A Fuzzy Group Decision Making Approach Construction Project Risk Management

Transcription

1 Internatonal Journal of Industral Engneerng & Producton Research March 03, Volume 4, Number pp Downloaded from at 4: IRST on Wednesday January nd 09 ISSN: A Fuzzy Group Decson Makng Approach Constructon Project Rsk Management to * F. Nasrzadeh, M. Khanzad & H. Manabad Farnad Nasrzadeh, Department of Cvl Engneerng-Faculty of Engneerng-Payame Noor Unversty, Tehran-Iran Mostafa Khanzad, Assstant Professor, Dept. of Cvl Engneerng - Iran Unversty of Scence and Technology, Tehran, Iran, khanzad@ust.ac.r Hojjat Manabad, M.Sc., Dept. of Cvl Engneerng Iran Unversty of Scence and Technology, Iran, h.manabad@tudelft.nl KEYWORDS ABSTRACT Constructon ndustry, Group decson makng, Fuzzy sets, Mult-crtera decson makng, Rsk management Implementaton of the rsk management concepts nto constructon practce may enhance the performance of project by takng approprate response actons aganst dentfed rsks. Ths research proposes a mult-crtera group decson makng approach for the evaluaton of dfferent alternatve response scenaros. To take nto account the uncertantes nherent n evaluaton process, fuzzy logc s ntegrated nto the evaluaton process. To evaluate alternatve response scenaros, frst the collectve group weght of each crteron s calculated consderng opnons of a group conssted of fve experts. As each expert has ts own deas, atttudes, knowledge and personaltes, dfferent experts wll gve ther preferences n dfferent ways. Fuzzy preference relatons are used to unfy the opnons of dfferent experts. After computaton of collectve weghts, the best alternatve response scenaro s selected by the use of proposed fuzzy group decson makng methodology whch aggregates opnons of dfferent experts. To evaluate the performance of the proposed methodology, t s mplemented n a real project and the best alternatve responses scenaro s selected for one of the dentfed rsks. 03 IUST Publcaton, IJIEPR, Vol. 4, No., All Rghts Reserved.. Introducton Many constructon projects have not yet secured good project goal achevement. Such falure could be realzed n terms of severe project delay, cost overrun and poor qualty []. The presence of rsks and uncertantes mght be responsble for such a falure. Thus, there s a consderable need to ncorporate the rsk management concepts nto constructon practce n order to enhance the performance of project. * Correspondng author: Farnad Nasrzadeh Emal: f.nasrzadeh@gmal.com Paper frst receved Jan. 8, 0, and n accepted form Jul. 07, 0. The dea that rsk management should be an mportant part of project management s currently wdely recognzed by the leadng project management nsttutons []. Dfferent levels of rsk management have been proposed by the researchers and organzatons snce 990. Al-Bahar and Crandall [3], the U.K. Mnstry of Defense [4], Wdeman [5], and the U.S. Department of Transportaton [6] are among those suggestng the use of a process wth four phases. These phases nclude rsk dentfcaton, rsk analyss, rsk response plannng, and control. Feylzadeha et. al. [7] used a fuzzy neural network model to determne the EAC (estmate at completon) cost of the project. The proposed approach consders both qualtatve and quanttatve factors affectng the EAC predcton. Abdelgawad and Fayek [8] extended

2 Downloaded from at 4: IRST on Wednesday January nd 09 F. Nasrzadeh, M. Khanzad & H. Manabad the applcaton of falure mode and effect analyss (FMEA) to rsk management n the constructon ndustry. They used fuzzy logc and fuzzy analytcal herarchy process (AHP) for the rsk analyss. Lu et. al. [9] hghlghted the dfferences between enterprse rsk management (ERM) and project rsk management (PRM). Creedy et. al. [0] addressed the problem of why hghway projects overrun ther predcted costs. It dentfed the owner rsk varables that contrbute to sgnfcant cost overruns. Molenaar [] modelled the rsk events n the constructon cost estmaton as ndvdual components. The rsk analyss was performed usng Monte Carlo smulaton approach. Jannad and Almshar [] used expected value technque to perform the rsk analyss phase for ndvdual rsk. Touran [3] used a