Internatonal Journal of Industral Engneerng & Producton Researc Marc 03, Volume 4, Number pp. 7-80 ISSN: 008-4889 ttp://ijiepr.ust.ac.r/ A Fuzzy Group Decson Makng Approac to Constructon Project Rsk Management F. Nasrzade *, M. Kanzad & H. Manabad Farnad Nasrzade, Department of Cvl Engneerng-Faculty of Engneerng-Payame Noor Unversty, Teran-Iran Mostafa Kanzad, Assstant Professor, Dept. of Cvl Engneerng - Iran Unversty of Scence and Tecnology, Teran, Iran, kanzad@ust.ac.r Hojjat Manabad, M.Sc., Dept. of Cvl Engneerng Iran Unversty of Scence and Tecnology, Iran,.manabad@tudelft.nl KEYWORDS Constructon ndustry, Group decson makng, Fuzzy sets, Mult-crtera decson makng, Rsk management ABSTRACT Implementaton of te rsk management concepts nto constructon practce may enance te performance of project by takng approprate response actons aganst dentfed rsks. Ts researc proposes a mult-crtera group decson makng approac for te evaluaton of dfferent alternatve response scenaros. To take nto account te uncertantes nerent n evaluaton process, fuzzy logc s ntegrated nto te evaluaton process. To evaluate alternatve response scenaros, frst te collectve group wegt of eac crteron s calculated consderng opnons of a group conssted of fve experts. As eac expert as ts own deas, atttudes, knowledge and personaltes, dfferent experts wll gve ter preferences n dfferent ways. Fuzzy preference relatons are used to unfy te opnons of dfferent experts. After computaton of collectve wegts, te best alternatve response scenaro s selected by te use of proposed fuzzy group decson makng metodology wc aggregates opnons of dfferent experts. To evaluate te performance of te proposed metodology, t s mplemented n a real project and te best alternatve responses scenaro s selected for one of te dentfed rsks. 03 IUST Publcaton, IJIEPR, Vol. 4, No., All Rgts Reserved.. Introducton Many constructon projects ave not yet secured good project goal acevement. Suc falure could be realzed n terms of severe project delay, cost overrun and poor qualty []. Te presence of rsks and uncertantes mgt be responsble for suc a falure. Tus, tere s a consderable need to ncorporate te rsk management concepts nto constructon practce n order to enance te performance of project. * Correspondng autor: Farnad Nasrzade Emal: f.nasrzade@gmal.com Paper frst receved Jan. 8, 0, and n accepted form Jul. 07, 0. Te dea tat rsk management sould be an mportant part of project management s currently wdely recognzed by te leadng project management nsttutons []. Dfferent levels of rsk management ave been proposed by te researcers and organzatons snce 990. Al-Baar and Crandall [3], te U.K. Mnstry of Defense [4], Wdeman [5], and te U.S. Department of Transportaton [6] are among tose suggestng te use of a process wt four pases. Tese pases nclude rsk dentfcaton, rsk analyss, rsk response plannng, and control. Feylzadea et. al. [7] used a fuzzy neural network model to determne te EAC (estmate at completon) cost of te project. Te proposed approac consders bot qualtatve and quanttatve factors affectng te EAC predcton. Abdelgawad and Fayek [8] extended
F. Nasrzade, M. Kanzad & H. Manabad A Fuzzy Group Decson Makng Approac 7 te applcaton of falure mode and effect analyss (FMEA) to rsk management n te constructon ndustry. Tey used fuzzy logc and fuzzy analytcal erarcy process (AHP) for te rsk analyss. Lu et. al. [9] glgted te dfferences between enterprse rsk management (ERM) and project rsk management (PRM). Creedy et. al. [0] addressed te problem of wy gway projects overrun ter predcted costs. It dentfed te owner rsk varables tat contrbute to sgnfcant cost overruns. Molenaar [] modelled te rsk events n te constructon cost estmaton as ndvdual components. Te rsk analyss was performed usng Monte Carlo ulaton approac. Jannad and Almsar [] used expected value tecnque to perform te rsk analyss pase for ndvdual rsk. Touran [3] used a probablstc model for te calculaton