Analytical Study of AHP and Fuzzy AHP Techniques

7/30/2019 Analytical Study of AHP and Fuzzy AHP Techniques

1/4

Analytical Study of AHP and Fuzzy AHP Techniques

Amit Mishra, and Sanjay Kumar Dubey

Abs tract Decision making is a comprehensive approach that involves selecting from several wide-ranging alternatives.Different analysis tools can be used in order to make decisions and solve problems in situations involving quantitative variablesand small number of criteria. However, many times beside the measurable variables, there exist qualitative variables, or peopleare supposed to prefer the best among the many choices, thus, an analytical way to make a successful decision is needed.Analytical Hierarchy Process (AHP ) is one of the best ways for deciding among the complex criteria structure in different levels.Fuzzy AHP is a synthetic extension of classical AHP method when the fuzziness of the decision makers is considered. The mainaim of this paper is to provide a detailed analytical comparison of classical AHP and fuzzy AHP.

Index Terms AHP, FAHP, MCDM, FMADM

u

1 INTRODUCTIONE all make decisions all the time consciously andunconsciously. The information we gather is tohelp us understand occurrences, in order to devel-

op good judgments to make decisions about these occur-rences. Human lives are the sum of their decisions-whether in business or in personal spheres. In daily lives,people often have to make decisions . When decision ismade is important as what decided. Deciding tooquickly can be hazardous; delaying too long can meanmissed opportunities. In the end, it is crucial that peoplemake up their mind. To make a decision we need to knowthe problem, the need and purpose of the decision, thecriteria of the decision, their sub criteria, stakeholders andgroups affected and the alternative actions to take. Wethen try to determine the best alternative, or in the case ofresource allocation, we need priorities for the alternativesto allocate their appropriate share of the resources. Whatpeople need is a systematic and comprehensive approachto decision making [15]. In such cases, Multi Criteria De-cision Making (MCDM) is required.MCDM is one of the most important fields of operationsresearch and deals with the problems that involve multi-ple and conflicting objectives. It is obvious that when

more than objective exists in the problem, making a deci-sion becomes more complex. MCDM is both an approachand a set of techniques, with the aim of providing anoverall ordering of options, from the most preferred tothe least preferred option (The London School of Econom-ics and Political Science, 2007). MCDM approaches pro-vide a systematic procedure to help decision makerschoose the most desirable and satisfactory alternative

under uncertain situation Y.K. Cheng [17].Analytic Hierarchy Process (AHP) is widely used for mul-ti-criteria decision making and has successfully been ap-plied to many practical decision-making problems. AHP,was proposed by T. L. Saaty [14], is a method for compli-cated and unstructured problems and also it is an ap-proach that uses a hierarchical model having levels ofgoal, criteria, possible sub-criteria, and alternatives. TheAHP, can be stated, a decision making and estimationmethod which gives the percentage distribution of deci-sion points according to factors affecting decision, that isused if there is a defined decision hierarchy. With AHP,the decision maker selects the alternative that best meetshis or her decision criteria developing a numerical scoreto rank each decision alternative based on how well eachalternative meets them. In spite of its popularity, thismethod is often criticized for its inability to adequatelyhandle the inherent uncertainty and imprecision associat-ed with the mapping of the decision makers perceptionto exact numbers.In the traditional formulation of the AHP, humans judg-ments are represented as exact (or crisp , according to thefuzzy logic terminology) numbers. However, in many

practical cases the human preference model is uncertainand decision-makers might be reluctant or unable to as-sign exact numerical values to the comparison judgments.For instance, when evaluating different services, the deci-sion-makers are usually unsure in their level of preferencedue to incomplete and uncertain information about pos-sible service providers and their performance. Since someof the service evaluation criteria are subjective and quali-tative, it is very difficult for the decision-maker to expressthe strength of his preferences and to provide exact pairwise comparison judgments. A natural way to cope withsuch uncertain judgments is to express the comparison

ratios as fuzzy sets or fuzzy numbers, which incorporatethe vagueness of the human thinking.