probablstc model for the calculaton of project cost contngency by consderng the expected number of changes and the average cost of change. Although there are several researches n the area of rsk management, almost all of them only concentrate on the rsk analyss phase. The rsk response plannng phase s not dscussed n the prevous works and the selecton of the most approprate rsk response acton s manly performed by personal judgment and there s no systematc approach to select the optmum response aganst the dentfed rsks [4]. Ths research proposes a methodology for the evaluaton of dfferent alternatve response scenaros based on ther mpacts on the project objectves n terms of project cost, project duraton and project qualty. The proposed approach s a fuzzy mult-crtera group decson makng approach. To evaluate alternatve response scenaros, frst the collectve group weght of each crteron s calculated consderng opnons of a group conssted of fve experts. As each expert has ts own deas, atttudes, knowledge, and personaltes, dfferent experts wll gve ther preferences n dfferent ways. Fuzzy preference relatons are used to unfy the opnons of dfferent experts. After computaton of collectve weghts, the best alternatve response scenaro s selected by the use of proposed ntegrated fuzzy mult-crtera group decson makng methodology. To evaluate the performance of the proposed methodology, t s mplemented n a real project and the best alternatve responses scenaro s selected for one of the most mportant dentfed rsks.. Concept of Fuzzy Sets Theory Fuzzy set theory ntroduced by Zadeh [5], s used ncreasngly for uncertanty assessment n stuatons where lttle determnstc data are avalable. The use of fuzzy sets theory allows the user to nclude the mprecson, arsng from the lack of avalable nformaton or randomness of a future stuaton. Usng fuzzy set theory n practcal problems would make the models more consstent wth realty. The central A Fuzzy Group Decson Makng Approach 7 concept of fuzzy sets theory s the membershp functon whch represents the degree to whch a member belongs to a set as represented by the followng equaton: ~ A ( x, A~ ( x)) x X () Where, A~ ( x ) s called the membershp functon of x ~ n A that maps x to the membershp space M. 3. Selecton of Optmum Response Aganst the Identfed Rsks Pror to the dscusson of optmum rsk response selecton process, t s necessary to ntroduce alternatve rsk response methods. Rsk response s an acton taken to avod rsks, to reduce the occurrng probablty of rsks, or to mtgate losses arsng from rsks. Rsk handlng methods are classfed nto four categores, ncludng rsk avodance, rsk transfer, rsk mtgaton, and rsk acceptance. Rsk avodance means the rejecton or change of an alternatve to remove some hdden rsk. For example, f a constructon method s contngent on ran, the contractor could avod schedule delay by adoptng another constructon method that wll not be nfluenced by ran. Rsk transfer means the swtch of rsk responsblty between contractng partes n a project. Contractors usually use three rsk transfer methods to offload rsk responsbltes. They are as follows: Insurance Subcontractng. Clams to the owner for fnancal losses or schedule delay. Rsk mtgaton denotes reducton of the occurrng probablty or the expected losses of some potental rsk by ether reducng the probablty or the mpacts of a rsk event. Rsk acceptance ncludes two condtons.e., () Unplanned rsk retenton, where the manager does not take any acton for some rsk; and () Planned rsk retenton, where the manager decdes to take no acton for some rsk after cautous evaluaton [6]. The rsk handlng strateges may nvolve one or a combnaton of multple approaches mentoned heren. To handle rsks approprately, managers need to realze the contents and effects of all alternatve response actons before makng decsons. The objectve of the study presented n ths paper s to provde dfferent constructon partes, wth a decson makng mechansm that wll ad them n the selecton of best alternatve response scenaro to the dentfed rsks whch allow them to make ntellgent and Internatonal Journal of Industral Engneerng & Producton Research, March 03, Vol. 4, No.