of project cost contngency by consderng te expected number of canges and te average cost of cange. Altoug tere are several researces n te area of rsk management, almost all of tem only concentrate on te rsk analyss pase. Te rsk response plannng pase s not dscussed n te prevous works and te selecton of te most approprate rsk response acton s manly performed by personal judgment and tere s no systematc approac to select te optmum response aganst te dentfed rsks [4]. Ts researc proposes a metodology for te evaluaton of dfferent alternatve response scenaros based on ter mpacts on te project objectves n terms of project cost, project duraton and project qualty. Te proposed approac s a fuzzy mult-crtera group decson makng approac. To evaluate alternatve response scenaros, frst te collectve group wegt of eac crteron s calculated consderng opnons of a group conssted of fve experts. As eac expert as ts own deas, atttudes, knowledge, and personaltes, dfferent experts wll gve ter preferences n dfferent ways. Fuzzy preference relatons are used to unfy te opnons of dfferent experts. After computaton of collectve wegts, te best alternatve response scenaro s selected by te use of proposed ntegrated fuzzy mult-crtera group decson makng metodology. To evaluate te performance of te proposed metodology, t s mplemented n a real project and te best alternatve responses scenaro s selected for one of te most mportant dentfed rsks.. Concept of Fuzzy Sets Teory Fuzzy set teory ntroduced by Zade [5], s used ncreasngly for uncertanty assesent n stuatons were lttle determnstc data are avalable. Te use of fuzzy sets teory allows te user to nclude te mprecson, arsng from te lack of avalable nformaton or randomness of a future stuaton. Usng fuzzy set teory n practcal problems would make te models more consstent wt realty. Te central concept of fuzzy sets teory s te membersp functon wc represents te degree to wc a member belongs to a set as represented by te followng equaton: ( ~ A x, ~ ) x X () A Were, ~ s called te membersp functon of x A n A ~ tat maps x to te membersp space M. 3. Selecton of Optmum Response Aganst te Identfed Rsks Pror to te dscusson of optmum rsk response selecton process, t s necessary to ntroduce alternatve rsk response metods. Rsk response s an acton taken to avod rsks, to reduce te occurrng probablty of rsks, or to mtgate losses arsng from rsks. Rsk andlng metods are classfed nto four categores, ncludng rsk avodance, rsk transfer, rsk mtgaton, and rsk acceptance. Rsk avodance means te rejecton or cange of an alternatve to remove some dden rsk. For example, f a constructon metod s contngent on ran, te contractor could avod scedule delay by adoptng anoter constructon metod tat wll not be nfluenced by ran. Rsk transfer means te swtc of rsk responsblty between contractng partes n a project. Contractors usually use tree rsk transfer metods to offload rsk responsbltes. Tey are as follows: Insurance Subcontractng. Clams to te owner for fnancal losses or scedule delay. Rsk mtgaton denotes reducton of te occurrng probablty or te expected losses of some potental rsk by eter reducng te probablty or te mpacts of a rsk event. Rsk acceptance ncludes two condtons.e., () Unplanned rsk retenton, were te manager does not take any acton for some rsk; and () Planned rsk retenton, were te manager decdes to take no acton for some rsk after cautous evaluaton [6]. Te rsk andlng strateges may nvolve one or a combnaton of multple approaces mentoned eren. To andle rsks approprately, managers need to realze te contents and effects of all alternatve response actons before makng decsons. Te objectve of te study presented n ts paper s to provde dfferent constructon partes, wt a decson makng mecan tat wll ad tem n te selecton of best alternatve response scenaro to te dentfed rsks wc allow tem to make ntellgent and Internatonal Journal of Industral Engneerng & Producton Researc, Marc 03, Vol. 4, No.