W

Amit Mishra is with Amity University Uttar Pradesh, NOIDA,India,201303.

Sanjay Kumar Dubey is with Amity University Uttar Pradesh, NOIDA,India,201303.

JOURNAL OF COMPUTING, VOLUME 5, ISSUE 3, MARCH 2013, ISSN (Online) 2151-9617https://sites.google.com/site/journalofcomputingWWW.JOURNALOFCOMPUTING.ORG 30


2/4

Hence fuzzy AHP came into existence. In fuzzy AHP,fuzzy theory is combined with AHP to analyze ambigu-ous real world problems. The fuzzy analytic hierarchyprocess (FAHP)-based decision-making method is effec-tive for constructing an evaluation method, which canassist software developers, users and procurers in evalu-ating software quality to identify the most appropriatequalities, or factors in software system development. Itcan also help software researchers and consumers assesssoftware quality, making it highly applicable for academicand commercial purposes. Fuzzy multiple attribute deci-sion-making (FMADM) methods have been developed toaddress the imprecision in assessing the relative im-portance of attributes and the performance ratings of al-ternatives with respect to attributes. Fuzzy applicationareas include estimation, prediction, control, approximatereasoning, intelligent system design, machine learning,image processing, machine vision, pattern recognition,medical computing, robotics, optimization, civil, chemicaland industrial engineering. Fuzzy techniques for treatinguncertain qualitative information include fuzzy set theo-ry, fuzzy arithmetic and mathematics, fuzzy logic, fuzzydecision making and fuzzy control. In general fuzzy pro-cedures transform through uncertain basic rules that re-flect the behavior of the system concerned and conse-quently the uncertain or crisp information as initial and

boundary conditions as well as the input variables aremapped so as to produce again uncertain or crisp results.Another elegance of the fuzzy set theory is that duringthe assimilation of input data it does not require any spec-ification concerning the data structure.

2 LITERATURE SURVEY

The Analytic Hierarchy Process (AHP) is an approachthat is suitable for dealing with complex systems relatedto making a choice from among several alternatives andwhich provides a comparison of the considered options.This method was first presented by T. L. Saaty [14]. TheAHP process has been successfully applied in diverseproblems E. W. T. Ngai [4]; S. S. Kima et al. [13]; W.Ossadnik, & O. Lange [16]; L. Zhu et al.[8]. But its inabil-ity to deal with uncertainties encountered in most of thereal world problems gave rise to fuzzy AHP.Fuzzy AHP allows decision makers to present their refer-ences within a reasonable interval if they are not sureabout them. Many FAHP methods were proposed basedon the concepts of the fuzzy set theory and hierarchicalstructure analysis. Some researchers have studied theFAHP which is the extension of the theory proposed by T.L. Saaty [14] and also have proved that the FAHP is moreeffective in these kinds of decision-making processescompared to traditional AHP. To deal with vagueness ofhuman thought, L. Zadeh [7] first introduced the fuzzyset theory, which was oriented to the rationality of uncer-tainty due to imprecision or vagueness. Van Laarhovenand W. Pedrycz [10] directly extended the AHP methodwith triangular fuzzy numbers (TFNs).

TABLE 1DIFFERENCES BETWEEN TRADITIONAL AHP AND FUZZY

AHP METHODS

Traditional AHP Fuzzy AHP

It is used in cases wherethe informationevaluations are certain.

If the informationevaluations are notcertain, fuzzy method ispreferred.

It is a robust way tosolve determineddecision makingproblem. However, itneglects the uncertaintyand vagueness caused bysubjective preference ofdecision maker in criteriascoring.

It can reduce or eveneliminate the fuzzinessand vagueness existingin many decision makingproblems.

It only offersdeterministic valueoptions, hence inflexibleapproach.

It can provide thedecision makers withflexible value optionswhich are in-between acertain range, thusmaking it more suitableto solve real worldproblems (fuzzyproblems).

It provides a lesscomprehensive rankingof the requirements for aproject.

It provides a morecomprehensive rankingof the requirements for aproject as compared toAHP.

