A decision support tool for the valuation of variations on ...RICS Research RICS Research paper series Volume 5, Number 7 May 2005 Monty Sutrisna, Kevan Buckley, Keith Potts and David

RICSResearch

RICS Research paper series

Volume 5, Number 7

May 2005

Monty Sutrisna, Kevan Buckley,

Keith Potts and David Proverbs

University of Wolverhampton

A decision support tool for the valuation ofvariations on civil engineering projects

2 � RICS Research

MMoonnttyy SSuuttrriissnnaa was a PhD student inthe Research Institute in AdvancedTechnologies, University ofWolverhampton. This paper, alongwith many other papers producedduring his studentship, aims todisseminate the findings of his PhDresearch into the valuation ofvariations in construction projects.His PhD research project involvedkey staff members of the Universityof Wolverhampton, including KeithPotts (School of Engineering and theBuilt Environment), Kevan Buckley(School of Computing andInformation Technology) and DavidProverbs (Research Institute inAdvanced Technologies.

Monty Sutrisna has recentlycompleted his PhD and is currentlyworking as a post-doctoral researcherin the Research Institute for the Builtand Human Environment at theUniversity of Salford. His researchinterests encompass generalconstruction procuremrent, thebriefing and design process,negotiation and decision-making inconstruction and the generalapplication of informationtechnology in construction.

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A decision supporttool for the valuationof variations on civilengineering projects

Monty Sutrisna, Keith Potts, David Proverbs andKevan BuckleyUniversity of Wolverhampton

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Professor Les RuddockSchool of Construction andProperty ManagementUniversity of SalfordSalfordLancs M7 1NUUnited Kimgdom

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Akintole AkintoyeGlasgow Caledonian UniversityScotland

Ghassan AouadUniversity of SalfordEngland

David BaldryUniversity of SalfordEngland

Malcolm BellLeeds Metropolitan UniversityEngland

Alistair BlythUniversity of WestminsterEngland

Thomas BohnUniversity of LeipzigGermany

Paul BowenUniversity of Cape Town South Africa

Terry BoydQueensland University ofTechnologyAustralia

David ChapmanUniversity College LondonEngland

Charles CowapHarper Adams University CollegeEngland

Hoffie CruywagenUniversity of Pretoria South Africa

Christopher FortuneHeriot-Watt UniversityScotland

Andy HamiltonUniversity of SalfordEngland

Barbara HawardUniversity of PortsmouthEngland

Michael HoxleyAnglia Polytechnic UniversityEngland

Will HughesUniversity of ReadingEngland

Eddie HuiHong Kong PolytechnicUniversityHong Kong

Norman HutchisonUniversity of Aberdeen Scotland

Ramin KeivaniOxford Brookes UniversityEngland

Richard LaingRobert Gordon’s UniversityScotland

S M LoCity University of Hong KongHong Kong

David LoweUniversity of ManchesterEngland

William McCluskeyUniversity of UlsterNorthern Ireland

John MansfieldNottingham Trent UniversityEngland

Jacob OpadeyiThe University of the West IndiesTrinidad and Tobago

Rob PickardNorthumbria UniversityEngland

David ProverbsWolverhampton UniversityEngland

Rainer SchulzUniversity of AberdeenScotland

Martin SextonUniversity of SalfordEngland

Low Sui PhengNational University of SingaporeSingapore

Thomas UherUniversity of New South WalesAustralia

Clive Warren University of QueenslandAustralia

Peter WyattUniversity of the West of EnglandEngland

Contents

Introduction 7

Valuation of variations 8

Research methodology 13

Data analysis 19

Conclusion 24

References 26

Appendix 1: The hypothetical case presented in the questionnaire 30

Appendix 2: Decision results from all respondents 32

A decision support tool for the valuation ofvariations on civil engineering projects

The valuation of variations has been recognised as a prime cause of conflict and dispute in constructionmanagement. Such disputes often concern the prices and/or rates to be applied to the varied works.Previous research has identified the subjectivity of the decision-maker in interpreting the valuation rules tobe the major problem, particularly with regard to defining the work conditions and/or characteristicsduring a variation event.

Findings of a survey, conducted to elicit the views and perceptions of experienced practitioners towardsinterpreting the valuation rules are presented. The development of a decision-making tool based on arobust framework for valuing variations in civil engineering projects is described. The tool was developedby analysing changes in various decision attributes. The result of the changes was then mapped to relevantsets developed using fuzzy-logic principles. Various operators were used to perform the fuzzy-aggregationoperation. The modelling technique was demonstrated to be reliable in replicating the decision-makingprocess performed by experienced practitioners. As such is considered a suitable aid for decision-makinginvolved in valuing variations on civil engineering works.

The results of the analysis reported here have suggested the fuzzy-logic as an appropriate tool to modelhuman decision-making, particularly in valuing variations on civil engineering works. This is consideredan essential progress of the current study in modelling human decision-making process, particularly sincethere are so many unknown aspects associated with such a process. The modelling technique successfullydeveloped here is then used as the main algorithm for decision making in the subsequently developedKnowledge Based System (KBS) which is intended to assist practitioers minimise conflict and diputearising from the valuation of vaiations.

Contact:

Monty SutrisnaResearch Institute in Advanced TechnologiesUniversity of WolverhamptonWolverhampton WV1 1SBUnited Kingdom.

e-mail: [email protected]

Acknowledgements:

The author wishes to acknowledge the contribution ofStephen Brown, head of research of the Royal Institutionof Chartered Surveyors, in finalising this paper.

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Monty Sutrisna Keith PottsSchool of Engineering and the Built Environment School of Engineering and the Built EnvironmentUniversity of Wolverhampton University of Wolverhampton

David Proverbs Kevan BuckleySchool of Engineering and the Built Environment School of Computing and Information TechnologyUniversity of Wolverhampton University of Wolverhampton

n construction project managementresearch, the subject of variations hasattracted considerable attention

(Hibberd, 1980; Hibberd, 1986; Dorter,1990; Akinsola, 1997). Variations havebecome an almost inevitable part of theconstruction process and in many cases, leadto conflict between the parties involved.Lack of effort in managing these conflictscan result in disputes (Fenn et al, 1997).When disputes are left unresolved, then thirdparty intervention, such as the services of anadjudicator, may be employed to help reachan agreement (Latham, 1994). Variationshave also been reported to significantlyreduce labour efficiency by up to 15%depending on which trades are concerned(Hanna et al, 1999a and 1999a).