73 F. Nasrzade, M. Kanzad & H. Manabad A Fuzzy Group Decson Makng Approac economcal decsons based on te proposed relable fuzzy metodology. 3.. Selecton of Evaluaton Crtera Eac potental rsk may ave a negatve mpact on project objectves n terms of project delay, cost overrun and poor qualty. Selecton crtera are drectly lnked wt project objectves, bot tangble, ncludng tme and cost and ntangble.e., qualty. Implementaton of alternatve response scenaros may decrease te negatve mpacts of rsks. However, te mplementaton of alternatve response scenaros wll mpose addtonal expenses on te project, Terefore, after mplementaton of alternatve response scenaros, te value of dfferent project performance objectves s determned as te deducton of two aforementoned terms. Fnally te selecton factors tat are relevant to te decson makng problem are selected as below:. Project duraton. Project cost 3. Project qualty 3.. Computaton of Collected Wegts of Crtera In ts secton te aggregated wegts of dfferent crtera s calculated. For calculaton of te group wegt of eac crteron, decson makers sould evaluate relatve mportance of crtera. Snce eac expert as ts own deas, atttudes, motvatons, and personaltes, tey wll gve ter preferences n dfferent ways. Herrera-Vedma et al [7] states tat group members may express ter opnons as ) preference orderng, ) utlty values, 3) fuzzy preference relatons and 4) multplcatve preference relatons. Tese opnons can be converted nto te varous representatons usng approprate transformatons [8]. In ts paper, fuzzy preference relatons are used to unfy opnons. Fuzzy relatonsps n te evaluaton are used to ncorporate te uncertantes n te decson opned by a partcular decson maker. In addton, decson makng becomes dffcult wen te avalable nformaton s ncomplete or mprecse [9], [0]. In tese assesents, preference orderngs of alternatves are represented by O, wc defnes preference orderng evaluaton gven s by to alternatve x s. Fuzzy preference relaton s expressed by k, were k X * X wt membersp functon k : X X 0,, and ( x, x ) k, were X x,..., s a fnte set k s m of alternatves. Value of k defnes a rato of te fuzzy preference ntensty of alternatve x s to x m. Multplcatve preference relatons are represented as A were A X * X, A a and a s a rato of te fuzzy preference ntensty of alternatve x s to x m gven by x n were s scaled n a to 9 scale. Utlty functon s sown as U were explans s/er preferences on alternatves as utlty values. Utlty value of alternatve x s gven by s presented by u s 0,. Before aggregatng s' assesents, te opnons sould be unfed nto fuzzy preference relatonsp by an approprate transformaton functon. A common transformaton functon between te varous preferences s presented below [8]: K ( us ) () ( u ) ( u ) s m om os K ( ) (3) n K ( log 9 a) (4) OWA operator s used to aggregate unfed opnons. OWA operator was ntroduced n 988 by Yager [], [], [3]. An OWA operator s an aggregaton operator wt an assocated vector of wegts n w, w 0, w n n suc tat: n F w. b, x I (5) wt b denotng te t largest element n x ; ; x n. Te most mportant caracterstc of OWA operator s tat t may produce many solutons based on decson maker s objectve caracterstcs. In te oter word, OWA operator consders decson maker s subjectve caracterstcs to estmate collectve value; wereas, oter aggregaton operators ave not ts mportant caracterstc. An mportant problem n usng OWA aggregaton operator s ow to obtan te assocated wegtng vector. Tere are two approaces to calculate te wegtng vector w. In te frst approac, te wegtng vector s calculated usng sample data as te functon of te values to be aggregated. In te second approac, owever, te wegtng vector w s calculated usng lngustc quantfers. In ts approac tat was ntroduced by Yager, te wegtng vector s calculated as follow [], [4]: w Q( ) Q( ),,..., n (6) n n Q s a fuzzy lngustc quantfer tat represents te concept of fuzzy majorty, s calculated as: 0 r-a Q( r) b-a f : f : f : r a b r a r b (7) Te most common lngustc fuzzy quantfers used are most, at least alf, and as many as possble. Internatonal Journal of Industral Engneerng & Producton Researc, Marc 03, Vol. 4, No.