The judgment matrix inAHP uses constant pairwise comparison value.

It has a judgment matrixthat uses triangular ortrapezoidal fuzzynumber.

It is used to solveproblems that involvemultiple decision makersalong with multiplecriteria decision making.

This approach is appliedto solve problems thatinvolve a single decisionmaker along withmultiple criteria decisionmaking.



3/4

D. Y. Chang [3] introduced a new approach of using TFNsfor pair wise comparison and also supplied the key pointof extent analysis method for deriving the synthetic ex-tent values. This approach is one of the most popular ap-proaches in the FAHP field. L. Mikhailov [6] provided agood discussion of the troubles with constructing fuzzyreciprocal matrices using fuzzy comparisons and theirreciprocals through the same fashion as the crisp prioriti-zation procedures. Kahraman [1] implemented Changsmethod to measure the customer satisfaction in cateringfirms in Turkey. C. Metin [2] proposed a practical deci-sion support mechanism on ensuring multiple criteriaanalysis of shipping registry selection using FAHP.As a powerful analytical procedure, FAHP is usuallycombined with other methods in applications. RJ Kuo [12]integrated FAHP and artificial neural network for the lo-cation selecting of convenience store. R. Rostamzadeh, S.Sofian [11] presented a hierarchy multiple criteria deci-sion-making model using FAHP and TOPSIS for prioritiz-ing effective 7Ms (Management, Manpower, Marketing,Method, Machine, Material and Money) to improve pro-duction systems performance. H Jung [5] proposed aFAHP goal programming approach for integrated pro-duction-planning problem considering manufacturingpartners at the background of a TFT-LCD manufacturingfirm. Lin Wang [9] proposed a valuable approach basedon FAHP and BSC for evaluating the performance of TPLenterprises. Furthermore, many fuzzy AHP methods de-veloped by various authors can be found in literature.

3 CONCLUSIONDecision making involves setting priorities and the AHPis the methodology for doing that. Decision making prob-lem is one of most common problems in almost everyfield. AHP approach is an effective and popular way todeal with this problem. It deals with crisp (real) values ofevaluation judgments. But human reasoning is imprecise,uncertain and fuzzy and the real world is highly ambigu-ous. Hence, AHP is ineffective when applied to resolvethe inherent uncertainty and imprecision associated withthe mapping of a decision makers perception to exactnumbers. Thus fuzzy theory has been combined withAHP to analyze ambiguous real world problems. Thispaper works on the differences between classical AHPand fuzzy AHP approaches, with the purpose of deter-mining the importance of fuzzy AHP over traditionalAHP.

REFERENCES[1] C. Kahraman, U. Cebeci, D. Ruan (2004).Multi-attribute com-

parison of catering service companies using fuzzy AHP: thecase of Turkey. Int. J. Prod. Econ., 87(2):171-184.

[2] C. Metin, Er ID, AF Ozok (2009). Application of fuzzy extended

AHP methodology on shipping registry selection: The case ofTurkish maritime industry. Expert Syst. Appl., 36(1):190-198.[3] D. Y. Chang, (1996), Applications of the Extent Analysis Meth-

od on Fuzzy AHP, European Journal of Operational Research,95, 649-655.

TABLE 2LITERATURE REVIEW

Author Year DescriptionZadeh 1965 Fuzzy set theory which was orient-

ed to the rationality of uncertaintydue to imprecision or vagueness ofhuman thought was proposed.

VanLaarhovenand Pedrycz

1983 AHP method was directly extend-ed with triangular fuzzy numbers(TFNs) and a fuzzy logarithmicleast squares method (LLSM) toobtain triangular fuzzy weightsfrom a triangular fuzzy compari-son matrix was suggested.

Chang 1996 A new method with the use of tri-angular fuzzy numbers and extentanalysis method for the pair wisecomparison scale of AHP and thesynthetic extent values of the pairwise comparisons was proposed.

Kuo et al. 2002 An algorithm that integrated fuzzyAHP and artificial neural networkfor determining the location of astore was proposed.