One of the main causes of disputes is in thevaluation of the variations (Potts, 1995;Seeley and Murray, 2001). The problemswithin the valuation of variations have beenmuch attributed to the failure of thetraditional cost model, i.e. the bill ofquantities (Barnes, 1971). For example arecent survey on the use of contracts in thebuilding and construction projects revealedthat on lump sum contracts, bills ofquantities are still being used in up to 20% ofthe projects in the UK (RICS, 2003). Thecurrent traditional approach to valuingvariations, favoured by many clients, hasbeen claimed incapable of providing anadequate scheme of compensation tocontractors for any delay or disruptioninvolved due to the variation. A particularconstraint within the current valuation rulesis the dependency on personal opinion orjudgement (Hibberd, 1986). That is, there is a

high degree of subjectivity involved in thedecision-making process when valuingvariations. A robust mechanism is needed toeliminate or at least reduce the level ofsubjectivity involved when deriving whichvaluation method is to be implemented(Winter, 2002).

The development of conceptual frameworksfor valuing variations in excavation works(Sutrisna and Potts, 2003a) and in concreteworks (Sutrisna et al, 2003a) has beenpreviously reported. Similarly, the potentialfeasibility for developing a Knowledge BasedSystem (KBS) capable of controlling thesubjectivity involved, using heuristicknowledge of the decision-makers, has alsobeen reported (Sutrisna et al, 2003b).However, in attempting to develop this KBS,several difficulties in knowledge acquisition,knowledge representation and associating theknowledge in the inference mechanism werefound. Applying the basic principles of fuzzy-logic to model the decision-making processwas found to help overcome these difficulties(Sutrisna et al, 2003c).

This paper reports the findings of asubsequent questionnaire survey, conductedfor the dual purpose of gathering thedecision-makers’ knowledge and forevaluating current levels of subjectivity. Thedevelopment of fuzzy-set models to replicatethe decision-making process is describedfollowed by the tests undertaken to validatethe decision-making tool.

Introduction

RICS Research � 7www.rics.org

A decision support tool for the valuation of variations on civil engineering projects

II

The valuation of variations has long beenrecognised as one of the commonest sourcesof dispute in the construction industry(McGowan et al, 1992; Potts, 1995; Seeleyand Murray, 2001; Winter, 2002). There areseveral ways to value variations, and differentcircumstances will require different methodsof valuation. Problems normally occur whenthere are different perceptions between theparties involved regarding the circumstances

of the variations that require differentmethods of valuation. As argued by Hibberd(1986), the valuation in many cases dependsupon a high degree of personal opinion orjudgment.

Following the rules for variations provided inthe form of contracts, a contractor must bearin mind the possibilities of becominginvolved in a contract that permits a widerange of variations; and also that ratesquoted in the bills of quantities, when

considered appropriate, may be used for thevaluation of the variations. However, theserates and prices may not be an accuratefigure for individual work items. This leads tofrequent claims arising from the contractorwhen the measured quantities of permanentworks priced at billed rates do not representthe true value of the construction works(Seeley and Murray, 2001). From thecontractor’s point of view, the rates and

prices included in thetender may contain a lowprofit margin with a highdegree of risk that is takento maintain thecompetitiveness of thetender. Thus, if such a lowrate and/or price is appliedfor further extensiveamounts of similar works,the contractor may sufferreduced profit or evensignificant losses. From theemployer’s point of view,an authorised variation,which is closely relatedand necessary for thecompletion of the overall

works, should be valued similarly to theoriginal works. Thus, an increase to the rateand price would increase the liability of theemployer to the project and may causesignificant discrepancies to the initialinvestment benefit analysis. Hence, theemployer can suffer losses in the longer termresulting in the project becoming lessprofitable or unprofitable due to theextensive additional expenses for variations.

As a result, it has been acknowledged that

Valuation of variations

8 � RICS Research

...a contractor mustbear in mind the

possibilities ofbecoming involvedin a contract that

permits a widerange of variations

the rules of valuation should not beimplemented in a loose way, simply becausethe rates to which they are applied may notbe appropriate (Hibberd, 1986). The ratesand prices applied in the event of valuationshould be the rate, which the contractorwould have inserted against that item, had itbeen included at the time of tender (Haswell,1963). Differences in evaluating theapplicability of rates and/or prices from billsof quantities for valuation of variations havebeen demonstrated in several legal cases withvarying results. In the legal case of DudleyCorporation v. Parsons & Morrin Ltd. (1959),the court decision to apply originalprices/rates from the bill of quantity hadresulted in a significant loss for thecontractor while in the legal case of HenryBoot Construction Ltd. v. Alstom CombinedCycles Ltd (2000), a similar decision to applyoriginal prices/rates from the bill of quantityhad resulted in a large profit for thecontractor.

In the earlier stages of this research, twoframeworks for valuing variations weredeveloped for excavation works and concreteworks, respectively. The FIDIC Conditions ofContract for Construction 1999 was selectedas the platform for the concrete worksframework whilst the excavation worksframework was based on the ICE Conditionsof Contract Measurement Version, 7thedition, 1999. The most significant problemsidentified during the development of bothframeworks concerned the subjectiveinterpretation of the classical three-tiervaluation scheme. While the extent ofchanges in the work characteristics and/orconditions determines whether the

rates/prices in the bill of quantity can beapplied directly [Clause 52(3)(a)], appliedwith adjustments [Clause 52(3)(b)] or a newrate/price is required [Clause 52(3)(b)]; thereremains a high degree of subjectivityinvolved in determining which of these isappropriate.

A subsequent phase of the research led tothe decision to focus on the framework forexcavation works as these are common tocivil engineering contracts in which thevaluation of variations have generally beenthe main cause of dispute (Seeley & Murray2001). Furthermore, the excavation workshave been found to be a main source ofvariations due to (e.q.) unforeseen groundconditions (Clayton 2001). Moreover,excavation works represent a basic workactivity, performed on most constructionprojects and therefore extend the potentialfor applying the findings of this research.