3 73 economcal decsons based on the proposed relable fuzzy methodology. Downloaded from at 4: IRST on Wednesday January nd 09 A Fuzzy Group Decson Makng Approach F. Nasrzadeh, M. Khanzad & H. Manabad 3.. Selecton of Evaluaton Crtera Each potental rsk may have a negatve mpact on project objectves n terms of project delay, cost overrun and poor qualty. Selecton crtera are drectly lnked wth project objectves, both tangble, ncludng tme and cost and ntangble.e., qualty. Implementaton of alternatve response scenaros may decrease the negatve mpacts of rsks. However, the mplementaton of alternatve response scenaros wll mpose addtonal expenses on the project, Therefore, after mplementaton of alternatve response scenaros, the value of dfferent project performance objectves s determned as the deducton of two aforementoned terms. Fnally the selecton factors that are relevant to the decson makng problem are selected as below:. Project duraton. Project cost 3. Project qualty DM where s scaled n a to 9 scale. Utlty functon s shown as U where DM explans hs/her preferences on alternatves as utlty values. Utlty value of alternatve xs gven by DM s presented by u s 0,. Before aggregatng DMs' assessments, the opnons should be unfed nto fuzzy preference relatonshp by an approprate transformaton functon. A common transformaton functon between the varous preferences s presented below [8]: K sm by DM to alternatve xs. Fuzzy preference relaton s expressed, ksm by membershp functon ( x s, xm ) k, sm k where k sm X * X k : X X 0,, wth and where X x,..., xn s a fnte set of alternatves. Value of k sm defnes a rato of the fuzzy preference ntensty of alternatve xs to xm. Multplcatve preference relatons are represented as A where and asm s a rato of the fuzzy A X * X, A asm preference ntensty of alternatve xs to xm gven by () o os K sm ( m ) n K sm ( log 9 a sm ) (3) (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 wth an assocated vector of weghts n 3.. Computaton of Collected Weghts of Crtera In ths secton the aggregated weghts of dfferent crtera s calculated. For calculaton of the group weght of each crteron, decson makers should evaluate relatve mportance of crtera. Snce each expert has ts own deas, atttudes, motvatons, and personaltes, they wll gve ther preferences n dfferent ways. Herrera-Vedma et al [7] states that group members may express ther opnons as ) preference orderng, ) utlty values, 3) fuzzy preference relatons and 4) multplcatve preference relatons. These opnons can be converted nto the varous representatons usng approprate transformatons [8]. In ths paper, fuzzy preference relatons are used to unfy opnons. Fuzzy relatonshps n the evaluaton are used to ncorporate the uncertantes n the decson opned by a partcular decson maker. In addton, decson makng becomes dffcult when the avalable nformaton s ncomplete or mprecse [9], [0]. In these assessments, preference orderngs of alternatves are represented by O s, whch defnes preference orderng evaluaton gven (u s ) (u ) (u m ) s w n, w 0, such that: n Fw ( x) w.b, x I n (5) wth b denotng the th largest element n x; ; xn. The most mportant characterstc of OWA operator s that t may produce many solutons based on decson maker s objectve characterstcs. In the other word, OWA operator consders decson maker s subjectve characterstcs to estmate collectve value; whereas, other aggregaton operators have not ths mportant characterstc. An mportant problem n usng OWA aggregaton operator s how to obtan the assocated weghtng vector. There are two approaches to calculate the weghtng vector w. In the frst approach, the weghtng vector s calculated usng sample data as the functon of the values to be aggregated. In the second approach, however, the weghtng vector w s calculated usng lngustc quantfers. In ths approach that was ntroduced by Yager, the weghtng vector s calculated as follow [], [4]: w Q ( ) Q ( ) n n,,..., n (6) Q s a fuzzy lngustc quantfer that represents the concept of fuzzy majorty, s calculated as: 0 r-a Q( r ) b-a f : r a f : b r a f : r b (7) The most common lngustc fuzzy quantfers used are most, at least half, and as many as possble. Internatonal Journal of Industral Engneerng & Producton Research, March 03, Vol. 4, No.