Mikhailov 2003 Fuzzy prioritization method fortackling the uncertainty and im-precision of the reasoning processwhile using decision support toolsduring pre-negotiations was pre-sented.

Kahramanet al.

2004 Implementation of Changs method(1996) to measure the customersatisfaction in Turkish cateringfirms.

Metin et al. 2009 Fuzzy AHP methodology used tomodel multiple criteria analysis ofshipping registry selection.

Rostamzade

h and Sofian

2011 A fuzzy decision-making approach

for prioritizing organization andproduction system inputs knownas the effective 7Ms to improveproduction systems performancewas presented.

Jung 2011 A fuzzy AHP goal programmingapproach for integrated produc-tion-planning problem was pro-posed.

Lin Wanget al.

2012 An approach based on fuzzy AHPand balanced scorecard (BSC) for

evaluating a Chinese TPL enter-prise was constructed.



4/4

[4] E. W. T. Ngai (2003). Selection of web sits for online advertisingusing the AHP. Information and Management, 46, 669678.

[5] H Jung (2011). A fuzzy AHP-GP approach for integratedproductionplanning considering manufacturing partners. Ex-pert Syst. Appl., 38(5): 5833-5840.

[6] L. Mikhailov,(2003) A fuzzy approach to deriving prioritiesfrom interval pairwise comparison judgments. European Jour-nal of Operational Research. v159. 687-704.

[7] L. Zadeh (1965). Fuzzy sets. Information Control, 8, 338353[8] L. Zhu, A. Aurum, I. Gorton, & R. (2005). Tradeoff and sensitiv-

ity analysis in software architecture evaluation using analytichierarchy process. Software Quality Journal, 13(4), 357375.

[9] Lin Wang, Hao Zhang and Yu-Rong Zeng (2012), Fuzzy analyt-ic hierarchy process (FAHP) and balanced scorecard approachfor evaluating performance of Third-Party Logistics (TPL) en-terprises in Chinese context, African Journal of Business Man-agement Vol.6(2), pp. 521-529,18 January, 2012

[10] P. Van Laarhoven, & W. Pedrycz (1983). A fuzzy extension ofSaaty's priority theory, Fuzzy Sets and Systems, 11, 199-227

[11] R. Rostamzadeh, S. Sofian (2011). Prioritizing effective 7Ms toimprove production systems performance using fuzzy AHPand fuzzy TOPSIS (case study). Expert Syst. Appl., 38(5):5166-5177.

[12] RJ Kuo, SC Chi, SS Kao (2002).A decision support system forselecting convenience store location through integration offuzzy AHP and artificial neural network. Comput. Ind.,47(2):199-214.

[13] S. S. Kima, I. O. Yang, M. S. Yeo, & K. W. Kim (2005). Develop-ment of a housing performance evaluation model for multi-family residential buildings in Korea. Building and Environ-ment, 40, 11031116.

[14] T. L. Saaty (1980). The analytic hierarchy process. New York:

McGraw Hill[15] T. L. Saaty (2001). Decision Making with Dependence and

Feedback: The Analytic Network Process (Second ed.), RWSPublications, Pittsburgh, USA

[16] W. Ossadnik, & O. Lange (1999). AHP-based evaluation ofAHP-Software. European Journal of Operational Research,118(2), 578588.

[17] Y.K. Cheng, (2000), Development of a Fuzzy Multi-CriteriaDecision Support System for Municipal Solid Waste Manage-ment, Regina, Saskatchewan.

Ami t Mishra is pursuing M. Tech (CSE) from Amity University UttarPradesh NOIDA, India. His interest area is Soft Computing andSoftware Engineering.

Sanjay Kumar Dubey is Assistant Professor and Proctor in AmityUniversity University Uttar Pradesh NOIDA, India. He has more than12 years of teaching experience in reputed engineering colleges anduniversities. He has published more than seventies research papersin national and international journals. He is member of IET and ACM.His interest area is Soft Computing and Usability Engineering.


Documents

Analytical Study of AHP and Fuzzy AHP Techniques