The framework identified factors to beconsidered during the valuation of variationsin excavation works and provided acomprehensive checklist of items to reducethe subjectivity involved (refer to Figure 1).In order to measure the extent of changesinvolved in a variation event, all changes inthe factors within the framework arerecorded under five criteria known as thedecision attributes. The five decisionattributes are the extent of changes occurredin the Construction Programme, HumanResources, Construction Equipment,Materials and Sundry Charges. Theframework for excavation work wascomposed from the checklist of the primaryfactors and secondary factors, presenting the



relationship and the effects to the decisionattributes. Primary factors are defined as thebasic factors to be considered in valuingvariations (i.e. nature of the site, weatherconditions, and nature of the works) whilstsecondary factors (i.e. ground conditions,ground water control, and excavatedmaterials and its disposal) are other factorsderived from the primary factors andstrongly affected by the combination of theprimary factors. The extent of changes ineach attribute measures the degree ofsimilarity of work character and/or workconditions of the varied works compared tothe ones in the bill of quantities.

Fuzzy logic

Fuzzy-logic is a superset of Boolean Logicthat deals with the concept of partial truthand the uncertainties of vague boundary thatwas first introduced by Zadeh (1965). Fuzzy-set theory and fuzzy-logic were established inorder to deal with the vagueness andambiguity associated with human thinking,reasoning, cognition, and the perceptionprocess (Zadeh, 1965; 1973; Zimmermann,1987). As human decision-making processesusually have to deal with making decisions inthe presence of incomplete or impreciseinformation (Prodanovic, 2001), fuzzy-logicthat replaces Boolean logic with degrees oftruth or degrees of membership, is capable ofmodelling decision-making in such acondition (Boshoff, 2002). Fuzzy-logic hasbeen proved successful in solving manydecision-making problems mostly ofindustrial control (Hruschka, 1988).

The concept of a fuzzy-logic system was

described as a non-linear mapping of aninput data vector into a scalar output, wherethe vector output decomposes into acollection of independent multi-input/single-output systems (Mendel, 2001). In otherwords, the fuzzy-logic system contains therichness of an enormous number of mappingpossibilities that is not provided by the crispBoolean logic (i.e. dual value concept of trueor false). Fuzzy-logic system shifts theparadigm of a crisp value in classicmathematics into a fuzzy value (i.e. degreesof membership in the range of 0 to 1) todefine a class without a clear boundary.These fuzzy values represent the degree ofmembership. The closer the degree ofmembership value to 1, the closer the objectcan be associated or belong to theclass/group.

As a set is defined as any collection ofobjects, a fuzzy-set is defined as ageneralisation of the characteristic functionto represent an indistinct boundary of a set(Miyamoto, 2000). In other words, in thecase when the boundary of a set cannotreally be appropriately defined, the particularset can be appropriately defined as a fuzzy-set.

The intention of applying fuzzy-logic in thisproblem area is mainly to accommodate theuncertainties and ambiguities resulting fromthe experts subjective semantic interpretationin the valuation of variations rules providedby the ICE 7th Measurement Version, 1999;particularly in the interpretation of similarwork characteristics and/or similar workconditions.

10 � RICS Research



Figure 1. Framew

orkfor

assessing work

similarities and/or

work

conditions orexcavation w

orks (Adapted from

Sutrisna & Potts 2003a)

Prior to its application in the problem area,the fuzzy-logic principle is explored. Let Ube the universe of discourse. A fuzzy set F inU is characterised by a membership functionas follows:

µF: U ∏ [0,1]

Where µF (u) represents the grade ofmembership of u∈ U in the fuzzy set. Thedegree of membership ranges from 0 to 1,where 0 demonstrates no membership and 1demonstrates a full degree of membership.In the problem domain, the valuation ofvariations, the universe of discourse U is thecollection of all possible value changes in thefive decision attributes. Three fuzzy sets(LOW, MEDIUM, and HIGH), which aredirectly associated with the three alternativesfor the decision-making, were defined for thevaluation of variations.


In order to operationalise the framework forexcavation works and to gather knowledgeand insight from practitioners, aquestionnaire survey was conducted toidentify and evaluate current practice invaluing variations. The questionnaire wasdesigned to elicit the decision-makers’knowledge and was used to evaluate theircurrent levels of subjectivity. The surveyutilised a hypothetical variation eventdeveloped specifically for this purpose (referto Appendix 1). The survey encompassedquantity surveying professional working forthe main parties involved in the valuation ofvariations, namely contractors,engineers/consultants and employers. Adetailed description of the survey design andquestionnaire design now follows prior to thepresentation of the results, analysis andconclusions.

The Questionnaire Survey

In order to utilise and validate the developeddecision-making tool, empirical data fromthe actual decision-maker was acquired via asemi structured questionnaire surveyencompassing open-ended and closed-endedquestions.

In performing surveys, the major concernsare sample size, data collection procedures,analysis and measurement. Statisticalapproaches that are utilised in the analyticalsurvey approach necessitate the priormeasurement of all pertinent variablesthrough their inclusion in a questionnaireformat (Ahlgren and Walberg, 1979). Thequestionnaire technique is defined as ageneral term to include all techniques of data

collection in which each person is asked torespond to the same set of questions in apredetermined order (deVaus, 1996). A self-administered postal questionnaire with spacefor feed back at the end of each section wasemployed. Respondents were asked to relatetheir answers towards a hypothetical casestudy (refer to Appendix 1) in order to elicitcomparable data for robust analysis, as usedin previous construction studies (Proverbs,1998; Xiao, 2002). The hypothetical caseinvolved an underground water tank andpumping station structure and presented avariation in the excavation works. Thehypothetical case was designed todemonstrate the simultaneous impact of avariation event on the decision attributes.The changes were deliberately set withinvarious arbitrary ranges for decisions inorder to capture the subjectivity of thedecision-makers (i.e. the practitioners).