F. Nasrzade, M. Kanzad & H. Manabad A Fuzzy Group Decson Makng Approac 74 Ter ranges are gven as (.3,.8), (0, ) and (, ), respectvely [0]. Fve consdered s represented ter vews on te varous crtera ncludng project duraton, project cost and project qualty n four dfferent ways. Te frst presented s vew n te form of utlty functons, te second remarked s vew n preference orderng of te alternatves, te trd proposed s vew n multplcatve preference relaton on a scale of to 9 and te fourt expressed s vew n fuzzy preference relaton, and te fft presented s vews n utlty functon, as follows:,,,.6, 3 5,,.3 3 3 5 4 3 5 4 4, 3.45.3 5.35 3.7.65 Te varous forms of presented opnons are transformed nto fuzzy preference relaton usng te prevously defned transformaton functons. Transformed and unformed values n prevous step are aggregated usng OWA operator and aggregaton wegts n te aggregaton step tat resulted from quantfer "most" wt te doman (.3,.8) are (0, 0., 0.4, 0.4, 0). Te resulted collectve fuzzy preference opnon s: Collectve soluton= 3 For calculaton of fnal aggregated wegt of eac crteron, te values of collectve soluton must be aggregated togeter. Fuzzy lngustc quantfer "as many as possble" wt doman (, ) s utlzed. Hence, correspondng wegt vector wt ts operator s W= (0,.33,.67) and collectve wegt of eac crteron s: G 7.443.97. Before assgnng tese values to wegts, tey sould be normalzed. Te normalzed G.447.383.7. wegt vector s:.46.84 5.4 3.79.76.4 9 3. 4.45 3.3 3.8.85 5.35, 3 3.7,.65.75 0 5 3 3 3,.75.34 3.3 3.74.74.6.6.66.8 3.87.8 3.3. Selecton of te Optmum Response Scenaro Usng te Proposed Fuzzy Mult-Crtera Group Decson Makng Approac Te structure of te proposed fuzzy mult-crtera decson makng approac s depcted n Fg.. Te proposed fuzzy mult-crtera decson makng approac was adapted from te model developed by Lee, Y. et al. [5] for dredged materal management. Converson of Scores nto Fuzzy Numbers DSS Structure Aggregaton Module Indexaton Converson of Fuzzy Numbers nto Indexes Aggregaton of Scores Fnal Rankng Fuzzfcaton of fnal Scores Rankng Module Fg.. Te structure of te proposed fuzzy mult-crtera group decson makng approac [adopted from 5 and 6] Te model comprses tree man sectors. At frst assgned scores are converted nto te fuzzy set. Tereafter scores for eac alternatve system would be aggregated at aggregaton module. Fnally alternatve response scenaros are ranked based on te acqured fnal scores at aggregaton module, wc are fuzzy numbers. If Z ( s assumed as a fuzzy value for t alternatve, ts membersp functon wll be [ Z ] as denoted n Fg. wt a trapezod membersp functon. Membersp degree for eac value would be assgned based on te expert's judgment. Internatonal Journal of Industral Engneerng & Producton Researc, Marc 03, Vol. 4, No.
75 F. Nasrzade, M. Kanzad & H. Manabad A Fuzzy Group Decson Makng Approac ( Z ) most lkely nterval largest lkely Interval Fg.. Fuzzy score of x t alternatve aganst t crteron As t s sown n Fg., Z, s an nterval n wc membersp degrees are ger tan. Ts nterval, wc as been assgned based on lkely nterval, s a sub-set of te fuzzy set and as been ntroduced based on level-cut concept. One of tese ntervals Z ) s (, x te most lkely nterval, were te membersp degrees are one. Moreover Z ) s largest lkely nterval and, 0 ( x f any of Z ( fall out of ts nterval ts membersp degree would be zero. Converson of Scores Into Indexes: Snce dfferent crtera, wt dfferent caracterstcs and unts, are gong to be ntegrated; Z, as score assgned to eac response scenaro regardng every crteron sould be converted nto an ndex. Ts ndex s n fact a rato and s comparable for varety of crtera. Subsequently fnal decson would be made based on aggregaton of opnons consderng all crtera. For tat reason, consderng (BES Z ) and (WOR Z ) respectvely as best and worst values a Z, b ( Z Z, could be converted nto S, ndex as follows:. If BES Z > WOR Z ten: S, Z, WORZ BESZ WORZ 0. If WOR Z >BES S, Z, WORZ BESZ WORZ 0 Z ten: Z, BESZ WORZ Z, BESZ Z, WORZ Z, BESZ BESZ Z, WORZ Z, WORZ (8) (9) Consequently Z, as a fuzzy functon s converted to S, and related trapezod dagram s transformed to te followng dagrams (Fg.3). Two condtons ave been consdered above, due to te reason tat usually caracterstcs are assessed n two drectons. Tat s, regardng some crtera lke Qualty, gettng greater score s equal to beng more approprate, so frst equaton would be assgned to tese types of crtera. In contrast concernng some crtera lke tme or cost, gettng greater score means less acceptablty, terefore second equaton would be assgned for tese types of crtera. Subsequently mpact of te scorng drecton s crossed out and results from all crtera could be summed up. Fg. 3. Transferrng fuzzy values to ndex value Fg. 4. Membersp functon of te fnal score regardng eac alternatve [adopted from 5 and 6] Aggregaton of Scores of Eac Alternatve Response Scenaro: For summng up all te scores and obtanng fnal score concernng eac response scenaro followng equaton could be exploted: I ( n W S, P p (0) Were n= te number of crtera; S, = Index for t crteron wt level of acceptance; w = Related Internatonal Journal of Industral Engneerng & Producton Researc, Marc 03, Vol. 4, No.