4 A Fuzzy Group Decson Makng Approach Downloaded from at 4: IRST on Wednesday January nd 09 F. Nasrzadeh, M. Khanzad & H. Manabad Ther ranges are gven as (.3,.8), (0,.5) and (.5, ), respectvely [0]. Fve consdered DMs represented ther vews on the varous crtera ncludng project duraton, project cost and project qualty n four dfferent ways. The frst DM presented hs vew n the form of utlty functons, the second DM remarked hs vew n preference orderng of the alternatves, the thrd DM proposed hs vew n multplcatve preference relaton on a scale of to 9 and the fourth DM expressed hs vew n fuzzy preference relaton, and the ffth DM presented hs vews n utlty functon, as follows: Transformed and unformed values n prevous step are aggregated usng OWA operator and aggregaton weghts n the aggregaton step that resulted from quantfer "most" wth the doman (.3,.8) are (0, 0., 0.4, 0.4, 0). The resulted collectve fuzzy preference opnon s: Collectve soluton= DM.5,.6,.5 DM,, 3 DM 5.5,.5,.3 DM For calculaton of fnal aggregated weght of each crteron, the values of collectve soluton must be aggregated together. Fuzzy lngustc quantfer "as many as possble" wth doman (.5, ) s utlzed. Hence, correspondng weght vector wth ths operator s W= (0,.33,.67) and collectve weght of each crteron s: DM G Before assgnng these values to weghts, they should be normalzed. The normalzed weght vector s: DM G , DM The varous forms of presented opnons are transformed nto fuzzy preference relaton usng the prevously defned transformaton functons , DM, DM 3 DM , DM 5 DM Selecton of the Optmum Response Scenaro Usng the Proposed Fuzzy Mult-Crtera Group Decson Makng Approach The structure of the proposed fuzzy mult-crtera decson makng approach s depcted n Fg.. The proposed fuzzy mult-crtera decson makng approach was adapted from the model developed by Lee, Y. et al. [5] for dredged materal management. DSS Structure Aggregaton Module Converson of Scores nto Fuzzy Numbers Indexaton Converson of Fuzzy Numbers nto Indexes Aggregaton of Scores Fnal Rankng Fuzzfcaton of fnal Scores Rankng Module Fg.. The structure of the proposed fuzzy mult-crtera group decson makng approach [adopted from 5 and 6] The model comprses three man sectors. At frst assgned scores are converted nto the fuzzy set. Thereafter scores for each alternatve system would be aggregated at aggregaton module. Fnally alternatve response scenaros are ranked based on the acqured fnal scores at aggregaton module, whch are fuzzy numbers. If Z (x) s assumed as a fuzzy value for th alternatve, ts membershp functon wll be [ Z ( x)] as denoted n Fg. wth a trapezod membershp functon. Membershp degree for each value would be assgned based on the expert's judgment. Internatonal Journal of Industral Engneerng & Producton Research, March 03, Vol. 4, No.

5 75 F. Nasrzadeh, M. Khanzad & H. Manabad ( Z ( x)) Z,h ( x) could be converted nto S, h ( x ) ndex as most lkely nterval follows:. If BES Z > WOR Z then: h Downloaded from at 4: IRST on Wednesday January nd 09 A Fuzzy Group Decson Makng Approach Z,h ( x) a Z (x) b largest lkely Interval th Z,h ( x) WORZ S,h ( x ) BESZ WORZ 0 th Fg.. Fuzzy score of x alternatve aganst crteron As t s shown n Fg., Z,h ( x) s an nterval n whch membershp degrees are hgher than h. Ths nterval, whch has been assgned based on h lkely nterval, s a sub-set of the fuzzy set and has been ntroduced based on level-cut concept. One of these ntervals Z, ( x ) s the most lkely nterval, where the membershp degrees are one. Moreover Z, 0 ( x) s largest lkely nterval and f any of Z (x) fall out of ths nterval ts membershp degree would be zero. Converson of Scores Into Indexes: Snce dfferent crtera, wth dfferent characterstcs and unts, are gong to be ntegrated; Z,h ( x ) as score assgned to each response scenaro regardng every crteron should be converted nto an ndex. Ths 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 that reason, consderng (BES Z ) and Z,h ( x ) BESZ WORZ Z,h ( x) BESZ (8) Z,h ( x ) WORZ. If WOR Z >BES Z then: Z,h ( x) WORZ S,h ( x ) BESZ WORZ 0 Consequently Z,h ( x ) BESZ BESZ Z,h ( x ) WORZ (9) Z,h ( x ) WORZ Z,h ( x) as a fuzzy functon s converted to S, h ( x ) and related trapezod dagram s transformed to the followng dagrams (Fg.3). Two condtons have been consdered above, due to the reason that usually characterstcs are assessed n two drectons. That s, regardng some crtera lke Qualty, gettng greater score s equal to beng more approprate, so frst equaton would be assgned to these types of crtera. In contrast concernng some crtera lke tme or cost, gettng greater score means less acceptablty, therefore second equaton would be assgned for these types of crtera. Subsequently mpact of the scorng drecton s crossed out and results from all crtera could be summed up. (WOR Z ) respectvely as best and worst values Fg. 3. Transferrng fuzzy values to ndex value Aggregaton of Scores of Each Alternatve Response Scenaro: For summng up all the scores and obtanng fnal score concernng each response scenaro followng equaton could be exploted: n p I h ( x) W S,h ( x) P Fg. 4. Membershp functon of the fnal score regardng each alternatve [adopted from 5 and 6] (0) Where n= the number of crtera; S,h = Index for th crteron wth h level of acceptance; w = Related Internatonal Journal of Industral Engneerng & Producton Research, March 03, Vol. 4, No.