Respondents

A major role of quantity surveyors is toprepare bills of quantities, performvaluations, and act as the economists of theproject (Seeley, 1984; Willis et al, 1994; TheAqua Group, 1996). Hence, thesepractitioners were considered appropriate toperform the decision-making in determiningthe valuation methods to be applied in avariation event (Sutrisna and Potts, 2003b).The target respondents were all memberslisted in the Construction CommercialManagement Practises Committee of theInstitution of Civil Engineering Surveyors2003 Yearbook and Directory of Members,excluding student members, graduatemembers and probationer members. The

Research Methodology



population validity of these sample groupswas demonstrated by their membershipstatus in the Institution of Civil EngineeringSurveyors (ICES) as the ConstructionCommercial Management PractisesCommittee of ICES embodied qualifiedsurveying practitioners.

1,420 questionnaires were distributed to thetargeted respondents. The complicatednature of the research problem and the lackof literature available in the problem areameant that many difficult questions had to beincluded in the questionnaire. As aconsequence, the expected rate of return wasrealistically set to below 10%. This required alarge number of questionnaires to bedistributed in order to acquire a sufficientnumber of completed questionnaires for dataanalysis purposes. 125 questionnaires werereturned, representing a response rate of

8.82%. However, following an initial nettingof these, only 73 questionnaires were used foranalysis purposes since the remaindercontained item non-response errors and wereconsidered unfit for use. Item non-responseerrors occur when only part of the returnedquestionnaire is completed. While theresponse rate was considered quite poor, 73questionnaires used in the analysis had anestimated margin of error equivalent to11.5% at the 95% confidence level, which wasconsidered acceptable for the intendedanalysis.

In order to apply inferential statistic analysis,a large sample from an infinite populationwas required. In practice, the threshold for alarge sample is normally set to be larger than30 (Holt 1998; Kvanli et al, 2000). However,larger samples are needed in performingcomplex human decision-making modelling


Number of responses analysed : 73

Respondents background Contractor: 40Consultant/Engineer: 17Employer/Client: 8N/A: 8

Respondents experience(in years) Min: 5

Max: 50Median: 40Mean: 28

Number of respondents interested to contribute further Interested: 44

Not interested: 29

Table 1. Respondents’ characteristic

using fuzzy logic. Umbers & King (1981)have demonstrated that the sample sizeacquired here was sufficient for such analysis.The characteristics of the respondents areprovided in table 1.

Decision-Making Modelling

The decision-making model was developedfor each respondent using the basicprinciples of fuzzy-logic as described inSutrisna et al (2003c). The intention ofapplying fuzzy-logic in this problem area isto accommodate the uncertainties resultingfrom the decision-makers subjectiveinterpretation in the valuation of variationsrules provided by the ICE 7th MeasurementVersion, 1999; particularly in theinterpretation of similar work characteristicsand/or similar work conditions. Theapplication of fuzzy-logic in this problemdomain requires minimum knowledgeacquisition from the decision-makers andavoids the potential combinatorial explosionof the rules. Further, the inferencemechanism developed from the fuzzy-logicsystem can be subsequently applied to theintended KBS.

All changes in the hypothetical case wereaccommodated and quantified into the fivedecision attributes (i.e. changes inProgramme, Human Resources, ConstructionEquipment, Materials, and Sundry Charges).Based on this, the respondents were asked todetermine the extent of the overall changesdescribed in the hypothetical case studybased on the three-tier valuation mechanism.If the decision was to apply the rate/price inthe bill of quantity, then it was labelled

LOW. Other decisions were labelledMEDIUM and HIGH respectively. Further,the respondents were asked to break downtheir decisions for each decision attribute.This was followed by requesting therespondents to generalise and identify theirsubjective thresholds to determine theshifting point between the LOW, MEDIUMand HIGH for every decision attribute. Thiswas followed by requesting the respondentsto generalise (i.e. to also provide theirdecision breakdown for a general conditionin typical excavation works) and identify theirown version of thresholds to determine tehshifting point in order to group the variationsinto LOW, MEDIUM or HIGH. Therespondents were then asked to do this foreach of the decision attributes (i.e. changesin Programme, Human resources.Construction Equipment, Materials andSundry Charges).

These shifting points were then incorporatedwith the decision breakdown into each fuzzy-set to construct the model for each decisionattribute and denoted as C1, C2, C3 and C4(refer to Figure 2). For instance, the areabetween C1 and C2 in a fuzzy-set forHumanResouces repesents the ‘grey area’ for thisparticular expert/decision-maker. Thisparticular expert/decision maker was not surewhether any changes of Human Resourcesoccured in between C1 and C2 (denoted atU) should be classified as LOW orMEDIUM and so on. The intention of thiswas to define the shifting point for eachrespondent. These shifting points are thenused to develop the fuzzy-sets for everydecision attribute from each respondent.



The extent of changes recorded in the fivedecision attributes were then mapped intorelated fuzzy-sets. The value of the changesunder each decision attributes were thenmapped into the corresponding fuzzy-sets todetermine their degree of membership inLOW, MEDIUM and HIGH. This groupingof LOW, MEDIUM and HIGH is related tothe three-tier decision-making alternativefrom the ICE 7th edition. LOW is associatedwith a certain degree of change in thedecision attributes that allows the originalrate/price from the bill of quantity to be

applied. MEDIUM is associated with acertain degree of change in the decisionattributes that requires adjustments to beapplied to the original rate/price from thebill of quantity. HIGH refers to a certaindegree of change in the decision attributesthat necessitates a new rate/price to bederived from a fair valuation.

An empirical symmetric membershipfunction consisting of the three fuzzy-setsused in the analysis is graphically illustratedin Figure 2.