F. Nasrzade, M. Kanzad & H. Manabad A Fuzzy Group Decson Makng Approac 76 wegt of eac crteron factor and ( I ( w ; P= balancng = Fnal ndex for eac crteron wt level of acceptance. Te balancng factor P ( P ) ) s a factor wc sows mportance of devaton magntude between a crteron value and te best crteron for tat value and would be proposed for a group of crtera. Terefore f P= ten all devatons wll get equal wegt, and f P= eac devaton wll get wegt n proporton to ts scale. In general P 3 would be used for lmtng crtera [6]. Furtermore f eac crteron comprses oter crtera, ts equaton could be extended for lower levels and ten fnal result would be reaced by addng up results of eac level. Consequently evaluaton process could be followed up n dfferent levels so as to obtan fnal score regardng eac alternatve [5]. Fg. 5. fnal dea's score functons wt related utlty functons [adopted from 5 and 6] Preparng Proposed Alternatve Response Scenaros for Rankng: After acqurng fnal ndex for eac alternatve, membersp functon of a fuzzy set [ I ( n)] wll be fgured out utlzng equaton (6). Te membersp functon s a pecewse lnear functon, n wc I ( s member of te fuzzy set assocated wt fnal score of te x t alternatve. Ts could be performed by calculatng I 0 ( x ), and I ( x ) wose levels of acceptance are zero and one respectvely. I( I r I r 0 mn R R R R mn mn r mn R r mn I( r I( r mn I( R oterwse r and r mn = lowest and gest value of I ( x ) for fnal ndex respectvely R and R mn = lowest and gest value of I 0 ( x ) for fnal ndex respectvely I ( ) and I ( ) are resulted from ( ) 0 x x Z, x 0 and Z, correspondngly. If n alternatve response scenaros ave been consdered for rankng, tere wll be n fuzzy sets as I ( n ) n,,..., n wose membersp functons wll be resulted from equaton (). Fnal Rankng of Alternatve Response Scenaros: Snce te values wc are assgned to eac alternatve response scenaro are fuzzy, ter rankng could not to () be done by conventonal stragtforward rankng metods. Terefore, a fuzzy rankng metod s requred to fulfll te objectve. Accordng to Cen and Hwang opnon, varety of te rankng metods wc are proposed for fuzzy MC's, can be categorzed nto four groups [7]:. Utlzng preferences rato, by applyng tecnques suc as degree of optmalty, ammng dstance, ɑ-cut and comparson functon.. Fuzzy mean and spread by applyng probablty dstrbuton. 3. Fuzzy scorng wc nvolves tecnques suc as proportonal optmal, left rgt scores, centrod ndex and area management. 4. Utlzng lngustc expresson. Te metod cosen for ts purpose s developed by Cen [8] troug applyng mnmzng and mzng sets [8]. Te mzng set M s a fuzzy subset wt membersp functon of M, defned as follows: M ( I) I I / I I mn 0 mn I mn I I oterwse () Imn mn (mn I 0 ) for x,.., n (3) I ( I 0 ) for x,.., n (4) Terefore rgt utlty value U R ( for x t alternatve would be determned as: U mn ( ( I(, ( I( ) (5) R M In te same way mnmzng set G s also ntroduced as a fuzzy subset wt membersp functon of : G Internatonal Journal of Industral Engneerng & Producton Researc, Marc 03, Vol. 4, No.
