms of aggregate score should be atminimum To meet these objectives a CI is definedas follows

CI frac14 13

Amn thorn Bnm

1thorn 0

5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiAmn Bnm

2 thorn 1q

8gtltgt

9gt=gt

where

Amn = aggregated score of nth female profile as permth malersquos preferencesBnm= aggregated score of mth male profile as per nthfemalersquos preferences

Final sorting in descending order has to be carriedout based on this index CI

Step 4 Stable matching based on Gale-ShapleyalgorithmStable matching problems consist of a set of agentseach of whom submits a preference list ranking asubset of the other agents in order of preference Theproblem is to form a matching M of the agents suchthat no two agents would prefer each other to theirassignment inM (Abraham 2003) The stable matchingproblem is to find such a match between pair of agentsso that neither of the pair finds any other match betterthan the allocated match

An instance of the stable marriage problem consistsof N men N women and each personrsquos preference listA preference list is a totally ordered list including allmembers of the opposite sex depending on his or herpreference For a matchingM betweenmen and womena pair of a man m and a woman w is called a blockingpair if both prefer each other to their current partnersA matching with no blocking pair is called stable Galeand Shapley showed that every instance admits at leastone stable matching and proposed a polynomial timealgorithm to find one which is known as the Gale-Shapley algorithm (Gale amp Shapley 1962) Teo et al(2001) studied the matching mechanism used by theMinistry of Education in the placement of primary sixstudents in secondary schools and discussed why thecurrent method has limited success in accommodatingthe preferences of the students and the specific needsof the schools (in terms of the lsquomixrsquo of admittedstudents) They showed that stable matching mechan-isms are more appropriate in this matching market andexplained why the strategic behaviour of the students

Figure 1 Current search and matchmaking process

K JOSHI AND S KUMAR60

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

need not be a major concern The final outcome of theprocess is a stable match profile and the list of mostrelevant profiles The Gale-Shapley framework is notjust a seminal theoretical benchmark in the economicanalysis of marriage markets it also provides anapproximation to the match outcomes from a realisticsearch and matching model that resembles the environ-ment of an online dating site (Adachi 2003)

An instance of a stable marriage problem may bespecified by the male and female ranking matricesRelative to arbitrary but fixed numberings of menand women these are defined by mr(i k) = j if womank is the jth choice of man i wr(i k) = j if man k is the jth

choice of woman i The problem of how to find a

stable marriage maximizing total satisfaction wasunsolved until Irving et al (1987) used theegalitarian measure of optimality under which totalsatisfaction is maximized

Suppose that for a given stable marriage instanceS = (m1 wl) (mn wn) is a stable matching Theydefined the value c(S) of S by

c Seth THORN frac14 Σn1mr miwieth THORNthornΣn

1wr wimieth THORN

and they said that a stable matching S is optimal if it hasminimum possible value c(S) In real online systemthere are m male and n female profiles as mentioned

Figure 2 Search process with fuzzy analytical hierarchy process and stable matching

Figure 3 Analytical hierarchy process

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 61

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Figure 4 Customerrsquos attribute-wise requirements in the form of fuzzy sets Please see Table VI for abbreviations used

K JOSHI AND S KUMAR62

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

earlier Every customer will receive a suggested stablematched profile and also his or her own preference listbased on lsquocompatibility indexrsquo This enhances the prob-ability of getting a positive response from recipient person

4 ILLUSTRATED EXAMPLE

To validate the proposed method we chose an advancedsearch process from a Web portal known as Jeevansathicom In this illustration we have assumed case of a manwho is looking for a woman as prospective partner formarriage The customer is interested in various profileswith following requirements that are arranged inhierarchical manner as shown in Figure 3

Usually in India partner search is based upon threebroad criteria of prospective partner viz educationoccupation wealth personality An education criterionis related to qualification like Undergraduate Mastersor PhD etc in diverse disciplines like arts commerceengineering and medicine etc Occupation criteriameans a person is an engineer a doctor a charteredaccountant or a professor etc A Wealth criterion con-sists of family status (low class middle class upperclass) earnings (annual income) and location (semi-urban urban metro city) A personality criterion con-sists of age (years) height (cm) complexion (darkwhitish brown brown fair) diet (vegetarian eggitariannon-vegetarian) and body type (slim athletic heavy)

Step 1 Defining attributes in terms of fuzzy setsThe male customer who is looking for a spouse ie awoman with various attributes with hierarchy as statedin Figure 3 Assume that the customer is looking for alsquovery fairrsquo girl in case of attribute type lsquocomplexionrsquoThe customer can define the acceptability with respectto complexion as fuzzy set for example 08 Thismeans that his satisfaction level with that particularattribute is 80 Similarly for every attribute underconsideration he defines his acceptability level iemembership level is asked and fuzzily definedrequirement is generated as shown in Figure 4

Step 2 Pairwise comparison and calculatingaggregate score of each profileA classic AHP procedure is conducted which consistsof a pairwise comparison of attributes at respective

Table I Pairwise comparison of education and occupation

Education Occupation

Education 1 4Occupation 14 1

Table II Pairwise comparison of family status earning andlocation

Family status Earning Location

Family status 1 14 17Earning 4 1 12Location 7 2 1

Table III Pairwise comparison of height age complexiondiet and body type

Height Age Complexion Diet Bodytype

Height 1 6 8 9 5Age 16 1 7 15 110Complexion 18 17 1 7 2Diet 19 5 17 1 5Body type 15 10 12 15 1

Table IV Pairwise comparison of education wealth andpersonality

Education Wealth Personality

Education 1 3 3Wealth 13 1 12Personality 13 3 1

Table V The weight of attributes

Attribute Education Height Occupation Location Body type

Weight () 3945 1513 986 811 621Rank 1 2 3 4 5Attribute Diet Complexion Earning Age Family statusWeight () 587 536 446 442 113Rank 6 7 8 9 10

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 63

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

hierarchy to calculate respective weight for each attri-bute (Tables IndashIV) In this case customer rates eachattribute with respect to other attribute at the samelevel and under the same group From the pairwisecomparisons we get relative weights of attributes asshown in Table V

In our example we consider 10 female memberrsquosdata with different attributes as shown in Table VIThere can be thousands of the profiles in the databaseof any website available Let us calculate profile scorefor profile no 2 This profile has attributes like 27years old 134 cm height complexion as whitishbrown qualification as chartered accountant (CA)belongs to Rich class annual income 22 lac livingin Metro Eating habit as Vegetarian and body typeis Athletic etc

For every profile according to fuzzily definedrequirements membership value can be calculatedComparing the membership values from respectivefuzzy sets and attributes of the profile we get variousmembership values as Education is CA and respectivesatisfaction level is 1 therefore Education=1 Likewiseremaining membership values are Occupation= 044Family status = 0 Earning=1 Location=07 Height =0 Age=06 Complexion=07 Diet = 1 and Bodytype=09

A profile score is calculated by multiplying thismembership value with respective weight fromTable V and aggregating for all attributes For exam-ple for education the weight is 0394

Profile score (A12) = 03945(1) + 00986(044) + 00113(0) + 00446(1) + 00811 (07) + 01513(0) + 00442(06) + 00536(07) + 00587(1) + 00621(09) = 07179

Thus the profile score is 07179 Similarlyprofile scores as per nomenclature describedearlier are as shown in Tables VII and VIII As men-tioned earlier in this mutual matching problem wemust consider what each woman is looking for Everywoman also has defined her requirements in termsof fuzzy sets and done pairwise comparisonThus profile score of this male customer who islooking for female partner can be calculated Tocalculate the compatibility score we use formuladefined in step 3

For example in case of pair male1 and female5ie A15 and B51

CI = 13 [(08372 + 05839) + (08372 + 05839)(2radic[(08372 05839)2 + 1])] = 06963

Thus CI based on male no1rsquos preference witheach female are listed in Table VIII Similarly forevery possible matching pair CI is calculated asrecorded in Table IX T

able

VI

Detailsof

femalemem

bers

No

Educatio

nOccupation

Fam

ilystatus

Earning

Location

Height

Age

Com

plexion

Diet

Bodytype

1BEBTech

Not

working

Upper

middleclass

0Urban

160

26Whitish

Eggitarian

Athletic

2Chartered

accountant

Businessm

anRichclass

22Metro

134

27Whitishbrow

nVegetarian

Athletic

3MCom

Banking

Middleclass

4Rural

137

24Fair

Eggitarian

Slim

4MEM

Tech

EngineeringRampD

Upper

middleclass

14Urban

139

27Fair

Eggitarian

Athletic

5MBAPGDM

LogisticsSCM

Richclass

16Urban

139

27Veryfair

Eggitarian

Heavy

6MCAPGDCA

Software

Middleclass

12Sem

iUrban

162

26Whitishbrow

nVegetarian

Slim

7MDM

S(M

edical)

Teaching

Middleclass

7Sem

iUrban

167

29Dark

Eggitarian

Athletic

8BAMS

Looking

forajob

Middleclass

0Rural

170

25Veryfair

Vegetarian

Slim

9MLLLM

Governm

entservices

Upper

middleclass

8Metro

144

27Whitish

Vegetarian

Athletic

10MBBSBDS

Governm

entservices

Richclass

8Metro

144

27Whitish

Vegetarian

Heavy

Bachelorrsquosof

Engineering

(BE)Masterrsquosof

EngineeringTechnology(M

EM

Tech)Chartered

Accountant(CA)Masterof

Com

merce

(MCom

)Masterof

BusinessAdm

inis-

tration(M

BA)PostG

raduateDiplomain

Managem

ent(PGDM)Masterof

Com

puterApplications

(MCA)PostGraduateDiplomain

Com

puterApplications

(PGDCA)Doctorof

Medicine(M

D)Masters

ofSurgery

(MS)Masterof

Law

(MLLLM)Bachelorof

Ayurveda

MedicineandSurgery

(BAMS)Bachelorof

DentalSurgery

(BDS)

Bachelorof

MedicineBachelorof

Surgery

(MBBS)ResearchandDevelopment(R

ampD)SupplyChain

Managem

ent(SCM)Governm

ent(G

ovt)

K JOSHI AND S KUMAR64

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Based on compatibility scores profiles getshortlisted and ranked in descending order Fur-thermore the customer has liberty to re-rank theprofiles after looking at each of the top 10 profilesSubsequently if the customer re-ranks the profiles thepreferences are taken as input for Gale-Shapleyalgorithm Otherwise profiles ranked based on CI aretreated with respect to their rank To demonstrateGale-Shapley algorithm in this context we assume thatthere are five male and five female profiles with theirpreferences as mentioned in the following table

M1=gtF1-F3-F2-F4-F5 F1 =gtM5-M2-M4-M3-M1M2=gtF2-F1-F3-F5-F4 F2 =gtM2-M4-M5-M1-M3M3=gtF2-F4-F5-F1-F3 F3 =gtM3-M1-M4-M5-M2M4=gtF3-F1-F4-F5-F2 F4 =gtM1-M3-M2-M4-M5M5=gtF5-F2-F4-F3-F1 F5 =gtM2-M1-M3-M5-M4