The memberhip funciton of th ethree fuzzysets can also be represented:

Five membership functions were developedfor five decision attributes with three fuzzysets on each. As the inference mechanism,the membership values were then aggregatedusing appropriate fuzzy intersectionoperators (I) to represent aggregation"AND". Several fuzzy intersection operatorswere considered appropriate to represent theaggregation "AND". The selection of anappropriate operator is based on the natureof the problem (Zadeh ,1965; 1973; Duboisand Prade, 1980; Zimmerman, 1987; Yager,2000). In order to improve the accuracy ofthe results; three operators were used toaggregate the membership values, namely theminimum operator (this has been consideredthe most commn operator for intersection),arithmetic-sum operator (to accommodate a fullcompensation between “AND” and “OR”aggregation operation) and algebraic-product

operator (to accommodate furthercontribution of all membership values thatmay not be covered in the minimum operator).The majority outcome is considered as afinal result of these aggregation operations. Afailure to have a majority results in aninconclusive operation.

The fuzzy-intersection operators are definedas follows:

Minimum operator: µLowTotal(u) = min{ µLOW(u1), µLOW(u2), µLOW(u3), µLOW(u4),µLOW(u5)}

Arithmetic-sum operator: µLowTotal(u) ={µLOW(u1)+ µLOW(u2)+ µLOW(u3)+ µLOW(u4)+µLOW(u5)}

Algebraic-product operator: µLowTotal(u) ={µLOW(u1)o µLOW(u2)o µLOW(u3)o µLOW(u4)oµLOW(u5)}

Where u1,…,u5 are the degrees ofmembership in the LOW of all of thedecision attributes. The values ofµMediumTotal(u) and µHighTotal(u) can becomputed respectively. The mapping of thesevalues to the output of the inferencemechanism is performed by OR operator, i.e.fuzzy union operation (U). The operator usedis maximum operator to represent theselection process of the most influentialintersection-aggregation-result into a decisionand defined as:

Decision = LOW OORR MEDIUM OORR HIGH = µLow Total(u) U µMedium Total(u) U µHigh Total(u)= max {µLowTotal(u), µMediumTotal(u), µHighTotal(u)}



For maximum operator, the highest value willbe selected as the decision. There is no needfor defuzzification of the result into a crispvalue as the objective of the operation hasbeen achieved, i.e. the resulting decision(Sutrisna et al, 2003c). An example of adetailed calculation is provided in appendix 2.

The decision-making modelling wasvalidated based on its capability to correctlypredict a majority of the actual decisions. Asthe success rate (non-error rate) is anarbitrary issue, a threshold value from anearlier study aimed at predicting humandecision-making using fuzzy-logic wasconsidered appropriate (Umbers and King,1981). Hence the model was consideredacceptable when capable of achieving a non-error rate above 60% at 90% significancelevel.


The discussion of the data analysis is focusedon two sets of analyses. The first involved acomparative analysis of the outcome of thefuzzy-sets with different aggregationoperators to the actual decision of thedecision-makers. As the main objective of themodelling was to replicate the decision-making process, validation is achieved whenthe model is competent in deriving a similardecision to the actual decision made by thedecision-maker. This part also reviews theapplicability and superiority of the fuzzy-intersection operators relatively from eachother for decision-making in the valuation ofvariations, particularly in excavation works.The second part of the analysis was on thedecision itself and set to investigate theinfluence of the background of the decision-makers on the decisions. That is, anevaluation of the objectivity found in thesedecisions is also described.

The Decision-Making Tool

The decisions resulted from the models werecompared to the actual decisions. Asummary of the comparison of actual andpredicted decisions is presented in Table 2.The results demonstrate the degree ofagreement betwen the decision makingcalculated by each aggregation operator andthe actual decisions of respondents.Appendix 2 provides full details of thisanalysis.

In modelling human decision-making usingfuzzy-logic, the developed model reliesentirely on the decision-makers’ explanationand therefore assumes that the statement wasa complete and correct explanation of thedecision-making process. Consequently, thedegree of agreement between the decisionsresulted by the developed model using fuzzy-logic and the actual decisions wererealistically expected to be above 60% for

Data Analysis



Table 2. Summary of the result

Min-max Arithmetic sum- Algebraic product- Combination ofoperator max operator max operator three operators

In agreement : 52 35 50 56

Not in agreementOverestimate : 2 2 2 1

Underestimate: 17 36 19 13Inconclusive : 2 0 2 3

Total : 73 73 73 73

most cases. The degree of agreement in thisresearch is presented below.The hypotheses test are: H0: p <0.6

H1: p > 0.6Significant level used is α = 0.1 since theerror type II was considered more significantthan error type I. Error type II relates to theacceptance of an incorrect operator. The null hypothesis is rejected if Z>Zα. The Z is calculated as follows:

p = estimated probability = (total numberin agreement/total number ofsampling).

p0 = expected probability.n = number of sampling.The results of the hypotheses test arepresented in Table 3.

As demonstrated by the hypotheses testresult, the minimum-maximum operator andthe algebraic-product-maximum operatorprovide relatively higher probability toachieve a non-error rate above 60%. Onlythe arithmetic-sum operator provides asignificant probability to achieve a non-errorrate below 60%. Based on this, it can beconcluded that the arithmetic-sum operator isnot an appropriate stand-alone-operator forthe decision-making modelling purpose forvaluing variations.

However, the initial inclusion of thearithmetic-sum was to accommodate thecompensation that may be required whenmodelling the "linguistic AND" into a"logical AND", the use of the arithmetic-sumin a collective manner with the other twooperators has increased the overall non-errorrate. Using the normal/Gaussianapproximation to the binomial distribution,the level of agreement resulted from a


Table 3.Hypotheses test result

Min-max Arithmetic sum Algebraic product- Combination of operator -max operator max operator three operators

0.712 0.479 0.685 0.767Z 1.955 -2.11 1.48 2.91Z0.1 1.28 1.28 1.28 1.28Result Reject Ho Accept Ho Reject Ho Reject Ho

collective use of the three aggregationoperators with a non-error rate of 76.7% hasa probability of p<<0.001 which issignificantly better than by chance.Therefore, it was decided to include thethree operators to generate an optimal resultfrom the modelling. Based on an analysisexplained in Sutrisna and Potts (2004), theuse of multiple experts/decision-makers canbe performed by applying a simple majorityrule. Thus, the majority of the decisions

resulted from the modelling process can berecommended to support decision-making inthe valuation of variations.