77 F. Nasrzade, M. Kanzad & H. Manabad A Fuzzy Group Decson Makng Approac I I / I I mn Imn I I G ( I) (6) 0 oterwse And ten left utlty value U L ( for alternatve system x would be determned as follows: U (mn ( ( L), ( I( )) (7) L G Consequently total utlty or rankng value for proposal x s: U U R( U L( (8) Te alternatve wt best total utlty value would be presented as te best opton, tus all alternatves would be sorted based on ter total utlty values. 4. Model Applcaton Te proposed fuzzy group decson makng approac can be used for te selecton of optmum response aganst te dentfed rsks. To evaluate te performance of te proposed metodology t as been mplemented n a sample real project. Ts project s related to te executon of a large massve concrete foundaton of a g rse buldng. Ts project nvolves 500 cubc meter of concretng and ts duraton as been estmated as 5 monts. Te total cost of te project, ncludng bot drect and ndrect costs, as been estmated as 00000 dollars. Facng to nclement weater rsk s one of te most mportant rsks dentfed for ts project. Te proposed fuzzy group decson makng approac s mplemented to select te most effectve alternatve response scenaro aganst ts rsk. In ts project case example, t s expected tat nclement weater rsk wll be occurred durng te 3rd and 4t monts. Te occurrence of ts rsk would ave negatve mpacts on te constructon productvty and may lead to project cost overrun, project delay and poor qualty. Te alternatve response scenaros wc ave been dentfed for ts rsk are explaned below brefly. Rsk avodance: Te frst alternatve response scenaro wc may be mplemented aganst te nclement weater rsk s to avod t by cange n project scedule. It means tat te executon plan of te project s canged n a manner tat te concretng work s postponed to te 5t mont to avod te negatve mpacts of te rsk. Rsk Acceptance: Te second alternatve response scenaro wc may be mplemented aganst nclement weater rsk s ts acceptance, were te manager does not take any acton aganst ts rsk. Rsk Mtgaton: In te 3rd alternatve response scenaro, te potental expected losses caused by te nclement weater rsk are reduced. To reduce te scedule delay caused by ts rsk, te overtme polcy s mplemented durng te 3rd and 4t monts. Rsk Transfer: Fnally n te last alternatve response scenaro, te potental losses arsng from nclement weater rsk are transferred troug subcontractng or nsurance. A group consstng of fve experts was consdered to carry out te case study, troug applcaton of te proposed model. A spread seet program s also provded n order to elp rsk analyss team durng te selecton process. Bref outcomes of te assesent performed by te proposed fuzzy group decson makng approac are presented n table. As sown n table, usng te proposed fuzzy group decson makng approac, t s concluded tat te rsk avodance s te best alternatve response scenaro. It sould be empaszed tat ts evaluaton was made based on te proposed case and n dfferent stuatons te outcome of te assesent could vary dependng on te actual requrements and restrants. It s beleved tat te proposed fuzzy group decson makng approac provdes a powerful tool for te selecton of optmum response scenaro aganst te dentfed rsks. Response Scenaro Acceptance Avod Mtgate Transfer nterval Tab.. Scorng and fnal results Project Cost Project Duraton Project Qualty most lkely nterval 75-84 65-79 40-6 least lkely nterval 78-80 66-7 50-55 most lkely nterval 5-67 8-95 74-83 least lkely nterval 57-60 88-9 80-8 most lkely nterval 80-97 57-65 5-7 least lkely nterval 8-9 60-64 6-70 most lkely nterval 64-7 63-7 48-57 least lkely nterval 68-69 68-69 5-55 left utlty value rgt utlty value total utlty value 0.468 0.70 0.66 0.335 0.83 0.747 0 0.698 099 03 073 0 Internatonal Journal of Industral Engneerng & Producton Researc, Marc 03, Vol. 4, No.