6 A Fuzzy Group Decson Makng Approach F. Nasrzadeh, M. Khanzad & H. Manabad weght of each crteron ( w ; P= balancng Downloaded from at 4: IRST on Wednesday January nd 09 factor and I h (x ) = Fnal ndex for each crteron wth h level of acceptance. The balancng factor P ( P ) ) s a factor whch shows mportance of devaton magntude between a crteron value and the best crteron for that value and would be proposed for a group of crtera. Therefore f P= then all devatons wll get equal weght, and f P= each devaton wll 76 get weght n proporton to ts scale. In general P 3 would be used for lmtng crtera [6]. Furthermore f each crteron comprses other crtera, ths equaton could be extended for lower levels and then fnal result would be reached by addng up results of each level. Consequently evaluaton process could be followed up n dfferent levels so as to obtan fnal score regardng each alternatve [5]. Fg. 5. fnal dea's score functons wth related utlty functons [adopted from 5 and 6] Preparng Proposed Alternatve Response Scenaros for Rankng: After acqurng fnal ndex for each alternatve, membershp functon of a fuzzy set [ I (n)] wll be fgured out utlzng equaton (6). The membershp functon s a pecewse lnear functon, n whch I (x ) s member of the fuzzy set assocated wth fnal score of the x th alternatve. Ths could be performed by calculatng I h 0 ( x ), and I h ( x) whose levels of acceptance are zero and one respectvely. I R mn ( x) rmn Rmn I ( x) I ( x ) Rmax rmax Rmax 0 rmn I ( x) rmax Rmn I ( x) rmn () rmax I ( x) Rmax otherwse rmax and rmn = lowest and hghest value of I h ( x) for fnal ndex respectvely Rmax and Rmn = lowest and hghest value of I h 0 ( x ) for fnal ndex respectvely I h 0 ( x) and I h ( x) are resulted from Z, h 0 ( x) and Z,h ( x) correspondngly. If n alternatve response scenaros have been consdered for rankng, there wll be n fuzzy sets as I ( n ) n,,..., n whose membershp functons wll be resulted from equaton (). Fnal Rankng of Alternatve Response Scenaros: Snce the values whch are assgned to each alternatve response scenaro are fuzzy, ther rankng could not to be done by conventonal straghtforward rankng methods. Therefore, a fuzzy rankng method s requred to fulfll the objectve. Accordng to Chen and Hwang opnon, varety of the rankng methods whch are proposed for fuzzy MCDM's, can be categorzed nto four groups [7]:. Utlzng preferences rato, by applyng technques such as degree of optmalty, hammng dstance, ɑ-cut and comparson functon.. Fuzzy mean and spread by applyng probablty dstrbuton. 3. Fuzzy scorng whch nvolves technques such as proportonal optmal, left rght scores, centrod ndex and area management. 4. Utlzng lngustc expresson. The method chosen for ths purpose s developed by Chen [8] through applyng mnmzng and maxmzng sets [8]. The maxmzng set M s a fuzzy subset wth membershp functon of M, defned as follows: I I mn / I max I mn M (I ) 0 I mn mn (mn I h 0 ( x)) I mn I I max () otherwse for x,.., n (3) I max max (max I h 0 ( x)) for x,.., n Therefore rght utlty value U R (x) for would be determned as: (4) x th alternatve U R ( x) max mn ( M ( I ( x), ( I ( x)) (5) In the same way mnmzng set G s also ntroduced as a fuzzy subset wth membershp functon of G : Internatonal Journal of Industral Engneerng & Producton Research, March 03, Vol. 4, No.