Furthermore, the analysis also has shownthat the majority of the errors in the resultsfrom the minimum-maximum operator, thearithmetic-sum-maximum operator and thealgebraic-product-maximum operator areunderestimation errors. An underestimationerror means that the model result is LOWwhen the actual decision isMEDIUM/HIGH and/or the result isMEDIUM when the actual decision isHIGH. This discrepancy may be attributableto the "personal biases effect", where inperforming their judgment, the decision-makers do not base their judgments on thelogical form of arguments but rather on whatthey believe should be the results (Revlin andLeirer, 1978). A full-scale exploration on this"personal biases effect", in order to minimisethe effect, covers the logic-field of decision-making area which has been extensivelyresearched within the psychology domain(Slovic, 1969; Johnson, 1972 ; Revlin andLeirer, 1978; Wyer and Podeschi, 1978).However, the "personal biases effect" canonly be explained and there has been noevidence of a satisfactory attempt to modelthe effect. Another explanation for thisdiscrepancy can be sought from the personalaggregation process of the decision attributesknown as the "interaction effects" thatdemonstrates the occurrence of a substantialconfigural processing of the information onthe separate dimension by a human decision-maker (Slovic, 1969; Johnson, 1972). Asimilar effect was also reported by Wyer andPodeschi (1978) who described that the

RICS Research � 21


www.rics.org

..decision-makers do not base theirjudgments on the logical form of

arguments but rather on what theybelieve should be the results.

decision-maker who gives subjectivereactions on a particular matter, in somecases, showed inconsistencies to thecomposite of their reactions to individualattributes of the matter. Therefore,discrepancies in the decisions resulting fromthis research are likely to be caused by thedecision-makers’ biases and/orinconsistencies in sharing their knowledge.

The Resultant Decision

The actual decisions from the decision-makers representing the various projectstakeholders are presented in Figure 3.

A majority of the contractors may haveunderstandably selected high changes, as thisrequires the development of a new rate/priceby fair valuation (i.e. with due profit for thecontractor). However, a majority of theemployers and the engineers/consultants alsoselected high changes. This demonstrated acertain level of convergence on behalf of thevarious decision-makers. Notwithstandingthis, approximately 40% of the decision-makers did not select high changes. Thisdemonstrates the subjectivity involved andthat the changes presented in thehypothetical case study do not implicitlyguide the respondents to choose one of the

decisions whilst demonstrating that otherdecision options were adequately populated.

In order to test whether the decisions weresignificantly influenced by the backgroundsof respondents, i.e. contractors,engineers/consultants or employers, anobjectivity test was performed, namely thenon-parametric chi-square ((X2) test for kindependent samples to measure thedistribution of respondents with differentbackground in answering the questions. Thenon-parametric X2 test for k independentsamples is a straightforward extension of the

non-parametric X2 test for two independentsamples. The results of the decision-makingmodelling are assumed as ordinal data sinceeach question presented a choice of decision-options. Since the frequencies in discretecategories (nominal/ordinal) constitute thedata of research, the X2 test can be used todetermine the significance of the differencesamong k independent groups (Siegel, 1956).As not all of the respondents disclosed theirbackgrounds, 65 responses were used for thepurpose of this objectivity test.


The hypotheses tests are:

H0: the respondents from each backgroundare not randomly selecting the answers H1: the respondents from each backgroundare randomly selecting the answers Significant level used is α = 0.05 since theerror type I and error type II wereperceived equally significant. The nullhypothesis is rejected if:

X2 < X2a,df

When the X2 is relatively small, the observedfrequencies are in close agreement with theexpected frequencies which means that theproportion of respondents are closer to beingequally distributed for all background andtherefore H0 is rejected. Following the rulesin the non-parametric X2 test for kindependent samples, responses choosingLOW and MEDIUM were combined inorder to achieve sufficient group members.Results of the test are presented in Table 4.

The results demonstrate that respondentsfrom each background were randomlychoosing HIGH and other options(MEDIUM or LOW) and none of theoptions can be typically associated to anyparticular stakeholder.

The nature of changes in the variation eventin the hypothetical case study wereconsidered HIGH, by a majority of thedecision-makers. Therefore, in accordancewith the simple majority rule applied in thisdecision-making tool, new rates/prices forthis particular excavation works based on afair valuation can be recommended as anappropriate outcome in view of thesecircumstances, i.e. favouring Clause 53(3)(b)from the ICE Conditions of ContractMeasurement Version, 7th edition, 1999.



Category N df X2 X2 a, df Description

LOW/MEDIUM/ 65 2 0.47 5.99 Respondents from HIGH each background

are randomlychoosing betweenHIGH and otheroptions (MEDIUMor LOW).

Table 4. Results of non-parametricX2 test for k independent samples

subsequent data analysis have beenpresented. The subjectivity of the decision-makers has been analysed. It has beendemonstrated that the background of thedecision-makers (i.e. contractors,consultants/engineers, or employers) did notsignificantly affect their decisions, as none ofthe decisions can be typically associated withany of the decision-makers groups.

An exploration of performance of eachproposed fuzzy-aggregation operators and thedecision-making tool has been described.Based on the results, the use of all threefuzzy-aggregation operators (i.e. minimum-maximum, arithmetic-sum, and algebraic-productoperators) were concluded appropriate andcan be recommended to represent the"semantic AND" in the valuation ofvariations.

The level of agreement resulted from acollective use of the three aggregationoperators proposed here is significantly

The valuation of variations has beenacknowledged as one of the commonestcauses of conflict and disputes. Referring tothe rules of valuing variations provided bythe ICE Conditions of ContractMeasurement Version, 7th edition, 1999, apotential problem is the subjectiveinterpretation of the human decision-makerin interpreting the changes in the workcondition and/or work characteristicsoccurring as a result of a variation event.

Frameworks for valuing variations inexcavation works and in concrete works havebeen previously reported, as has a feasibilitystudy of using a KBS for the valuation ofvariations. In tackling further difficulties inknowledge acquisition and representation,the conceptualisation of applying fuzzy-logicas an inference mechanism in order to modelthe decision-making in valuing variations hasalso been performed.