Gale-Shapley algorithm generates the followingmatches

Male1 is paired with female5 male2 is paired withfemale3 male3 is paired with female4 male4 is pairedwith female2 and male5 is paired with female1

This is an add-on facility for a customer where heor she will receive a suggested stable matched profileIf they contact this suggested profile as well as a few

profiles listed based on their CI then the probabilityof getting positive response increases

5 CONCLUSIONS

In todayrsquos Internet era services seeking efficiency isof paramount importance The approach presented inthis paper attempts to exploit current IT-enabledpartner search for marriage through Web portals

Salient features of this proposed method are asfollows

bull Integrated way to quantify the online profiles withimplicit needs

bull Two-phase short listing ie FAHP and stablematching algorithm

bull Reducing customerrsquos effort to find their mateonline according to their implicit needs (definedfuzzily)

bull Enhancing the probability of getting positiveresponse and matchmaking

A sorting based on CI in descending orderenhances the probability of matchmaking It thus leadsto reduction in lead time of waiting of the positive ornegative reply from the opposite party This opera-tional viewpoint has been presented in this paper with

Table IX Ranking based on compatibility index

A16 A17 A19 A11 A14 A18 A12 A15 A13 A110

Score 09684 08954 07958 08756 08974 08009 07179 08372 04858 08317B61 B71 B91 B11 B41 B81 B21 B51 B31 B101

Score 08517 08692 09306 08142 06982 07576 07743 05839 08824 05079CI 09059 08821 08580 08438 07876 07787 07453 06963 06531 06486Rank 1 2 3 4 5 6 7 8 9 10

CI compatibility index

Table VII Profile scores when female rated by male no 1

A11 A12 A13 A14 A15 A16 A17 A18 A19 A110

Score 08756 07179 04858 08974 08372 09684 08954 08009 07958 08317

Table VIII Profile scores of male no 1 rated by each female

B11 B21 B31 B41 B51 B61 B71 B81 B91 B101

Score 08142 07743 08824 06982 05839 08517 08692 07576 09306 05079

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 65

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

introduction of a CI This index helps user to maxi-mize their requirements while mutual matching

Future studies might cover an enhancement inrating parameters Few Web portals have incorporatedmatchmaking based on personality behaviour Morequalitative and quantitative factors can be includedwith involvement of ratings by parents and relativesSuch study will lead to multi-criteria group decision-making kind of problem

REFERENCES

Abraham DJ 2003 Algorithmics of two-sided matchingproblems Masterrsquos thesis University of GlasgowDepartment of Computing Science Accessed September2010

Adachi H 2003 A search model of two-sided matchingunder nontransferable utility Journal of Economic Theory113(2) 182ndash198

Banerjee Abhijit V Duflo Esther Ghatak MaitreeshLafortune J 20009 Marry for What Caste and MateSelection in Modern India NBER Working Paper Seriesw14958 Available at SSRN httpssrncomabstract=1405966 accessed July 2010

Batabyal A DeAngelo G 2008 To match or not to matchaspects of marital matchmaking under uncertainty Opera-tions Research Letters 36(1) 94ndash98

Belot M Francesconi M 2010 Meeting opportunities and part-ner selection a field study 1ndash40 Available at httpwwwtauacil~weissfam_econRESTAT-13763-1-manuscriptpdf(accessed on 18 December 2010)

Celik O Knoblauch V 2007 Marriage matching withcorrelated preferences Working Paper 1ndash10 Universityof Connecticut

Chang S Wang R Wang S 2006 Applying fuzzy linguisticquantifier to select supply chain partners at differentphases of product life cycle International Journal ofProduction Economics 100 348ndash359

Dugar S Bhattacharya H Reiley DH 2010 Canrsquot buy melove a field experiment exploring the trade-off betweenincome and caste status in an Indian matrimonial marketAvailable at SSRN httpssrncomabstract=1288987Accessed July 2010

Gale D Shapley LS 1962 College admissions and the stabilityof marriage American Mathematical Monthly 69(1) 9ndash15

Gordon J Gupta P 2003 Understanding Indiarsquos servicesevolution httpimforgexternalnpapdseminars2003newdelhigordonpdf Accessed August 2010

Hajeeh M Lairi S 2009 Marriage partner selection inKuwait an analytical hierarchy process approach Journalof Mathematical Sociology 33 222ndash240

Hitsch GJ Hortaccedilsu A Ariely D 2010 What makes youclick mdash mate preferences in online dating QuantitativeMarketing and Economics 8(4) 393ndash427

Irving RW Leather P Gusfield D 1987 An efficientalgorithm for the ldquooptimalrdquo stable marriage Journal ofthe ACM 34(3) 532ndash543

Korkmaz I 2008 An analytic hierarchy process and two-sided matching based decision support system formilitary personnel assignment Information Sciences 1782915ndash2927

Li X Murata T 2009 Priority based matchmaking method ofbuyers and suppliers in B2B e-marketplace using multi-objective optimization Proceedings of the InternationalMulti Conference of Engineers and Computer Scientists1 18ndash20

Pathak RS 2005 Matrimonial advertisements in India asociolinguistic profile South Asian Language Review 15(2)1ndash18

Saaty TL 1980 The Analytic Hierarchy Process PlanningPriority Setting Resource Allocation McGraw-HillNew York

Salo AA Hamalainen RP 1997 On the measurement ofpreferences in the AHP Journal of Multi-criteriaDecision Analysis 6 303ndash319

Sipahi S Timor M 2010 The analytic hierarchy process andanalytic network process an overview of applicationsManagement Decision 48(5) 775ndash808

Teo CP Sethuraman J Tan WP 2001 Gale-Shapley stablemarriage problem revisited strategic issues and applica-tions Management Science 47(9) 1252ndash1267

Thomaidis F Mavrakis D 2006 Optimum route of the southtranscontinental gas pipeline in SE Europe using AHPJournal of Multi-CriteriaDecision Analysis 14(1ndash3) 77ndash88

Triantaphyllou E 2001 Two new cases of rank reversalswhen the AHP and some of its additive variants are usedthat do not occur with the multiplicative AHP Journal ofMulti-Criteria Decision Analysis 10(1) 11ndash25

Vaidya OS Kumar S 2006 Analytic hierarchy process anoverview of applications European Journal of OperationalResearch 169(1) 1ndash29

Vaillant N 2004 Estimating the time elapsed betweenending a relationship and joining a matchmaking agencyevidence from a French marriage bureau Journal ofEconomic Psychology 25(6) 789ndash802

Vi N Fragniegravere E Gauthier J Sapin M Widmer ED 2010Optimizing the marriage market an application of thelinear assignment model European Journal of OperationalResearch 202(2) 547ndash553

K JOSHI AND S KUMAR66

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

need not be a major concern The final outcome of theprocess is a stable match profile and the list of mostrelevant profiles The Gale-Shapley framework is notjust a seminal theoretical benchmark in the economicanalysis of marriage markets it also provides anapproximation to the match outcomes from a realisticsearch and matching model that resembles the environ-ment of an online dating site (Adachi 2003)

An instance of a stable marriage problem may bespecified by the male and female ranking matricesRelative to arbitrary but fixed numberings of menand women these are defined by mr(i k) = j if womank is the jth choice of man i wr(i k) = j if man k is the jth

choice of woman i The problem of how to find a

stable marriage maximizing total satisfaction wasunsolved until Irving et al (1987) used theegalitarian measure of optimality under which totalsatisfaction is maximized

Suppose that for a given stable marriage instanceS = (m1 wl) (mn wn) is a stable matching Theydefined the value c(S) of S by

c Seth THORN frac14 Σn1mr miwieth THORNthornΣn

1wr wimieth THORN

and they said that a stable matching S is optimal if it hasminimum possible value c(S) In real online systemthere are m male and n female profiles as mentioned

Figure 2 Search process with fuzzy analytical hierarchy process and stable matching

Figure 3 Analytical hierarchy process

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 61

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Figure 4 Customerrsquos attribute-wise requirements in the form of fuzzy sets Please see Table VI for abbreviations used

K JOSHI AND S KUMAR62

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

earlier Every customer will receive a suggested stablematched profile and also his or her own preference listbased on lsquocompatibility indexrsquo This enhances the prob-ability of getting a positive response from recipient person

4 ILLUSTRATED EXAMPLE

To validate the proposed method we chose an advancedsearch process from a Web portal known as Jeevansathicom In this illustration we have assumed case of a manwho is looking for a woman as prospective partner formarriage The customer is interested in various profileswith following requirements that are arranged inhierarchical manner as shown in Figure 3

Usually in India partner search is based upon threebroad criteria of prospective partner viz educationoccupation wealth personality An education criterionis related to qualification like Undergraduate Mastersor PhD etc in diverse disciplines like arts commerceengineering and medicine etc Occupation criteriameans a person is an engineer a doctor a charteredaccountant or a professor etc A Wealth criterion con-sists of family status (low class middle class upperclass) earnings (annual income) and location (semi-urban urban metro city) A personality criterion con-sists of age (years) height (cm) complexion (darkwhitish brown brown fair) diet (vegetarian eggitariannon-vegetarian) and body type (slim athletic heavy)

Step 1 Defining attributes in terms of fuzzy setsThe male customer who is looking for a spouse ie awoman with various attributes with hierarchy as statedin Figure 3 Assume that the customer is looking for alsquovery fairrsquo girl in case of attribute type lsquocomplexionrsquoThe customer can define the acceptability with respectto complexion as fuzzy set for example 08 Thismeans that his satisfaction level with that particularattribute is 80 Similarly for every attribute underconsideration he defines his acceptability level iemembership level is asked and fuzzily definedrequirement is generated as shown in Figure 4

Step 2 Pairwise comparison and calculatingaggregate score of each profileA classic AHP procedure is conducted which consistsof a pairwise comparison of attributes at respective

Table I Pairwise comparison of education and occupation

Education Occupation

Education 1 4Occupation 14 1

Table II Pairwise comparison of family status earning andlocation

Family status Earning Location

Family status 1 14 17Earning 4 1 12Location 7 2 1

Table III Pairwise comparison of height age complexiondiet and body type

Height Age Complexion Diet Bodytype

Height 1 6 8 9 5Age 16 1 7 15 110Complexion 18 17 1 7 2Diet 19 5 17 1 5Body type 15 10 12 15 1

Table IV Pairwise comparison of education wealth andpersonality

Education Wealth Personality

Education 1 3 3Wealth 13 1 12Personality 13 3 1

Table V The weight of attributes

Attribute Education Height Occupation Location Body type

Weight () 3945 1513 986 811 621Rank 1 2 3 4 5Attribute Diet Complexion Earning Age Family statusWeight () 587 536 446 442 113Rank 6 7 8 9 10