7 77 A Fuzzy Group Decson Makng Approach F. Nasrzadeh, M. Khanzad & H. Manabad I I max / I mn I max G ( I ) 0 I mn I I max otherwse The frst alternatve response scenaro whch may be mplemented aganst the nclement weather rsk s to avod t by change n project schedule. It means that the executon plan of the project s changed n a manner that the concretng work s postponed to the 5th month to avod the negatve mpacts of the rsk. (6) Downloaded from at 4: IRST on Wednesday January nd 09 And then left utlty value U L (x) for alternatve system x would be determned as follows: U L ( x) max(mn ( G ( L), ( I ( x))) (7) Rsk Acceptance: The second alternatve response scenaro whch may be mplemented aganst nclement weather rsk s ts acceptance, where the manager does not take any acton aganst ths rsk. Consequently total utlty or rankng value for proposal x s: U ( x) U R ( x) U L ( x) (8) Rsk Mtgaton: In the 3rd alternatve response scenaro, the potental expected losses caused by the nclement weather rsk are reduced. To reduce the schedule delay caused by ths rsk, the overtme polcy s mplemented durng the 3rd and 4th months. The alternatve wth best total utlty value would be presented as the best opton, thus all alternatves would be sorted based on ther total utlty values. 4. Model Applcaton The proposed fuzzy group decson makng approach can be used for the selecton of optmum response aganst the dentfed rsks. To evaluate the performance of the proposed methodology t has been mplemented n a sample real project. Ths project s related to the executon of a large massve concrete foundaton of a hgh rse buldng. Ths project nvolves 500 cubc meter of concretng and ts duraton has been estmated as 5 months. The total cost of the project, ncludng both drect and ndrect costs, has been estmated as dollars. Facng to nclement weather rsk s one of the most mportant rsks dentfed for ths project. The proposed fuzzy group decson makng approach s mplemented to select the most effectve alternatve response scenaro aganst ths rsk. In ths project case example, t s expected that nclement weather rsk wll be occurred durng the 3rd and 4th months. The occurrence of ths rsk would have negatve mpacts on the constructon productvty and may lead to project cost overrun, project delay and poor qualty. The alternatve response scenaros whch have been dentfed for ths rsk are explaned below brefly. Rsk avodance: Rsk Transfer: Fnally n the last alternatve response scenaro, the potental losses arsng from nclement weather rsk are transferred through subcontractng or nsurance. A group consstng of fve experts was consdered to carry out the case study, through applcaton of the proposed model. A spread sheet program s also provded n order to help rsk analyss team durng the selecton process. Bref outcomes of the assessment performed by the proposed fuzzy group decson makng approach are presented n table. As shown n table, usng the proposed fuzzy group decson makng approach, t s concluded that the rsk avodance s the best alternatve response scenaro. It should be emphaszed that ths evaluaton was made based on the proposed case and n dfferent stuatons the outcome of the assessment could vary dependng on the actual requrements and restrants. It s beleved that the proposed fuzzy group decson makng approach provdes a powerful tool for the selecton of optmum response scenaro aganst the dentfed rsks. Tab.. Scorng and fnal results Response Scenaro Acceptance Avod Mtgate Transfer nterval Project Cost Project Duraton Project Qualty most lkely nterval least lkely nterval most lkely nterval least lkely nterval most lkely nterval least lkely nterval most lkely nterval least lkely nterval left utlty value rght utlty value total utlty value Internatonal Journal of Industral Engneerng & Producton Research, March 03, Vol. 4, No.