The results of the questionnaire survey and

Conclusion


...the system is capable of providing a consistent and objectiverecommendation of the most appropriate decision.

better than by chance and way above thethreshold set for acceptance. Therefore, it canbe concluded that the decision-makingsupport tool developed is capable ofreplicating human decision-making processin the valuation of variations. Therefore, theapplication of fuzzy-logic principles wasfound to be appropriate for this problemarea and is to be used in a subsequentdevelopment of this research as a platformfor developing a KBS for the valuation ofvariations.

The decision-making modelling reported inthis paper has provided a robust algorithmfor the subsequent development of a KBSaimed to reduce conflicts and disputes in thevaluationof variations, particularly on civilengineering works. Thus, by including themodels of the decision-making process of theexperts/decision-makers in the KBS, thesystem is capable of providing a consistentand objective recommendation of the mostappropriate decision (i.e. LOW, MEDIUM,or HIGH) for various project conditionsinputted by the user of the system. Thedevelopment of the KBS intends to provideassistance and support to the projectstakeholders (i.e. contractors, consultants andemployers) in deciding the appropriatenessof the rate/price in the bill of quantity to beapplied to value a particular variation. At themoment of preparing this paper, a prototypeversion of the KBS has been developed. Thisprototype has been demonstrated topractitioners in the UK construction industry.The responses from practitioners are

generally supportive and various inputs andfeedbacks for further development of theKBS have been obtained and will bereported in subsequent publications.



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McGowan, P. H., Malcolm, R., Horner, W.,Jones, D. & Thompson, P. A. (1992). Allocation and Evaluation of Risk inConstruction Contracts. CIOB OccasionalPaper No. 52. Ascot: The Chartered Instituteof Building.

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2) Henry Boot Construction Ltd. v. AlstomCombined Cycles Ltd (2000) 16 Const.L.J. 6



The hypothetical project is a pumping station as shown in Appendix A. The pumping station willsupply hydrant water for a newly built factory. A contractor has been selected.• Location of pumping station: southwest part of the factory premises. • The contract is based on the ICE 7th edition, Measurement version, 1999. CESMM 3 applies. • The total lump sump project value including the supply and installation of the pumps, electricaland all plumbing inside the pumping station is £ 245,000 • To be completed in 4 months, from July to October. • The excavation work, to be executed as the earliest activities, is quoted:

Just one month before the execution, the employer, through his Engineer, instructed the project to bevaried. The pumping station is now to be built in the northeast part of the factory and withadditional 1 m depth. Since the contractor has not yet mobilised his team, there are no standingcharges. However, several changes have occurred as the result of the variation order.

• The initial methodology for excavation is battered open-cut. However since the new location is tooclose to adjacent structures, two sides of the excavation now requires steeper sides to the excavation,therefore requiring wire mesh as slope support.• The intended new location is still occupied by another contractor; the new location will be readyby November. As previously mentioned, there are no standing charges. However, the contractor isnow excavating in the autumn-winter period. The rainfall is anticipated to be 75% higher than insummer time and necessitates steel platforms to be provided for the plant to work in the muddyconditions.• The excavation is now 1 m deeper and the ground water level in the new location is higher; it isrequired to have pumping to provide a dry condition for excavation.• The ground condition in the new location is not really similar to the initial location. From theinvestigation it was found that the swelling factor is now higher and causes significant additionaldisposal. The type of the soil has also changed from a softer type of clay to a stiffer type of clay thatnecessitates the contractor to up-grade the excavator plant type to maintain his rate of productivity.

Appendix 1. The hypothetical casepresented in the questionnaire


Excavation for foundation, max depth 5 – 10 m @ £ 20.45 1076 m3 £ 22,004.20

The breakdown of the excavation work is as follows:

Programme 40 working daysLabour £ 7,500.00Plant £ 8,500.00Material £ 3,500.00Sundry Charges £ 2,504.20

These changes has resulted in this following aaddddiittiioonnaall ccoosstt to the contractor: (Changes in Programme are in days and assumed to represent the additional overhead)

Changes in Programme

Changes in Labour



EEvveennttss Programme Labour Plant Materials Sundry Charges

1.Wire mesh slope support 3 days £ 250 £ 275 £ 375 -

2.Reduced productivitydue to rain 4 days - - - -

3.Steel platform forplant due to rain - £ 150 £ 75 £ 115 -

4.Pumping - £ 75 £ 150 - -5.Additional soil

disposal - - - - £ 4006.Excavator up-grade - - £ 450 - -

TTOOTTAALL 77 ddaayyss ££ 447755 ££ 995500 ££ 449900 ££ 440000

Appendix 2. Decision results from allrespondents


Appendix 2. Decision result from all respondents

RReessppoonn-- MMiinn--mmaaxx AArriitthhmmeettiicc ssuumm-- AAllggeebbrraaiicc pprroodduucctt-- MMooddeell AAccttuuaall ddeennttss ooppeerraattoorr mmaaxx ooppeerraattoorr mmaaxx ooppeerraattoorr ddeecciissiioonn ddeecciissiioonn

1 HIGH MED HIGH HIGH HIGH2 LOW/MED MED LOW/MED MED MED3 HIGH MED LOW Inconclusive HIGH4 HIGH LOW LOW LOW HIGH5 MED MED MED MED MED6 HIGH HIGH HIGH HIGH HIGH7 MED MED MED MED MED8 MED HIGH MED MED MED9 MED LOW MED MED MED10 MED MED HIGH MED MED11 HIGH HIGH HIGH HIGH HIGH12 LOW LOW LOW LOW LOW13 MED/HIGH HIGH MED/HIGH HIGH HIGH14 MED MED MED MED MED15 LOW LOW LOW LOW HIGH16 HIGH MED HIGH HIGH HIGH17 LOW MED HIGH Inconclusive HIGH18 LOW/MED LOW LOW/MED LOW HIGH19 MED/HIGH HIGH MED/HIGH HIGH MED20 HIGH HIGH HIGH HIGH HIGH21 LOW LOW LOW LOW HIGH22 LOW LOW LOW LOW MED23 LOW LOW LOW LOW LOW24 MED MED MED MED MED25 LOW LOW LOW LOW LOW26 MED LOW MED MED MED27 LOW/MED LOW LOW/MED LOW HIGH28 HIGH MED HIGH HIGH HIGH29 Inconclusive MED Inconclusive MED HIGH30 HIGH HIGH LOW HIGH HIGH31 LOW LOW LOW LOW LOW32 LOW LOW LOW LOW LOW33 HIGH HIGH HIGH HIGH HIGH34 LOW/HIGH HIGH LOW/HIGH HIGH HIGH35 HIGH HIGH HIGH HIGH HIGH36 Inconclusive HIGH Inconclusive HIGH HIGH37 HIGH LOW HIGH HIGH HIGH38 HIGH MED HIGH HIGH HIGH39 MED MED MED MED MED40 HIGH LOW HIGH HIGH HIGH