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 63

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

hierarchy to calculate respective weight for each attri-bute (Tables IndashIV) In this case customer rates eachattribute with respect to other attribute at the samelevel and under the same group From the pairwisecomparisons we get relative weights of attributes asshown in Table V

In our example we consider 10 female memberrsquosdata with different attributes as shown in Table VIThere can be thousands of the profiles in the databaseof any website available Let us calculate profile scorefor profile no 2 This profile has attributes like 27years old 134 cm height complexion as whitishbrown qualification as chartered accountant (CA)belongs to Rich class annual income 22 lac livingin Metro Eating habit as Vegetarian and body typeis Athletic etc

For every profile according to fuzzily definedrequirements membership value can be calculatedComparing the membership values from respectivefuzzy sets and attributes of the profile we get variousmembership values as Education is CA and respectivesatisfaction level is 1 therefore Education=1 Likewiseremaining membership values are Occupation= 044Family status = 0 Earning=1 Location=07 Height =0 Age=06 Complexion=07 Diet = 1 and Bodytype=09

A profile score is calculated by multiplying thismembership value with respective weight fromTable V and aggregating for all attributes For exam-ple for education the weight is 0394

Profile score (A12) = 03945(1) + 00986(044) + 00113(0) + 00446(1) + 00811 (07) + 01513(0) + 00442(06) + 00536(07) + 00587(1) + 00621(09) = 07179

Thus the profile score is 07179 Similarlyprofile scores as per nomenclature describedearlier are as shown in Tables VII and VIII As men-tioned earlier in this mutual matching problem wemust consider what each woman is looking for Everywoman also has defined her requirements in termsof fuzzy sets and done pairwise comparisonThus profile score of this male customer who islooking for female partner can be calculated Tocalculate the compatibility score we use formuladefined in step 3

For example in case of pair male1 and female5ie A15 and B51

CI = 13 [(08372 + 05839) + (08372 + 05839)(2radic[(08372 05839)2 + 1])] = 06963

Thus CI based on male no1rsquos preference witheach female are listed in Table VIII Similarly forevery possible matching pair CI is calculated asrecorded in Table IX T

able

VI

Detailsof

femalemem

bers

No

Educatio

nOccupation

Fam

ilystatus

Earning

Location

Height

Age

Com

plexion

Diet

Bodytype

1BEBTech

Not

working

Upper

middleclass

0Urban

160

26Whitish

Eggitarian

Athletic

2Chartered

accountant

Businessm

anRichclass

22Metro

134

27Whitishbrow

nVegetarian

Athletic

3MCom

Banking

Middleclass

4Rural

137

24Fair

Eggitarian

Slim

4MEM

Tech

EngineeringRampD

Upper

middleclass

14Urban

139

27Fair

Eggitarian

Athletic

5MBAPGDM

LogisticsSCM

Richclass

16Urban

139

27Veryfair

Eggitarian

Heavy

6MCAPGDCA

Software

Middleclass

12Sem

iUrban

162

26Whitishbrow

nVegetarian

Slim

7MDM

S(M

edical)

Teaching

Middleclass

7Sem

iUrban

167

29Dark

Eggitarian

Athletic

8BAMS

Looking

forajob

Middleclass

0Rural

170

25Veryfair

Vegetarian

Slim

9MLLLM

Governm

entservices

Upper

middleclass

8Metro

144

27Whitish

Vegetarian

Athletic

10MBBSBDS

Governm

entservices

Richclass

8Metro

144

27Whitish

Vegetarian

Heavy

Bachelorrsquosof

Engineering

(BE)Masterrsquosof

EngineeringTechnology(M

EM

Tech)Chartered

Accountant(CA)Masterof

Com

merce

(MCom

)Masterof

BusinessAdm

inis-

tration(M

BA)PostG

raduateDiplomain

Managem

ent(PGDM)Masterof

Com

puterApplications

(MCA)PostGraduateDiplomain

Com

puterApplications

(PGDCA)Doctorof

Medicine(M

D)Masters

ofSurgery

(MS)Masterof

Law

(MLLLM)Bachelorof

Ayurveda

MedicineandSurgery

(BAMS)Bachelorof

DentalSurgery

(BDS)

Bachelorof

MedicineBachelorof

Surgery

(MBBS)ResearchandDevelopment(R

ampD)SupplyChain

Managem

ent(SCM)Governm

ent(G

ovt)

K JOSHI AND S KUMAR64

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Based on compatibility scores profiles getshortlisted and ranked in descending order Fur-thermore the customer has liberty to re-rank theprofiles after looking at each of the top 10 profilesSubsequently if the customer re-ranks the profiles thepreferences are taken as input for Gale-Shapleyalgorithm Otherwise profiles ranked based on CI aretreated with respect to their rank To demonstrateGale-Shapley algorithm in this context we assume thatthere are five male and five female profiles with theirpreferences as mentioned in the following table

M1=gtF1-F3-F2-F4-F5 F1 =gtM5-M2-M4-M3-M1M2=gtF2-F1-F3-F5-F4 F2 =gtM2-M4-M5-M1-M3M3=gtF2-F4-F5-F1-F3 F3 =gtM3-M1-M4-M5-M2M4=gtF3-F1-F4-F5-F2 F4 =gtM1-M3-M2-M4-M5M5=gtF5-F2-F4-F3-F1 F5 =gtM2-M1-M3-M5-M4

Gale-Shapley algorithm generates the followingmatches

Male1 is paired with female5 male2 is paired withfemale3 male3 is paired with female4 male4 is pairedwith female2 and male5 is paired with female1

This is an add-on facility for a customer where heor she will receive a suggested stable matched profileIf they contact this suggested profile as well as a few

profiles listed based on their CI then the probabilityof getting positive response increases

5 CONCLUSIONS

In todayrsquos Internet era services seeking efficiency isof paramount importance The approach presented inthis paper attempts to exploit current IT-enabledpartner search for marriage through Web portals

Salient features of this proposed method are asfollows

bull Integrated way to quantify the online profiles withimplicit needs

bull Two-phase short listing ie FAHP and stablematching algorithm

bull Reducing customerrsquos effort to find their mateonline according to their implicit needs (definedfuzzily)

bull Enhancing the probability of getting positiveresponse and matchmaking

A sorting based on CI in descending orderenhances the probability of matchmaking It thus leadsto reduction in lead time of waiting of the positive ornegative reply from the opposite party This opera-tional viewpoint has been presented in this paper with

Table IX Ranking based on compatibility index

A16 A17 A19 A11 A14 A18 A12 A15 A13 A110

Score 09684 08954 07958 08756 08974 08009 07179 08372 04858 08317B61 B71 B91 B11 B41 B81 B21 B51 B31 B101

Score 08517 08692 09306 08142 06982 07576 07743 05839 08824 05079CI 09059 08821 08580 08438 07876 07787 07453 06963 06531 06486Rank 1 2 3 4 5 6 7 8 9 10

CI compatibility index

Table VII Profile scores when female rated by male no 1

A11 A12 A13 A14 A15 A16 A17 A18 A19 A110

Score 08756 07179 04858 08974 08372 09684 08954 08009 07958 08317

Table VIII Profile scores of male no 1 rated by each female

B11 B21 B31 B41 B51 B61 B71 B81 B91 B101

Score 08142 07743 08824 06982 05839 08517 08692 07576 09306 05079

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 65

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

introduction of a CI This index helps user to maxi-mize their requirements while mutual matching

Future studies might cover an enhancement inrating parameters Few Web portals have incorporatedmatchmaking based on personality behaviour Morequalitative and quantitative factors can be includedwith involvement of ratings by parents and relativesSuch study will lead to multi-criteria group decision-making kind of problem

REFERENCES

Abraham DJ 2003 Algorithmics of two-sided matchingproblems Masterrsquos thesis University of GlasgowDepartment of Computing Science Accessed September2010

Adachi H 2003 A search model of two-sided matchingunder nontransferable utility Journal of Economic Theory113(2) 182ndash198

Banerjee Abhijit V Duflo Esther Ghatak MaitreeshLafortune J 20009 Marry for What Caste and MateSelection in Modern India NBER Working Paper Seriesw14958 Available at SSRN httpssrncomabstract=1405966 accessed July 2010

Batabyal A DeAngelo G 2008 To match or not to matchaspects of marital matchmaking under uncertainty Opera-tions Research Letters 36(1) 94ndash98

Belot M Francesconi M 2010 Meeting opportunities and part-ner selection a field study 1ndash40 Available at httpwwwtauacil~weissfam_econRESTAT-13763-1-manuscriptpdf(accessed on 18 December 2010)

Celik O Knoblauch V 2007 Marriage matching withcorrelated preferences Working Paper 1ndash10 Universityof Connecticut

Chang S Wang R Wang S 2006 Applying fuzzy linguisticquantifier to select supply chain partners at differentphases of product life cycle International Journal ofProduction Economics 100 348ndash359

Dugar S Bhattacharya H Reiley DH 2010 Canrsquot buy melove a field experiment exploring the trade-off betweenincome and caste status in an Indian matrimonial marketAvailable at SSRN httpssrncomabstract=1288987Accessed July 2010

Gale D Shapley LS 1962 College admissions and the stabilityof marriage American Mathematical Monthly 69(1) 9ndash15

Gordon J Gupta P 2003 Understanding Indiarsquos servicesevolution httpimforgexternalnpapdseminars2003newdelhigordonpdf Accessed August 2010

Hajeeh M Lairi S 2009 Marriage partner selection inKuwait an analytical hierarchy process approach Journalof Mathematical Sociology 33 222ndash240

Hitsch GJ Hortaccedilsu A Ariely D 2010 What makes youclick mdash mate preferences in online dating QuantitativeMarketing and Economics 8(4) 393ndash427

Irving RW Leather P Gusfield D 1987 An efficientalgorithm for the ldquooptimalrdquo stable marriage Journal ofthe ACM 34(3) 532ndash543

Korkmaz I 2008 An analytic hierarchy process and two-sided matching based decision support system formilitary personnel assignment Information Sciences 1782915ndash2927

Li X Murata T 2009 Priority based matchmaking method ofbuyers and suppliers in B2B e-marketplace using multi-objective optimization Proceedings of the InternationalMulti Conference of Engineers and Computer Scientists1 18ndash20

Pathak RS 2005 Matrimonial advertisements in India asociolinguistic profile South Asian Language Review 15(2)1ndash18

Saaty TL 1980 The Analytic Hierarchy Process PlanningPriority Setting Resource Allocation McGraw-HillNew York

Salo AA Hamalainen RP 1997 On the measurement ofpreferences in the AHP Journal of Multi-criteriaDecision Analysis 6 303ndash319

Sipahi S Timor M 2010 The analytic hierarchy process andanalytic network process an overview of applicationsManagement Decision 48(5) 775ndash808

Teo CP Sethuraman J Tan WP 2001 Gale-Shapley stablemarriage problem revisited strategic issues and applica-tions Management Science 47(9) 1252ndash1267