F. Nasrzade, M. Kanzad & H. Manabad A Fuzzy Group Decson Makng Approac 78 5. Senstvty Analyss In OWA metod, rsk level of s s accounted n an explct manner. At ts decson-makng problem, senstvty analyss s carred out consderng te cange n te s optm degree or ter rsk level and ts mpact on wegtng coeffcents and fnal ranks of alternatves. For senstvty Analyss, anoter equaton was used to calculate te functon Q to fnd te order wegts of OWA operator. Te equaton Q ( r) r, 0 avng many applcatons n calculaton of membersp functon of a quantfer can be used n wc α s optmstc coeffcent of. If α >, t ndcates pes or rsk-averse decsonmaker. If α=, t means decson-maker s neutral. Fnally, α<, represents optmstc or rsk-prone decson-maker. Te order wegts of OWA operator depend on te manager s optm/pes vew on te rsk. If te as an optmstc vew ten larger wegts wll be assgned to te frst ranks n te OWA operator and terefore te model wll ave larger outputs. Based on ts percepton, Yager (988) as defned te optm degree θ n te followng way: ( r) dr 0 Q (9) Transformed and unformed values of s n secton 3. are aggregated usng OWA operator wt regard to dfferent optm degree (α=0.0, 0., o,,, 0). For calculaton of fnal aggregated wegts of crtera, te calculated collectve fuzzy preference opnons are aggregated usng fuzzy lngustc quantfer "most" wt doman (.3,.8) and correspondng wegt vector W= (.067,.663,.7). Te fnal normalzed wegt vector of crtera s sown n Table. Tab.. Senstvty analyss for te normalzed wegts of crtera at dfferent rsk levels Crtera Rsk Prone Neutral Rsk Averson α=0.0 α=0. α=0 α= α= α=0 w 0.439 0.43 0.436 0.436 0.443 0.486 w 0.344 0.359 0.366 0.38 0.393 0.395 w3 0.7 0. 0.98 0.84 0.64 0.9 It can be clearly seen tat by ncreasng α and decreasng optm degree or rsk level of s, te relatve wegts of te frst and second attrbute s ncreased. In contrast, te relatve wegt of trd crteron s declned n lar stuaton. In table 3 te results of te senstvty analyss carred out for te scorng and fnal results s presented at dfferent rsk levels. Tab. 3. Senstvty analyss for te scorng and fnal results at dfferent rsk levels Response Scenaro Rsk Prone Neutral Rsk Averson α=0.0 α=0. α=0 α= α= α=0 Acceptance 0.608 0.608 0.6 0.63 0.67 0.67 Avod 0.745 0.748 0.747 0.749 0.749 0.740 Mtgate 098 096 097 097 098 0.606 Transfer 05 06 08 09 0 07 6. Conclusons and Remarks In ts study a fuzzy group decson makng approac s exerted to perform constructon project rsk management wc assst dfferent project partes to select te optmum response aganst dentfed rsks. Te model s well suted for stuatons were crtera ave varyng degree of mportance as well as uncertan values. Snce te rsk response plannng sould be performed at te earler stages of te project and takng account of more ndefnteness exsted n tose stages, ntroducng fuzzy sets teory could beneft decson makers to make more tangble and realstc evaluaton. In te proposed metodology, frst te group wegt of eac crteron s calculated. As eac expert as ts own deas, atttudes and personaltes, dfferent experts wll gve ter preferences n dfferent ways. Te fuzzy preference relatons ave been used to unfy tese opnons for calculaton of te collectve wegts of eac crteron. Te best alternatve response scenaro s ten selected by te use of te proposed fuzzy group decson makng metodology. It sould be taken nto account tat n spte of superfcal complexty, te model s rater practcal and stragtforward and could be utlzed n order to aceve more relable assesent of te alternatve response scenaros. More plfcaton, owever, could encourage rsk Internatonal Journal of Industral Engneerng & Producton Researc, Marc 03, Vol. 4, No.
79 F. Nasrzade, M. Kanzad & H. Manabad A Fuzzy Group Decson Makng Approac management teams to more utlze t. Te proposed model was mplemented n a real project. Te alternatve response scenaros aganst one of te most mportant dentfed rsks,.e., nclement weater rsk were dentfed. Te outcome of te case study ndcated tat te rsk management team as selected te rsk avodance as te best alternatve response scenaro. It s beleved tat te proposed fuzzy group decson makng approac provdes a powerful tool for te selecton of optmum response scenaro aganst te dentfed rsks. References [] Nasrzade, F., Afsar, A., Kanzad, M., Dynamc rsk analyss n constructon projects, Canadan Journal of Cvl Engneerng. 35, 008, pp. 80 83. [] Project Management Insttute PMI., A Gude to te Project Management Body of Knowledge. (PMBoK Gude), Project Management Insttute, New town Square, Pa, 008. [3] Alabar, j., Crandall K., "Systematc Rsk Management Approac for Constructon Projects.", J. Constr. Engrg. and Mgmt. ASCE.6(3). 