RReessppoonn-- MMiinn--mmaaxx AArriitthhmmeettiicc ssuumm-- AAllggeebbrraaiicc pprroodduucctt-- MMooddeell AAccttuuaall ddeennttss ooppeerraattoorr mmaaxx ooppeerraattoorr mmaaxx ooppeerraattoorr ddeecciissiioonn ddeecciissiioonn

41 LOW LOW LOW LOW LOW42 HIGH LOW HIGH HIGH HIGH43 MED MED MED MED MED44 LOW LOW LOW LOW LOW45 MED MED MED MED MED46 LOW LOW LOW LOW HIGH47 HIGH HIGH HIGH HIGH HIGH48 HIGH HIGH HIGH HIGH HIGH49 HIGH MED HIGH HIGH HIGH50 HIGH MED HIGH HIGH HIGH51 LOW LOW LOW LOW MED52 HIGH HIGH HIGH HIGH HIGH53 HIGH MED HIGH HIGH HIGH54 MED MED LOW MED MED55 HIGH MED HIGH HIGH HIGH56 MED MED HIGH MED HIGH57 HIGH MED HIGH HIGH HIGH58 HIGH MED HIGH HIGH HIGH59 LOW LOW LOW LOW HIGH60 LOW LOW LOW LOW LOW61 HIGH MED HIGH HIGH HIGH62 LOW/HIGH HIGH HIGH HIGH HIGH63 HIGH MED HIGH HIGH HIGH64 LOW MED LOW LOW HIGH65 MED LOW MED MED MED66 HIGH MED MED MED MED67 MED MED MED MED MED68 HIGH MED LOW Inconclusive HIGH69 HIGH MED HIGH HIGH HIGH70 MED/HIGH HIGH MED/HIGH HIGH HIGH71 MED MED MED MED MED72 LOW LOW LOW LOW HIGH73 HIGH MED HIGH HIGH HIGH

Appendix 2. Decision result from all respondents......continued

SSaammppllee ooff ccaallccuullaattiioonn uussiinngg tthhee fuzzy-sets

Respondent Number: 67

Position in the organisation: Quantity surveyor/project manager

Type of organisation: Contractor

Experience: 15 years

Further contribution : Yes

Changes in Programme

C2 = C3, C3<u<C4, therefore,Membership functions:


Changes in labour

C1 = 0, C1<u<C2, therefore,Membership functions:



Changes in Plant

C1 = 0, C2<C3, therefore,Membership functions:

Changes in Material


C1 <u<C2, therefore,Membership functions:

Changes in Sundry Cost

C2 = C3, C1<u<C2, therefore,Membership functions:




Summary of the results

Minimum-Maximum operator:µLowTotal(u) = min {µLOW(u1), µLOW(u2), µLOW(u3), µLOW(u4), µLOW(u5)}

= 0.1µMediumTotal(u) = min {µMEDIUM(u1), µMEDIUM(u2), µMEDIUM(u3), µMEDIUM(u4), µMEDIUM(u5)}

= 0.6µHighTotal(u) = min {µHIGH(u1), µHIGH(u2), µHIGH(u3), µHIGH(u4), µHIGH(u5)}

= 0.25

Membership functions [µ(u) ] LOW MEDIUM HIGH Respondent’s actual decision:

Changes in Programme - 0.75 0.25 MEDIUMChanges in Labour 0.37 0.63 - MEDIUMChanges in Plant - 1 - MEDIUMChanges in Material 0.1 0.9 - MEDIUMChanges in Sundry-Cost 0.4 0.6 - MEDIUM

DDeecciissiioonn = LOW OORR MEDIUM OORR HIGH= max {µLowTotal(u), µMediumTotal(u), µHighTotal(u)}= 0.6= MEDIUM

Arithmetic-sum Maximum operator: µLowTotal(u) = {µLOW(u1)+ µLOW(u2)+ µLOW(u3)+ µLOW(u4)+ µLOW(u5)}

= 0.87µMediumTotal(u) = {µMEDIUM(u1)+ µMEDIUM(u2)+ µMEDIUM(u3)+ µMEDIUM(u4)+ µMEDIUM(u5)}

= 3.88µHighTotal(u) = {µHIGH(u1)+ µHIGH(u2)+ µHIGH(u3)+ µHIGH(u4)+ µHIGH(u5)}

= 0.25


Algebraic-product Maximum operator:µLowTotal(u) = {µLOW(u1)� µLOW(u2)� µLOW(u3)� µLOW(u4)� µLOW(u5)}

= 0.0148µMediumTotal(u) = {µMEDIUM(u1)� µMEDIUM(u2)� µMEDIUM(u3)� µMEDIUM(u4)� µMEDIUM(u5)}

= 0.3402µHighTotal(u) = {µHIGH(u1)� µHIGH(u2)� µHIGH(u3)� µHIGH(u4)� µHIGH(u5)}

= 0.25




Summary of decision results


Respondent’s actual decision: MEDIUM

Minimum-Maximum operator: MEDIUMArithmetic-sum Maximum operator: MEDIUM Overall: MEDIUMAlgebraic-product Maximum operator: MEDIUM



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Brown, G.R. and Matysiak, G.A. (2000) Real

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Documents

A decision support tool for the valuation of variations on ...RICS Research RICS Research paper series Volume 5, Number 7 May 2005 Monty Sutrisna, Kevan Buckley, Keith Potts and David