Thomaidis F Mavrakis D 2006 Optimum route of the southtranscontinental gas pipeline in SE Europe using AHPJournal of Multi-CriteriaDecision Analysis 14(1ndash3) 77ndash88

Triantaphyllou E 2001 Two new cases of rank reversalswhen the AHP and some of its additive variants are usedthat do not occur with the multiplicative AHP Journal ofMulti-Criteria Decision Analysis 10(1) 11ndash25

Vaidya OS Kumar S 2006 Analytic hierarchy process anoverview of applications European Journal of OperationalResearch 169(1) 1ndash29

Vaillant N 2004 Estimating the time elapsed betweenending a relationship and joining a matchmaking agencyevidence from a French marriage bureau Journal ofEconomic Psychology 25(6) 789ndash802

Vi N Fragniegravere E Gauthier J Sapin M Widmer ED 2010Optimizing the marriage market an application of thelinear assignment model European Journal of OperationalResearch 202(2) 547ndash553

K JOSHI AND S KUMAR66

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Figure 4 Customerrsquos attribute-wise requirements in the form of fuzzy sets Please see Table VI for abbreviations used

K JOSHI AND S KUMAR62

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

earlier Every customer will receive a suggested stablematched profile and also his or her own preference listbased on lsquocompatibility indexrsquo This enhances the prob-ability of getting a positive response from recipient person

4 ILLUSTRATED EXAMPLE

To validate the proposed method we chose an advancedsearch process from a Web portal known as Jeevansathicom In this illustration we have assumed case of a manwho is looking for a woman as prospective partner formarriage The customer is interested in various profileswith following requirements that are arranged inhierarchical manner as shown in Figure 3

Usually in India partner search is based upon threebroad criteria of prospective partner viz educationoccupation wealth personality An education criterionis related to qualification like Undergraduate Mastersor PhD etc in diverse disciplines like arts commerceengineering and medicine etc Occupation criteriameans a person is an engineer a doctor a charteredaccountant or a professor etc A Wealth criterion con-sists of family status (low class middle class upperclass) earnings (annual income) and location (semi-urban urban metro city) A personality criterion con-sists of age (years) height (cm) complexion (darkwhitish brown brown fair) diet (vegetarian eggitariannon-vegetarian) and body type (slim athletic heavy)

Step 1 Defining attributes in terms of fuzzy setsThe male customer who is looking for a spouse ie awoman with various attributes with hierarchy as statedin Figure 3 Assume that the customer is looking for alsquovery fairrsquo girl in case of attribute type lsquocomplexionrsquoThe customer can define the acceptability with respectto complexion as fuzzy set for example 08 Thismeans that his satisfaction level with that particularattribute is 80 Similarly for every attribute underconsideration he defines his acceptability level iemembership level is asked and fuzzily definedrequirement is generated as shown in Figure 4

Step 2 Pairwise comparison and calculatingaggregate score of each profileA classic AHP procedure is conducted which consistsof a pairwise comparison of attributes at respective

Table I Pairwise comparison of education and occupation

Education Occupation

Education 1 4Occupation 14 1

Table II Pairwise comparison of family status earning andlocation

Family status Earning Location

Family status 1 14 17Earning 4 1 12Location 7 2 1

Table III Pairwise comparison of height age complexiondiet and body type

Height Age Complexion Diet Bodytype

Height 1 6 8 9 5Age 16 1 7 15 110Complexion 18 17 1 7 2Diet 19 5 17 1 5Body type 15 10 12 15 1

Table IV Pairwise comparison of education wealth andpersonality

Education Wealth Personality

Education 1 3 3Wealth 13 1 12Personality 13 3 1

Table V The weight of attributes

Attribute Education Height Occupation Location Body type

Weight () 3945 1513 986 811 621Rank 1 2 3 4 5Attribute Diet Complexion Earning Age Family statusWeight () 587 536 446 442 113Rank 6 7 8 9 10

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 63

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

hierarchy to calculate respective weight for each attri-bute (Tables IndashIV) In this case customer rates eachattribute with respect to other attribute at the samelevel and under the same group From the pairwisecomparisons we get relative weights of attributes asshown in Table V

In our example we consider 10 female memberrsquosdata with different attributes as shown in Table VIThere can be thousands of the profiles in the databaseof any website available Let us calculate profile scorefor profile no 2 This profile has attributes like 27years old 134 cm height complexion as whitishbrown qualification as chartered accountant (CA)belongs to Rich class annual income 22 lac livingin Metro Eating habit as Vegetarian and body typeis Athletic etc

For every profile according to fuzzily definedrequirements membership value can be calculatedComparing the membership values from respectivefuzzy sets and attributes of the profile we get variousmembership values as Education is CA and respectivesatisfaction level is 1 therefore Education=1 Likewiseremaining membership values are Occupation= 044Family status = 0 Earning=1 Location=07 Height =0 Age=06 Complexion=07 Diet = 1 and Bodytype=09

A profile score is calculated by multiplying thismembership value with respective weight fromTable V and aggregating for all attributes For exam-ple for education the weight is 0394

Profile score (A12) = 03945(1) + 00986(044) + 00113(0) + 00446(1) + 00811 (07) + 01513(0) + 00442(06) + 00536(07) + 00587(1) + 00621(09) = 07179

Thus the profile score is 07179 Similarlyprofile scores as per nomenclature describedearlier are as shown in Tables VII and VIII As men-tioned earlier in this mutual matching problem wemust consider what each woman is looking for Everywoman also has defined her requirements in termsof fuzzy sets and done pairwise comparisonThus profile score of this male customer who islooking for female partner can be calculated Tocalculate the compatibility score we use formuladefined in step 3

For example in case of pair male1 and female5ie A15 and B51

CI = 13 [(08372 + 05839) + (08372 + 05839)(2radic[(08372 05839)2 + 1])] = 06963

Thus CI based on male no1rsquos preference witheach female are listed in Table VIII Similarly forevery possible matching pair CI is calculated asrecorded in Table IX T

able

VI

Detailsof

femalemem

bers

No

Educatio

nOccupation

Fam

ilystatus

Earning

Location

Height

Age

Com

plexion

Diet

Bodytype

1BEBTech

Not

working

Upper

middleclass

0Urban

160

26Whitish

Eggitarian

Athletic

2Chartered

accountant

Businessm

anRichclass

22Metro

134

27Whitishbrow

nVegetarian

Athletic

3MCom

Banking

Middleclass

4Rural

137

24Fair

Eggitarian

Slim

4MEM

Tech

EngineeringRampD

Upper

middleclass

14Urban

139

27Fair

Eggitarian

Athletic

5MBAPGDM

LogisticsSCM

Richclass

16Urban

139

27Veryfair

Eggitarian

Heavy

6MCAPGDCA

Software

Middleclass

12Sem

iUrban

162

26Whitishbrow

nVegetarian

Slim

7MDM

S(M

edical)

Teaching

Middleclass

7Sem

iUrban

167

29Dark

Eggitarian

Athletic

8BAMS

Looking

forajob

Middleclass

0Rural

170

25Veryfair

Vegetarian

Slim

9MLLLM

Governm

entservices

Upper

middleclass

8Metro

144

27Whitish

Vegetarian

Athletic

10MBBSBDS

Governm

entservices

Richclass

8Metro

144

27Whitish

Vegetarian

Heavy

Bachelorrsquosof

Engineering

(BE)Masterrsquosof

EngineeringTechnology(M

EM

Tech)Chartered

Accountant(CA)Masterof

Com

merce

(MCom

)Masterof

BusinessAdm

inis-

tration(M

BA)PostG

raduateDiplomain

Managem

ent(PGDM)Masterof

Com

puterApplications

(MCA)PostGraduateDiplomain

Com

puterApplications

(PGDCA)Doctorof

Medicine(M

D)Masters

ofSurgery

(MS)Masterof

Law

(MLLLM)Bachelorof

Ayurveda

MedicineandSurgery

(BAMS)Bachelorof

DentalSurgery

(BDS)

Bachelorof

MedicineBachelorof

Surgery

(MBBS)ResearchandDevelopment(R

ampD)SupplyChain

Managem

ent(SCM)Governm

ent(G

ovt)

K JOSHI AND S KUMAR64

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Based on compatibility scores profiles getshortlisted and ranked in descending order Fur-thermore the customer has liberty to re-rank theprofiles after looking at each of the top 10 profilesSubsequently if the customer re-ranks the profiles thepreferences are taken as input for Gale-Shapleyalgorithm Otherwise profiles ranked based on CI aretreated with respect to their rank To demonstrateGale-Shapley algorithm in this context we assume thatthere are five male and five female profiles with theirpreferences as mentioned in the following table

M1=gtF1-F3-F2-F4-F5 F1 =gtM5-M2-M4-M3-M1M2=gtF2-F1-F3-F5-F4 F2 =gtM2-M4-M5-M1-M3M3=gtF2-F4-F5-F1-F3 F3 =gtM3-M1-M4-M5-M2M4=gtF3-F1-F4-F5-F2 F4 =gtM1-M3-M2-M4-M5M5=gtF5-F2-F4-F3-F1 F5 =gtM2-M1-M3-M5-M4

Gale-Shapley algorithm generates the followingmatches

Male1 is paired with female5 male2 is paired withfemale3 male3 is paired with female4 male4 is pairedwith female2 and male5 is paired with female1

This is an add-on facility for a customer where heor she will receive a suggested stable matched profileIf they contact this suggested profile as well as a few

profiles listed based on their CI then the probabilityof getting positive response increases

5 CONCLUSIONS

In todayrsquos Internet era services seeking efficiency isof paramount importance The approach presented inthis paper attempts to exploit current IT-enabledpartner search for marriage through Web portals

Salient features of this proposed method are asfollows

bull Integrated way to quantify the online profiles withimplicit needs

bull Two-phase short listing ie FAHP and stablematching algorithm

bull Reducing customerrsquos effort to find their mateonline according to their implicit needs (definedfuzzily)

bull Enhancing the probability of getting positiveresponse and matchmaking

A sorting based on CI in descending orderenhances the probability of matchmaking It thus leadsto reduction in lead time of waiting of the positive ornegative reply from the opposite party This opera-tional viewpoint has been presented in this paper with

Table IX Ranking based on compatibility index

A16 A17 A19 A11 A14 A18 A12 A15 A13 A110

Score 09684 08954 07958 08756 08974 08009 07179 08372 04858 08317B61 B71 B91 B11 B41 B81 B21 B51 B31 B101

Score 08517 08692 09306 08142 06982 07576 07743 05839 08824 05079CI 09059 08821 08580 08438 07876 07787 07453 06963 06531 06486Rank 1 2 3 4 5 6 7 8 9 10

CI compatibility index

Table VII Profile scores when female rated by male no 1

A11 A12 A13 A14 A15 A16 A17 A18 A19 A110

Score 08756 07179 04858 08974 08372 09684 08954 08009 07958 08317

Table VIII Profile scores of male no 1 rated by each female

B11 B21 B31 B41 B51 B61 B71 B81 B91 B101

Score 08142 07743 08824 06982 05839 08517 08692 07576 09306 05079

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 65

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

introduction of a CI This index helps user to maxi-mize their requirements while mutual matching