990, pp. 533-546. [4] Mnstry of Defence, Procurement Executve, Drectorate of Procurement Polcy MoD-PE-DPP.99. Rsk Management n Defence Procurement., Document ref. D/DPP (PM)///, Wteall, London. [5] Wdeman, R.M., Project and Program Rsk Management, Project Management Insttute, New town Square, Pa, 99. [6] Dept. of Transportaton DoT., 000. Project Management n te DoT., ttp://www.fta.dot.gov/lbrary/program/constructon/c HAPTER3.tm. [7] Feylzade, M.R., Hendalanpour, A., Bagerpour, M., A Fuzzy Neural Network to Estmate at Completon Costs of Constructon Projects. Internatonal Journal of Industral Engneerng Computatons, do: 067/j.jec.0..003. [8] Abdelgawad, M., Fayek, A.R., Rsk Management n te Constructon Industry usng Combned Fuzzy FMEA and Fuzzy AHP. Journal of Constructon Engneerng and Management. 36(9). 00, pp. 08-036. [9] Lu, J.Y.a., Low, S.P., He, X.a, Current Practces and Callenges of Implementng Enterprse Rsk Management (ERM) n Cnese Constructon Enterprses. Internatonal Journal of Constructon Management, (4). 0, pp. 49-63. [0] Creedy. G., Sktmore. M., Wong. J., Evaluaton of Rsk Factors Leadng to Cost Overrun n Delvery of Hgway Constructon Projects. Journal of Constructon Engneerng and Management. 36(5). 0, pp. 58-537. [] Molenaar, K.R., Programmatc Cost Rsk Analyss for Hgway Mega Projects. ASCE Journal of Constructon Engneerng and Management, 3(3), 005, pp. 343 53. [] Jannad, O., Almsar, S., Rsk Assesent n Constructon. ASCE Journal of Constructon Engneerng and Management, 9(5), 003, pp. 49 500. [3] Touran, A., Probablstc Model for Cost Contngency. ASCE Journal of Constructon Engneerng and Management, 9(3), 003, pp. 80 4. [4] Ppattanapwong, J., "Development of Mult-Party Rsk and Uncertanty Management Process for an Infrastructure Project.", P.H.D Tess, Koc Unversty of Tecnology, 004. [5] Zade, L.A., Fuzzy Sets. Informaton and control. 8(3): 965, pp. 338-353. [6] Wang, M. and Cou, H., "Rsk Allocaton and Rsk Handlng of Hgway Projects n Tawan", J. of Mgmt. n Engrg. ASCE., 003, pp. 60-68. [7] Herrera-Vedma, E., Herrera F., Cclana F., A Consensus Model for Multperson Decson Makng wt Dfferent Preference Structures, Systems, Man and Cybernetcs, Part A, IEEE Transactons on, v 3(3), 00, pp. 394-40. [8] Cclana, F., Herrera, F., Herrera-Vedma, E., Integratng Tree Representaton, Models n Fuzzy Multpurpose Decson Makng Based on Fuzzy Preference Relatons, Fuzzy Sets Systems., Vol. 97, 998, pp. 33 48. [9] Zadrozny S., An Approac to te Consensus Reacng Support n Fuzzy Envronment. Consensus Under Fuzzness, Kluwer, Norwell, MA, 997. [0] Coudurya, A.K., Sankarb, R., Twar, M.K., Consensus-Based Intellgent Group Decson-Makng Model for te Selecton of Advanced Tecnology. J. Decson Support Systems, 4. 006, pp. 776 799. [] Yager, R.R., On Ordered Wegted Averagng Aggregaton Operators n Mult-Crtera Decson Makng, IEEE Trans.Systems, Man Cybernet. Vol. 8, 988, pp. 83 90. [] Yager, R.R., Famles of OWA Operators, Fuzzy Sets and Systems, Vol. 59, 993, pp 48. [3] Yager, R.R., Aggregaton Operators and Fuzzy Systems Modelng, Fuzzy Sets and Systems, Vol. 67, pp.9 45. [4] Yager, R.R., Quantfer Guded Aggregaton Usng OWA Operators. Internatonal Journal of Intellgent Systems,, 996, pp. 49-73. [5] Lee, Y.W., Bogard, I., Stansbury, J., "Fuzzy Decson Makng n Dredged-Materal Management", J. Envr. Engrg. ASCE., 7(5). 99, pp. 64-630. Internatonal Journal of Industral Engneerng & Producton Researc, Marc 03, Vol. 4, No.
F. Nasrzade, M. Kanzad & H. Manabad A Fuzzy Group Decson Makng Approac 80 [6] Paek, J.H., Lee, Y.W., Naper, T.R., "Selecton of Desgn Buld Proposal Usng Fuzzy-Logc System" J. Constr. Engrg. and Mgmt. ASCE., 8(). 99, pp. 303-37. [7] Cen, S.J., Hwang, C.L., "Fuzzy Multple Attrbute Decson Makng, Metods and Applcatons.", Sprnger, Berln, 99. [8] Cen, S.H., "Rankng Fuzzy Sets wt Maxmzng Set and Mnmzng Set", Fuzzy Sets and Systems, 7(), 985, pp. 3-9. [9] Sobe, O., Ardt, D., "Managng Owners Rsk of Contractor Default.", J. Constr. Engrg. and Mgmt. ASCE.3. 005, pp. 973-978. Internatonal Journal of Industral Engneerng & Producton Researc, Marc 03, Vol. 4, No.