Future studies might cover an enhancement inrating parameters Few Web portals have incorporatedmatchmaking based on personality behaviour Morequalitative and quantitative factors can be includedwith involvement of ratings by parents and relativesSuch study will lead to multi-criteria group decision-making kind of problem

REFERENCES

Abraham DJ 2003 Algorithmics of two-sided matchingproblems Masterrsquos thesis University of GlasgowDepartment of Computing Science Accessed September2010

Adachi H 2003 A search model of two-sided matchingunder nontransferable utility Journal of Economic Theory113(2) 182ndash198

Banerjee Abhijit V Duflo Esther Ghatak MaitreeshLafortune J 20009 Marry for What Caste and MateSelection in Modern India NBER Working Paper Seriesw14958 Available at SSRN httpssrncomabstract=1405966 accessed July 2010

Batabyal A DeAngelo G 2008 To match or not to matchaspects of marital matchmaking under uncertainty Opera-tions Research Letters 36(1) 94ndash98

Belot M Francesconi M 2010 Meeting opportunities and part-ner selection a field study 1ndash40 Available at httpwwwtauacil~weissfam_econRESTAT-13763-1-manuscriptpdf(accessed on 18 December 2010)

Celik O Knoblauch V 2007 Marriage matching withcorrelated preferences Working Paper 1ndash10 Universityof Connecticut

Chang S Wang R Wang S 2006 Applying fuzzy linguisticquantifier to select supply chain partners at differentphases of product life cycle International Journal ofProduction Economics 100 348ndash359

Dugar S Bhattacharya H Reiley DH 2010 Canrsquot buy melove a field experiment exploring the trade-off betweenincome and caste status in an Indian matrimonial marketAvailable at SSRN httpssrncomabstract=1288987Accessed July 2010

Gale D Shapley LS 1962 College admissions and the stabilityof marriage American Mathematical Monthly 69(1) 9ndash15

Gordon J Gupta P 2003 Understanding Indiarsquos servicesevolution httpimforgexternalnpapdseminars2003newdelhigordonpdf Accessed August 2010

Hajeeh M Lairi S 2009 Marriage partner selection inKuwait an analytical hierarchy process approach Journalof Mathematical Sociology 33 222ndash240

Hitsch GJ Hortaccedilsu A Ariely D 2010 What makes youclick mdash mate preferences in online dating QuantitativeMarketing and Economics 8(4) 393ndash427

Irving RW Leather P Gusfield D 1987 An efficientalgorithm for the ldquooptimalrdquo stable marriage Journal ofthe ACM 34(3) 532ndash543

Korkmaz I 2008 An analytic hierarchy process and two-sided matching based decision support system formilitary personnel assignment Information Sciences 1782915ndash2927

Li X Murata T 2009 Priority based matchmaking method ofbuyers and suppliers in B2B e-marketplace using multi-objective optimization Proceedings of the InternationalMulti Conference of Engineers and Computer Scientists1 18ndash20

Pathak RS 2005 Matrimonial advertisements in India asociolinguistic profile South Asian Language Review 15(2)1ndash18

Saaty TL 1980 The Analytic Hierarchy Process PlanningPriority Setting Resource Allocation McGraw-HillNew York

Salo AA Hamalainen RP 1997 On the measurement ofpreferences in the AHP Journal of Multi-criteriaDecision Analysis 6 303ndash319

Sipahi S Timor M 2010 The analytic hierarchy process andanalytic network process an overview of applicationsManagement Decision 48(5) 775ndash808

Teo CP Sethuraman J Tan WP 2001 Gale-Shapley stablemarriage problem revisited strategic issues and applica-tions Management Science 47(9) 1252ndash1267

Thomaidis F Mavrakis D 2006 Optimum route of the southtranscontinental gas pipeline in SE Europe using AHPJournal of Multi-CriteriaDecision Analysis 14(1ndash3) 77ndash88

Triantaphyllou E 2001 Two new cases of rank reversalswhen the AHP and some of its additive variants are usedthat do not occur with the multiplicative AHP Journal ofMulti-Criteria Decision Analysis 10(1) 11ndash25

Vaidya OS Kumar S 2006 Analytic hierarchy process anoverview of applications European Journal of OperationalResearch 169(1) 1ndash29

Vaillant N 2004 Estimating the time elapsed betweenending a relationship and joining a matchmaking agencyevidence from a French marriage bureau Journal ofEconomic Psychology 25(6) 789ndash802

Vi N Fragniegravere E Gauthier J Sapin M Widmer ED 2010Optimizing the marriage market an application of thelinear assignment model European Journal of OperationalResearch 202(2) 547ndash553

K JOSHI AND S KUMAR66

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

earlier Every customer will receive a suggested stablematched profile and also his or her own preference listbased on lsquocompatibility indexrsquo This enhances the prob-ability of getting a positive response from recipient person

4 ILLUSTRATED EXAMPLE

To validate the proposed method we chose an advancedsearch process from a Web portal known as Jeevansathicom In this illustration we have assumed case of a manwho is looking for a woman as prospective partner formarriage The customer is interested in various profileswith following requirements that are arranged inhierarchical manner as shown in Figure 3

Usually in India partner search is based upon threebroad criteria of prospective partner viz educationoccupation wealth personality An education criterionis related to qualification like Undergraduate Mastersor PhD etc in diverse disciplines like arts commerceengineering and medicine etc Occupation criteriameans a person is an engineer a doctor a charteredaccountant or a professor etc A Wealth criterion con-sists of family status (low class middle class upperclass) earnings (annual income) and location (semi-urban urban metro city) A personality criterion con-sists of age (years) height (cm) complexion (darkwhitish brown brown fair) diet (vegetarian eggitariannon-vegetarian) and body type (slim athletic heavy)

Step 1 Defining attributes in terms of fuzzy setsThe male customer who is looking for a spouse ie awoman with various attributes with hierarchy as statedin Figure 3 Assume that the customer is looking for alsquovery fairrsquo girl in case of attribute type lsquocomplexionrsquoThe customer can define the acceptability with respectto complexion as fuzzy set for example 08 Thismeans that his satisfaction level with that particularattribute is 80 Similarly for every attribute underconsideration he defines his acceptability level iemembership level is asked and fuzzily definedrequirement is generated as shown in Figure 4

Step 2 Pairwise comparison and calculatingaggregate score of each profileA classic AHP procedure is conducted which consistsof a pairwise comparison of attributes at respective

Table I Pairwise comparison of education and occupation

Education Occupation

Education 1 4Occupation 14 1

Table II Pairwise comparison of family status earning andlocation

Family status Earning Location

Family status 1 14 17Earning 4 1 12Location 7 2 1

Table III Pairwise comparison of height age complexiondiet and body type

Height Age Complexion Diet Bodytype

Height 1 6 8 9 5Age 16 1 7 15 110Complexion 18 17 1 7 2Diet 19 5 17 1 5Body type 15 10 12 15 1

Table IV Pairwise comparison of education wealth andpersonality

Education Wealth Personality

Education 1 3 3Wealth 13 1 12Personality 13 3 1

Table V The weight of attributes

Attribute Education Height Occupation Location Body type

Weight () 3945 1513 986 811 621Rank 1 2 3 4 5Attribute Diet Complexion Earning Age Family statusWeight () 587 536 446 442 113Rank 6 7 8 9 10

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 63

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

hierarchy to calculate respective weight for each attri-bute (Tables IndashIV) In this case customer rates eachattribute with respect to other attribute at the samelevel and under the same group From the pairwisecomparisons we get relative weights of attributes asshown in Table V

In our example we consider 10 female memberrsquosdata with different attributes as shown in Table VIThere can be thousands of the profiles in the databaseof any website available Let us calculate profile scorefor profile no 2 This profile has attributes like 27years old 134 cm height complexion as whitishbrown qualification as chartered accountant (CA)belongs to Rich class annual income 22 lac livingin Metro Eating habit as Vegetarian and body typeis Athletic etc

For every profile according to fuzzily definedrequirements membership value can be calculatedComparing the membership values from respectivefuzzy sets and attributes of the profile we get variousmembership values as Education is CA and respectivesatisfaction level is 1 therefore Education=1 Likewiseremaining membership values are Occupation= 044Family status = 0 Earning=1 Location=07 Height =0 Age=06 Complexion=07 Diet = 1 and Bodytype=09

A profile score is calculated by multiplying thismembership value with respective weight fromTable V and aggregating for all attributes For exam-ple for education the weight is 0394

Profile score (A12) = 03945(1) + 00986(044) + 00113(0) + 00446(1) + 00811 (07) + 01513(0) + 00442(06) + 00536(07) + 00587(1) + 00621(09) = 07179

Thus the profile score is 07179 Similarlyprofile scores as per nomenclature describedearlier are as shown in Tables VII and VIII As men-tioned earlier in this mutual matching problem wemust consider what each woman is looking for Everywoman also has defined her requirements in termsof fuzzy sets and done pairwise comparisonThus profile score of this male customer who islooking for female partner can be calculated Tocalculate the compatibility score we use formuladefined in step 3

For example in case of pair male1 and female5ie A15 and B51

CI = 13 [(08372 + 05839) + (08372 + 05839)(2radic[(08372 05839)2 + 1])] = 06963

Thus CI based on male no1rsquos preference witheach female are listed in Table VIII Similarly forevery possible matching pair CI is calculated asrecorded in Table IX T

able

VI

Detailsof

femalemem

bers

No

Educatio

nOccupation

Fam

ilystatus

Earning

Location

Height

Age

Com

plexion

Diet

Bodytype

1BEBTech

Not

working

Upper

middleclass

0Urban

160

26Whitish

Eggitarian

Athletic

2Chartered

accountant

Businessm

anRichclass

22Metro

134

27Whitishbrow

nVegetarian

Athletic

3MCom

Banking

Middleclass

4Rural

137

24Fair

Eggitarian

Slim

4MEM

Tech

EngineeringRampD

Upper

middleclass

14Urban

139

27Fair

Eggitarian

Athletic

5MBAPGDM

LogisticsSCM

Richclass

16Urban

139

27Veryfair

Eggitarian

Heavy

6MCAPGDCA

Software

Middleclass

12Sem

iUrban

162

26Whitishbrow

nVegetarian

Slim

7MDM

S(M

edical)

Teaching

Middleclass

7Sem

iUrban

167

29Dark

Eggitarian

Athletic

8BAMS

Looking

forajob

Middleclass

0Rural

170

25Veryfair

Vegetarian

Slim

9MLLLM

Governm

entservices

Upper

middleclass

8Metro

144

27Whitish

Vegetarian

Athletic

10MBBSBDS

Governm

entservices

Richclass

8Metro

144

27Whitish

Vegetarian

Heavy

Bachelorrsquosof

Engineering

(BE)Masterrsquosof

EngineeringTechnology(M

EM

Tech)Chartered

Accountant(CA)Masterof

Com

merce

(MCom

)Masterof

BusinessAdm

inis-

tration(M

BA)PostG

raduateDiplomain

Managem

ent(PGDM)Masterof

Com

puterApplications

(MCA)PostGraduateDiplomain

Com

puterApplications

(PGDCA)Doctorof

Medicine(M

D)Masters

ofSurgery

(MS)Masterof

Law

(MLLLM)Bachelorof

Ayurveda

MedicineandSurgery

(BAMS)Bachelorof

DentalSurgery

(BDS)

Bachelorof

MedicineBachelorof

Surgery

(MBBS)ResearchandDevelopment(R

ampD)SupplyChain

Managem

ent(SCM)Governm

ent(G

ovt)

K JOSHI AND S KUMAR64

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Based on compatibility scores profiles getshortlisted and ranked in descending order Fur-thermore the customer has liberty to re-rank theprofiles after looking at each of the top 10 profilesSubsequently if the customer re-ranks the profiles thepreferences are taken as input for Gale-Shapleyalgorithm Otherwise profiles ranked based on CI aretreated with respect to their rank To demonstrateGale-Shapley algorithm in this context we assume thatthere are five male and five female profiles with theirpreferences as mentioned in the following table

M1=gtF1-F3-F2-F4-F5 F1 =gtM5-M2-M4-M3-M1M2=gtF2-F1-F3-F5-F4 F2 =gtM2-M4-M5-M1-M3M3=gtF2-F4-F5-F1-F3 F3 =gtM3-M1-M4-M5-M2M4=gtF3-F1-F4-F5-F2 F4 =gtM1-M3-M2-M4-M5M5=gtF5-F2-F4-F3-F1 F5 =gtM2-M1-M3-M5-M4

Gale-Shapley algorithm generates the followingmatches

Male1 is paired with female5 male2 is paired withfemale3 male3 is paired with female4 male4 is pairedwith female2 and male5 is paired with female1

This is an add-on facility for a customer where heor she will receive a suggested stable matched profileIf they contact this suggested profile as well as a few

profiles listed based on their CI then the probabilityof getting positive response increases

5 CONCLUSIONS

In todayrsquos Internet era services seeking efficiency isof paramount importance The approach presented inthis paper attempts to exploit current IT-enabledpartner search for marriage through Web portals

Salient features of this proposed method are asfollows

bull Integrated way to quantify the online profiles withimplicit needs

bull Two-phase short listing ie FAHP and stablematching algorithm

bull Reducing customerrsquos effort to find their mateonline according to their implicit needs (definedfuzzily)

bull Enhancing the probability of getting positiveresponse and matchmaking

A sorting based on CI in descending orderenhances the probability of matchmaking It thus leadsto reduction in lead time of waiting of the positive ornegative reply from the opposite party This opera-tional viewpoint has been presented in this paper with

Table IX Ranking based on compatibility index

A16 A17 A19 A11 A14 A18 A12 A15 A13 A110

Score 09684 08954 07958 08756 08974 08009 07179 08372 04858 08317B61 B71 B91 B11 B41 B81 B21 B51 B31 B101

Score 08517 08692 09306 08142 06982 07576 07743 05839 08824 05079CI 09059 08821 08580 08438 07876 07787 07453 06963 06531 06486Rank 1 2 3 4 5 6 7 8 9 10

CI compatibility index

Table VII Profile scores when female rated by male no 1

A11 A12 A13 A14 A15 A16 A17 A18 A19 A110

Score 08756 07179 04858 08974 08372 09684 08954 08009 07958 08317

Table VIII Profile scores of male no 1 rated by each female

B11 B21 B31 B41 B51 B61 B71 B81 B91 B101

Score 08142 07743 08824 06982 05839 08517 08692 07576 09306 05079

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 65

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

introduction of a CI This index helps user to maxi-mize their requirements while mutual matching

Future studies might cover an enhancement inrating parameters Few Web portals have incorporatedmatchmaking based on personality behaviour Morequalitative and quantitative factors can be includedwith involvement of ratings by parents and relativesSuch study will lead to multi-criteria group decision-making kind of problem

REFERENCES

Abraham DJ 2003 Algorithmics of two-sided matchingproblems Masterrsquos thesis University of GlasgowDepartment of Computing Science Accessed September2010

Adachi H 2003 A search model of two-sided matchingunder nontransferable utility Journal of Economic Theory113(2) 182ndash198

Banerjee Abhijit V Duflo Esther Ghatak MaitreeshLafortune J 20009 Marry for What Caste and MateSelection in Modern India NBER Working Paper Seriesw14958 Available at SSRN httpssrncomabstract=1405966 accessed July 2010

Batabyal A DeAngelo G 2008 To match or not to matchaspects of marital matchmaking under uncertainty Opera-tions Research Letters 36(1) 94ndash98

Belot M Francesconi M 2010 Meeting opportunities and part-ner selection a field study 1ndash40 Available at httpwwwtauacil~weissfam_econRESTAT-13763-1-manuscriptpdf(accessed on 18 December 2010)

Celik O Knoblauch V 2007 Marriage matching withcorrelated preferences Working Paper 1ndash10 Universityof Connecticut

Chang S Wang R Wang S 2006 Applying fuzzy linguisticquantifier to select supply chain partners at differentphases of product life cycle International Journal ofProduction Economics 100 348ndash359

Dugar S Bhattacharya H Reiley DH 2010 Canrsquot buy melove a field experiment exploring the trade-off betweenincome and caste status in an Indian matrimonial marketAvailable at SSRN httpssrncomabstract=1288987Accessed July 2010

Gale D Shapley LS 1962 College admissions and the stabilityof marriage American Mathematical Monthly 69(1) 9ndash15

Gordon J Gupta P 2003 Understanding Indiarsquos servicesevolution httpimforgexternalnpapdseminars2003newdelhigordonpdf Accessed August 2010

Hajeeh M Lairi S 2009 Marriage partner selection inKuwait an analytical hierarchy process approach Journalof Mathematical Sociology 33 222ndash240

Hitsch GJ Hortaccedilsu A Ariely D 2010 What makes youclick mdash mate preferences in online dating QuantitativeMarketing and Economics 8(4) 393ndash427

Irving RW Leather P Gusfield D 1987 An efficientalgorithm for the ldquooptimalrdquo stable marriage Journal ofthe ACM 34(3) 532ndash543

Korkmaz I 2008 An analytic hierarchy process and two-sided matching based decision support system formilitary personnel assignment Information Sciences 1782915ndash2927

Li X Murata T 2009 Priority based matchmaking method ofbuyers and suppliers in B2B e-marketplace using multi-objective optimization Proceedings of the InternationalMulti Conference of Engineers and Computer Scientists1 18ndash20

Pathak RS 2005 Matrimonial advertisements in India asociolinguistic profile South Asian Language Review 15(2)1ndash18

Saaty TL 1980 The Analytic Hierarchy Process PlanningPriority Setting Resource Allocation McGraw-HillNew York

Salo AA Hamalainen RP 1997 On the measurement ofpreferences in the AHP Journal of Multi-criteriaDecision Analysis 6 303ndash319

Sipahi S Timor M 2010 The analytic hierarchy process andanalytic network process an overview of applicationsManagement Decision 48(5) 775ndash808

Teo CP Sethuraman J Tan WP 2001 Gale-Shapley stablemarriage problem revisited strategic issues and applica-tions Management Science 47(9) 1252ndash1267

Thomaidis F Mavrakis D 2006 Optimum route of the southtranscontinental gas pipeline in SE Europe using AHPJournal of Multi-CriteriaDecision Analysis 14(1ndash3) 77ndash88

Triantaphyllou E 2001 Two new cases of rank reversalswhen the AHP and some of its additive variants are usedthat do not occur with the multiplicative AHP Journal ofMulti-Criteria Decision Analysis 10(1) 11ndash25

Vaidya OS Kumar S 2006 Analytic hierarchy process anoverview of applications European Journal of OperationalResearch 169(1) 1ndash29

Vaillant N 2004 Estimating the time elapsed betweenending a relationship and joining a matchmaking agencyevidence from a French marriage bureau Journal ofEconomic Psychology 25(6) 789ndash802

Vi N Fragniegravere E Gauthier J Sapin M Widmer ED 2010Optimizing the marriage market an application of thelinear assignment model European Journal of OperationalResearch 202(2) 547ndash553

K JOSHI AND S KUMAR66

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

hierarchy to calculate respective weight for each attri-bute (Tables IndashIV) In this case customer rates eachattribute with respect to other attribute at the samelevel and under the same group From the pairwisecomparisons we get relative weights of attributes asshown in Table V

In our example we consider 10 female memberrsquosdata with different attributes as shown in Table VIThere can be thousands of the profiles in the databaseof any website available Let us calculate profile scorefor profile no 2 This profile has attributes like 27years old 134 cm height complexion as whitishbrown qualification as chartered accountant (CA)belongs to Rich class annual income 22 lac livingin Metro Eating habit as Vegetarian and body typeis Athletic etc

For every profile according to fuzzily definedrequirements membership value can be calculatedComparing the membership values from respectivefuzzy sets and attributes of the profile we get variousmembership values as Education is CA and respectivesatisfaction level is 1 therefore Education=1 Likewiseremaining membership values are Occupation= 044Family status = 0 Earning=1 Location=07 Height =0 Age=06 Complexion=07 Diet = 1 and Bodytype=09

A profile score is calculated by multiplying thismembership value with respective weight fromTable V and aggregating for all attributes For exam-ple for education the weight is 0394

Profile score (A12) = 03945(1) + 00986(044) + 00113(0) + 00446(1) + 00811 (07) + 01513(0) + 00442(06) + 00536(07) + 00587(1) + 00621(09) = 07179

Thus the profile score is 07179 Similarlyprofile scores as per nomenclature describedearlier are as shown in Tables VII and VIII As men-tioned earlier in this mutual matching problem wemust consider what each woman is looking for Everywoman also has defined her requirements in termsof fuzzy sets and done pairwise comparisonThus profile score of this male customer who islooking for female partner can be calculated Tocalculate the compatibility score we use formuladefined in step 3

For example in case of pair male1 and female5ie A15 and B51

CI = 13 [(08372 + 05839) + (08372 + 05839)(2radic[(08372 05839)2 + 1])] = 06963

Thus CI based on male no1rsquos preference witheach female are listed in Table VIII Similarly forevery possible matching pair CI is calculated asrecorded in Table IX T

able

VI

Detailsof

femalemem

bers

No

Educatio

nOccupation

Fam

ilystatus

Earning

Location

Height

Age

Com

plexion

Diet

Bodytype

1BEBTech

Not

working

Upper

middleclass

0Urban

160

26Whitish

Eggitarian

Athletic

2Chartered

accountant

Businessm

anRichclass

22Metro

134

27Whitishbrow

nVegetarian

Athletic

3MCom

Banking

Middleclass

4Rural

137

24Fair

Eggitarian

Slim

4MEM

Tech

EngineeringRampD

Upper

middleclass

14Urban

139

27Fair

Eggitarian

Athletic

5MBAPGDM

LogisticsSCM

Richclass

16Urban

139

27Veryfair

Eggitarian

Heavy

6MCAPGDCA

Software

Middleclass

12Sem

iUrban

162

26Whitishbrow

nVegetarian

Slim

7MDM

S(M

edical)

Teaching

Middleclass

7Sem

iUrban

167

29Dark

Eggitarian

Athletic

8BAMS

Looking

forajob

Middleclass

0Rural

170

25Veryfair

Vegetarian

Slim

9MLLLM

Governm

entservices

Upper

middleclass

8Metro

144

27Whitish

Vegetarian

Athletic

10MBBSBDS

Governm

entservices

Richclass

8Metro

144

27Whitish

Vegetarian

Heavy

Bachelorrsquosof

Engineering

(BE)Masterrsquosof

EngineeringTechnology(M

EM

Tech)Chartered

Accountant(CA)Masterof

Com

merce

(MCom

)Masterof

BusinessAdm

inis-

tration(M

BA)PostG

raduateDiplomain

Managem

ent(PGDM)Masterof

Com

puterApplications

(MCA)PostGraduateDiplomain

Com

puterApplications

(PGDCA)Doctorof

Medicine(M

D)Masters

ofSurgery

(MS)Masterof

Law

(MLLLM)Bachelorof

Ayurveda

MedicineandSurgery

(BAMS)Bachelorof

DentalSurgery

(BDS)

Bachelorof

MedicineBachelorof

Surgery

(MBBS)ResearchandDevelopment(R

ampD)SupplyChain

Managem

ent(SCM)Governm

ent(G

ovt)

K JOSHI AND S KUMAR64

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Based on compatibility scores profiles getshortlisted and ranked in descending order Fur-thermore the customer has liberty to re-rank theprofiles after looking at each of the top 10 profilesSubsequently if the customer re-ranks the profiles thepreferences are taken as input for Gale-Shapleyalgorithm Otherwise profiles ranked based on CI aretreated with respect to their rank To demonstrateGale-Shapley algorithm in this context we assume thatthere are five male and five female profiles with theirpreferences as mentioned in the following table

M1=gtF1-F3-F2-F4-F5 F1 =gtM5-M2-M4-M3-M1M2=gtF2-F1-F3-F5-F4 F2 =gtM2-M4-M5-M1-M3M3=gtF2-F4-F5-F1-F3 F3 =gtM3-M1-M4-M5-M2M4=gtF3-F1-F4-F5-F2 F4 =gtM1-M3-M2-M4-M5M5=gtF5-F2-F4-F3-F1 F5 =gtM2-M1-M3-M5-M4

Gale-Shapley algorithm generates the followingmatches

Male1 is paired with female5 male2 is paired withfemale3 male3 is paired with female4 male4 is pairedwith female2 and male5 is paired with female1

This is an add-on facility for a customer where heor she will receive a suggested stable matched profileIf they contact this suggested profile as well as a few

profiles listed based on their CI then the probabilityof getting positive response increases

5 CONCLUSIONS

In todayrsquos Internet era services seeking efficiency isof paramount importance The approach presented inthis paper attempts to exploit current IT-enabledpartner search for marriage through Web portals

Salient features of this proposed method are asfollows

bull Integrated way to quantify the online profiles withimplicit needs

bull Two-phase short listing ie FAHP and stablematching algorithm

bull Reducing customerrsquos effort to find their mateonline according to their implicit needs (definedfuzzily)

bull Enhancing the probability of getting positiveresponse and matchmaking

A sorting based on CI in descending orderenhances the probability of matchmaking It thus leadsto reduction in lead time of waiting of the positive ornegative reply from the opposite party This opera-tional viewpoint has been presented in this paper with

Table IX Ranking based on compatibility index

A16 A17 A19 A11 A14 A18 A12 A15 A13 A110

Score 09684 08954 07958 08756 08974 08009 07179 08372 04858 08317B61 B71 B91 B11 B41 B81 B21 B51 B31 B101

Score 08517 08692 09306 08142 06982 07576 07743 05839 08824 05079CI 09059 08821 08580 08438 07876 07787 07453 06963 06531 06486Rank 1 2 3 4 5 6 7 8 9 10

CI compatibility index

Table VII Profile scores when female rated by male no 1

A11 A12 A13 A14 A15 A16 A17 A18 A19 A110

Score 08756 07179 04858 08974 08372 09684 08954 08009 07958 08317

Table VIII Profile scores of male no 1 rated by each female

B11 B21 B31 B41 B51 B61 B71 B81 B91 B101

Score 08142 07743 08824 06982 05839 08517 08692 07576 09306 05079

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 65

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

introduction of a CI This index helps user to maxi-mize their requirements while mutual matching

Future studies might cover an enhancement inrating parameters Few Web portals have incorporatedmatchmaking based on personality behaviour Morequalitative and quantitative factors can be includedwith involvement of ratings by parents and relativesSuch study will lead to multi-criteria group decision-making kind of problem

REFERENCES

Abraham DJ 2003 Algorithmics of two-sided matchingproblems Masterrsquos thesis University of GlasgowDepartment of Computing Science Accessed September2010

Adachi H 2003 A search model of two-sided matchingunder nontransferable utility Journal of Economic Theory113(2) 182ndash198

Banerjee Abhijit V Duflo Esther Ghatak MaitreeshLafortune J 20009 Marry for What Caste and MateSelection in Modern India NBER Working Paper Seriesw14958 Available at SSRN httpssrncomabstract=1405966 accessed July 2010

Batabyal A DeAngelo G 2008 To match or not to matchaspects of marital matchmaking under uncertainty Opera-tions Research Letters 36(1) 94ndash98

Belot M Francesconi M 2010 Meeting opportunities and part-ner selection a field study 1ndash40 Available at httpwwwtauacil~weissfam_econRESTAT-13763-1-manuscriptpdf(accessed on 18 December 2010)

Celik O Knoblauch V 2007 Marriage matching withcorrelated preferences Working Paper 1ndash10 Universityof Connecticut

Chang S Wang R Wang S 2006 Applying fuzzy linguisticquantifier to select supply chain partners at differentphases of product life cycle International Journal ofProduction Economics 100 348ndash359

Dugar S Bhattacharya H Reiley DH 2010 Canrsquot buy melove a field experiment exploring the trade-off betweenincome and caste status in an Indian matrimonial marketAvailable at SSRN httpssrncomabstract=1288987Accessed July 2010

Gale D Shapley LS 1962 College admissions and the stabilityof marriage American Mathematical Monthly 69(1) 9ndash15

Gordon J Gupta P 2003 Understanding Indiarsquos servicesevolution httpimforgexternalnpapdseminars2003newdelhigordonpdf Accessed August 2010

Hajeeh M Lairi S 2009 Marriage partner selection inKuwait an analytical hierarchy process approach Journalof Mathematical Sociology 33 222ndash240

Hitsch GJ Hortaccedilsu A Ariely D 2010 What makes youclick mdash mate preferences in online dating QuantitativeMarketing and Economics 8(4) 393ndash427

Irving RW Leather P Gusfield D 1987 An efficientalgorithm for the ldquooptimalrdquo stable marriage Journal ofthe ACM 34(3) 532ndash543

Korkmaz I 2008 An analytic hierarchy process and two-sided matching based decision support system formilitary personnel assignment Information Sciences 1782915ndash2927

Li X Murata T 2009 Priority based matchmaking method ofbuyers and suppliers in B2B e-marketplace using multi-objective optimization Proceedings of the InternationalMulti Conference of Engineers and Computer Scientists1 18ndash20

Pathak RS 2005 Matrimonial advertisements in India asociolinguistic profile South Asian Language Review 15(2)1ndash18

Saaty TL 1980 The Analytic Hierarchy Process PlanningPriority Setting Resource Allocation McGraw-HillNew York

Salo AA Hamalainen RP 1997 On the measurement ofpreferences in the AHP Journal of Multi-criteriaDecision Analysis 6 303ndash319

Sipahi S Timor M 2010 The analytic hierarchy process andanalytic network process an overview of applicationsManagement Decision 48(5) 775ndash808

Teo CP Sethuraman J Tan WP 2001 Gale-Shapley stablemarriage problem revisited strategic issues and applica-tions Management Science 47(9) 1252ndash1267

Thomaidis F Mavrakis D 2006 Optimum route of the southtranscontinental gas pipeline in SE Europe using AHPJournal of Multi-CriteriaDecision Analysis 14(1ndash3) 77ndash88

Triantaphyllou E 2001 Two new cases of rank reversalswhen the AHP and some of its additive variants are usedthat do not occur with the multiplicative AHP Journal ofMulti-Criteria Decision Analysis 10(1) 11ndash25

Vaidya OS Kumar S 2006 Analytic hierarchy process anoverview of applications European Journal of OperationalResearch 169(1) 1ndash29

Vaillant N 2004 Estimating the time elapsed betweenending a relationship and joining a matchmaking agencyevidence from a French marriage bureau Journal ofEconomic Psychology 25(6) 789ndash802

Vi N Fragniegravere E Gauthier J Sapin M Widmer ED 2010Optimizing the marriage market an application of thelinear assignment model European Journal of OperationalResearch 202(2) 547ndash553

K JOSHI AND S KUMAR66

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

Based on compatibility scores profiles getshortlisted and ranked in descending order Fur-thermore the customer has liberty to re-rank theprofiles after looking at each of the top 10 profilesSubsequently if the customer re-ranks the profiles thepreferences are taken as input for Gale-Shapleyalgorithm Otherwise profiles ranked based on CI aretreated with respect to their rank To demonstrateGale-Shapley algorithm in this context we assume thatthere are five male and five female profiles with theirpreferences as mentioned in the following table

M1=gtF1-F3-F2-F4-F5 F1 =gtM5-M2-M4-M3-M1M2=gtF2-F1-F3-F5-F4 F2 =gtM2-M4-M5-M1-M3M3=gtF2-F4-F5-F1-F3 F3 =gtM3-M1-M4-M5-M2M4=gtF3-F1-F4-F5-F2 F4 =gtM1-M3-M2-M4-M5M5=gtF5-F2-F4-F3-F1 F5 =gtM2-M1-M3-M5-M4

Gale-Shapley algorithm generates the followingmatches

Male1 is paired with female5 male2 is paired withfemale3 male3 is paired with female4 male4 is pairedwith female2 and male5 is paired with female1

This is an add-on facility for a customer where heor she will receive a suggested stable matched profileIf they contact this suggested profile as well as a few

profiles listed based on their CI then the probabilityof getting positive response increases

5 CONCLUSIONS

In todayrsquos Internet era services seeking efficiency isof paramount importance The approach presented inthis paper attempts to exploit current IT-enabledpartner search for marriage through Web portals

Salient features of this proposed method are asfollows

bull Integrated way to quantify the online profiles withimplicit needs

bull Two-phase short listing ie FAHP and stablematching algorithm

bull Reducing customerrsquos effort to find their mateonline according to their implicit needs (definedfuzzily)

bull Enhancing the probability of getting positiveresponse and matchmaking

A sorting based on CI in descending orderenhances the probability of matchmaking It thus leadsto reduction in lead time of waiting of the positive ornegative reply from the opposite party This opera-tional viewpoint has been presented in this paper with

Table IX Ranking based on compatibility index

A16 A17 A19 A11 A14 A18 A12 A15 A13 A110

Score 09684 08954 07958 08756 08974 08009 07179 08372 04858 08317B61 B71 B91 B11 B41 B81 B21 B51 B31 B101

Score 08517 08692 09306 08142 06982 07576 07743 05839 08824 05079CI 09059 08821 08580 08438 07876 07787 07453 06963 06531 06486Rank 1 2 3 4 5 6 7 8 9 10

CI compatibility index

Table VII Profile scores when female rated by male no 1

A11 A12 A13 A14 A15 A16 A17 A18 A19 A110

Score 08756 07179 04858 08974 08372 09684 08954 08009 07958 08317

Table VIII Profile scores of male no 1 rated by each female

B11 B21 B31 B41 B51 B61 B71 B81 B91 B101

Score 08142 07743 08824 06982 05839 08517 08692 07576 09306 05079

MATCHMAKING USING FAHP COMPATIBILITY MEASURE amp STABLE MATCHING 65

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

introduction of a CI This index helps user to maxi-mize their requirements while mutual matching

Future studies might cover an enhancement inrating parameters Few Web portals have incorporatedmatchmaking based on personality behaviour Morequalitative and quantitative factors can be includedwith involvement of ratings by parents and relativesSuch study will lead to multi-criteria group decision-making kind of problem

REFERENCES

Abraham DJ 2003 Algorithmics of two-sided matchingproblems Masterrsquos thesis University of GlasgowDepartment of Computing Science Accessed September2010

Adachi H 2003 A search model of two-sided matchingunder nontransferable utility Journal of Economic Theory113(2) 182ndash198

Banerjee Abhijit V Duflo Esther Ghatak MaitreeshLafortune J 20009 Marry for What Caste and MateSelection in Modern India NBER Working Paper Seriesw14958 Available at SSRN httpssrncomabstract=1405966 accessed July 2010

Batabyal A DeAngelo G 2008 To match or not to matchaspects of marital matchmaking under uncertainty Opera-tions Research Letters 36(1) 94ndash98

Belot M Francesconi M 2010 Meeting opportunities and part-ner selection a field study 1ndash40 Available at httpwwwtauacil~weissfam_econRESTAT-13763-1-manuscriptpdf(accessed on 18 December 2010)

Celik O Knoblauch V 2007 Marriage matching withcorrelated preferences Working Paper 1ndash10 Universityof Connecticut

Chang S Wang R Wang S 2006 Applying fuzzy linguisticquantifier to select supply chain partners at differentphases of product life cycle International Journal ofProduction Economics 100 348ndash359

Dugar S Bhattacharya H Reiley DH 2010 Canrsquot buy melove a field experiment exploring the trade-off betweenincome and caste status in an Indian matrimonial marketAvailable at SSRN httpssrncomabstract=1288987Accessed July 2010

Gale D Shapley LS 1962 College admissions and the stabilityof marriage American Mathematical Monthly 69(1) 9ndash15

Gordon J Gupta P 2003 Understanding Indiarsquos servicesevolution httpimforgexternalnpapdseminars2003newdelhigordonpdf Accessed August 2010

Hajeeh M Lairi S 2009 Marriage partner selection inKuwait an analytical hierarchy process approach Journalof Mathematical Sociology 33 222ndash240

Hitsch GJ Hortaccedilsu A Ariely D 2010 What makes youclick mdash mate preferences in online dating QuantitativeMarketing and Economics 8(4) 393ndash427

Irving RW Leather P Gusfield D 1987 An efficientalgorithm for the ldquooptimalrdquo stable marriage Journal ofthe ACM 34(3) 532ndash543

Korkmaz I 2008 An analytic hierarchy process and two-sided matching based decision support system formilitary personnel assignment Information Sciences 1782915ndash2927

Li X Murata T 2009 Priority based matchmaking method ofbuyers and suppliers in B2B e-marketplace using multi-objective optimization Proceedings of the InternationalMulti Conference of Engineers and Computer Scientists1 18ndash20

Pathak RS 2005 Matrimonial advertisements in India asociolinguistic profile South Asian Language Review 15(2)1ndash18

Saaty TL 1980 The Analytic Hierarchy Process PlanningPriority Setting Resource Allocation McGraw-HillNew York

Salo AA Hamalainen RP 1997 On the measurement ofpreferences in the AHP Journal of Multi-criteriaDecision Analysis 6 303ndash319

Sipahi S Timor M 2010 The analytic hierarchy process andanalytic network process an overview of applicationsManagement Decision 48(5) 775ndash808

Teo CP Sethuraman J Tan WP 2001 Gale-Shapley stablemarriage problem revisited strategic issues and applica-tions Management Science 47(9) 1252ndash1267

Thomaidis F Mavrakis D 2006 Optimum route of the southtranscontinental gas pipeline in SE Europe using AHPJournal of Multi-CriteriaDecision Analysis 14(1ndash3) 77ndash88

Triantaphyllou E 2001 Two new cases of rank reversalswhen the AHP and some of its additive variants are usedthat do not occur with the multiplicative AHP Journal ofMulti-Criteria Decision Analysis 10(1) 11ndash25

Vaidya OS Kumar S 2006 Analytic hierarchy process anoverview of applications European Journal of OperationalResearch 169(1) 1ndash29

Vaillant N 2004 Estimating the time elapsed betweenending a relationship and joining a matchmaking agencyevidence from a French marriage bureau Journal ofEconomic Psychology 25(6) 789ndash802

Vi N Fragniegravere E Gauthier J Sapin M Widmer ED 2010Optimizing the marriage market an application of thelinear assignment model European Journal of OperationalResearch 202(2) 547ndash553

K JOSHI AND S KUMAR66

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda

introduction of a CI This index helps user to maxi-mize their requirements while mutual matching

Future studies might cover an enhancement inrating parameters Few Web portals have incorporatedmatchmaking based on personality behaviour Morequalitative and quantitative factors can be includedwith involvement of ratings by parents and relativesSuch study will lead to multi-criteria group decision-making kind of problem

REFERENCES

Abraham DJ 2003 Algorithmics of two-sided matchingproblems Masterrsquos thesis University of GlasgowDepartment of Computing Science Accessed September2010

Adachi H 2003 A search model of two-sided matchingunder nontransferable utility Journal of Economic Theory113(2) 182ndash198

Banerjee Abhijit V Duflo Esther Ghatak MaitreeshLafortune J 20009 Marry for What Caste and MateSelection in Modern India NBER Working Paper Seriesw14958 Available at SSRN httpssrncomabstract=1405966 accessed July 2010

Batabyal A DeAngelo G 2008 To match or not to matchaspects of marital matchmaking under uncertainty Opera-tions Research Letters 36(1) 94ndash98

Belot M Francesconi M 2010 Meeting opportunities and part-ner selection a field study 1ndash40 Available at httpwwwtauacil~weissfam_econRESTAT-13763-1-manuscriptpdf(accessed on 18 December 2010)

Celik O Knoblauch V 2007 Marriage matching withcorrelated preferences Working Paper 1ndash10 Universityof Connecticut

Chang S Wang R Wang S 2006 Applying fuzzy linguisticquantifier to select supply chain partners at differentphases of product life cycle International Journal ofProduction Economics 100 348ndash359

Dugar S Bhattacharya H Reiley DH 2010 Canrsquot buy melove a field experiment exploring the trade-off betweenincome and caste status in an Indian matrimonial marketAvailable at SSRN httpssrncomabstract=1288987Accessed July 2010

Gale D Shapley LS 1962 College admissions and the stabilityof marriage American Mathematical Monthly 69(1) 9ndash15

Gordon J Gupta P 2003 Understanding Indiarsquos servicesevolution httpimforgexternalnpapdseminars2003newdelhigordonpdf Accessed August 2010

Hajeeh M Lairi S 2009 Marriage partner selection inKuwait an analytical hierarchy process approach Journalof Mathematical Sociology 33 222ndash240

Hitsch GJ Hortaccedilsu A Ariely D 2010 What makes youclick mdash mate preferences in online dating QuantitativeMarketing and Economics 8(4) 393ndash427

Irving RW Leather P Gusfield D 1987 An efficientalgorithm for the ldquooptimalrdquo stable marriage Journal ofthe ACM 34(3) 532ndash543

Korkmaz I 2008 An analytic hierarchy process and two-sided matching based decision support system formilitary personnel assignment Information Sciences 1782915ndash2927

Li X Murata T 2009 Priority based matchmaking method ofbuyers and suppliers in B2B e-marketplace using multi-objective optimization Proceedings of the InternationalMulti Conference of Engineers and Computer Scientists1 18ndash20

Pathak RS 2005 Matrimonial advertisements in India asociolinguistic profile South Asian Language Review 15(2)1ndash18

Saaty TL 1980 The Analytic Hierarchy Process PlanningPriority Setting Resource Allocation McGraw-HillNew York

Salo AA Hamalainen RP 1997 On the measurement ofpreferences in the AHP Journal of Multi-criteriaDecision Analysis 6 303ndash319

Sipahi S Timor M 2010 The analytic hierarchy process andanalytic network process an overview of applicationsManagement Decision 48(5) 775ndash808

Teo CP Sethuraman J Tan WP 2001 Gale-Shapley stablemarriage problem revisited strategic issues and applica-tions Management Science 47(9) 1252ndash1267

Thomaidis F Mavrakis D 2006 Optimum route of the southtranscontinental gas pipeline in SE Europe using AHPJournal of Multi-CriteriaDecision Analysis 14(1ndash3) 77ndash88

Triantaphyllou E 2001 Two new cases of rank reversalswhen the AHP and some of its additive variants are usedthat do not occur with the multiplicative AHP Journal ofMulti-Criteria Decision Analysis 10(1) 11ndash25

Vaidya OS Kumar S 2006 Analytic hierarchy process anoverview of applications European Journal of OperationalResearch 169(1) 1ndash29

Vaillant N 2004 Estimating the time elapsed betweenending a relationship and joining a matchmaking agencyevidence from a French marriage bureau Journal ofEconomic Psychology 25(6) 789ndash802

Vi N Fragniegravere E Gauthier J Sapin M Widmer ED 2010Optimizing the marriage market an application of thelinear assignment model European Journal of OperationalResearch 202(2) 547ndash553

K JOSHI AND S KUMAR66

Copyright copy 2012 John Wiley amp Sons Ltd J Multi-Crit Decis Anal 19 57ndash66 (2012)DOI 101002mcda