8 A Fuzzy Group Decson Makng Approach F. Nasrzadeh, M. Khanzad & H. Manabad Downloaded from at 4: IRST on Wednesday January nd Senstvty Analyss In OWA method, rsk level of DMs s accounted n an explct manner. At ths decson-makng problem, senstvty analyss s carred out consderng the change n the DMs optmsm degree or ther rsk level and ts mpact on weghtng coeffcents and fnal ranks of alternatves. For senstvty Analyss, another equaton was used to calculate the functon Q to fnd the order weghts of OWA operator. The equaton Q(r ) r, 0 havng many applcatons n calculaton of membershp functon of a quantfer can be used n whch α s optmstc coeffcent of DM. If α >, t ndcates pessmsm or rsk-averse decsonmaker. If α=, t means decson-maker s neutral. Fnally, α<, represents optmstc or rsk-prone decson-maker. The order weghts of OWA operator depend on the manager s optmsm/pessmsm vew on the rsk. If the DM has an optmstc vew then larger 78 weghts wll be assgned to the frst ranks n the OWA operator and therefore the model wll have larger outputs. Based on ths percepton, Yager (988) has defned the optmsm degree θ n the followng way: Q(r )dr 0 (9) Transformed and unformed values of DMs n secton 3. are aggregated usng OWA operator wth regard to dfferent optmsm degree (α=0.0, 0., o.5,,, 0). For calculaton of fnal aggregated weghts of crtera, the calculated collectve fuzzy preference opnons are aggregated usng fuzzy lngustc quantfer "most" wth doman (.3,.8) and correspondng weght vector W= (.067,.663,.7). The fnal normalzed weght vector of crtera s shown n Table. Tab.. Senstvty analyss for the normalzed weghts of crtera at dfferent rsk levels Rsk Prone Neutral Rsk Averson Crtera w w w3 α=0.0 α=0. α=0.5 α= α= α= It can be clearly seen that by ncreasng α and decreasng optmsm degree or rsk level of DMs, the relatve weghts of the frst and second attrbute s ncreased. In contrast, the relatve weght of thrd crteron s declned n smlar stuaton. In table 3 the results of the senstvty analyss carred out for the scorng and fnal results s presented at dfferent rsk levels. Tab. 3. Senstvty analyss for the scorng and fnal results at dfferent rsk levels Rsk Prone Neutral Rsk Averson Response Scenaro α=0.0 α=0. α=0.5 α= α= α=0 Acceptance Avod Mtgate Transfer Conclusons and Remarks In ths study a fuzzy group decson makng approach s exerted to perform constructon project rsk management whch assst dfferent project partes to select the optmum response aganst dentfed rsks. The model s well suted for stuatons where crtera have varyng degree of mportance as well as uncertan values. Snce the rsk response plannng should be performed at the earler stages of the project and takng account of more ndefnteness exsted n those stages, ntroducng fuzzy sets theory could beneft decson makers to make more tangble and realstc evaluaton. In the proposed methodology, frst the group weght of each crteron s calculated. As each expert has ts own deas, atttudes and personaltes, dfferent experts wll gve ther preferences n dfferent ways. The fuzzy preference relatons have been used to unfy these opnons for calculaton of the collectve weghts of each crteron. The best alternatve response scenaro s then selected by the use of the proposed fuzzy group decson makng methodology. It should be taken nto account that n spte of superfcal complexty, the model s rather practcal and straghtforward and could be utlzed n order to acheve more relable assessment of the alternatve response scenaros. More smplfcaton, however, could encourage rsk Internatonal Journal of Industral Engneerng & Producton Research, March 03, Vol. 4, No.

9 Downloaded from at 4: IRST on Wednesday January nd A Fuzzy Group Decson Makng Approach F. Nasrzadeh, M. Khanzad & H. Manabad management teams to more utlze t. The proposed model was mplemented n a real project. The alternatve response scenaros aganst one of the most mportant dentfed rsks,.e., nclement weather rsk were dentfed. The outcome of the case study ndcated that the rsk management team has selected the rsk avodance as the best alternatve response scenaro. It s beleved that the proposed fuzzy group decson makng approach provdes a powerful tool for the selecton of optmum response scenaro aganst the dentfed rsks. [] Molenaar, K.R., Programmatc Cost Rsk Analyss for Hghway Mega Projects. ASCE Journal of Constructon Engneerng and Management, 3(3), 005, pp References [4] Ppattanapwong, J., "Development of Mult-Party Rsk and Uncertanty Management Process for an Infrastructure Project.", P.H.D Thess, Koch Unversty of Technology, 004. [] Nasrzadeh, F., Afshar, A., Khanzad, M., Dynamc rsk analyss n constructon projects, Canadan Journal of Cvl Engneerng. 35, 008, pp [] Project Management Insttute PMI., A Gude to the Project Management Body of Knowledge. (PMBoK Gude), Project Management Insttute, New town Square, Pa, 008. [3] Alabar, j., Crandall K., "Systematc Rsk Management Approach for Constructon Projects.", J. Constr. Engrg. and Mgmt. ASCE.6(3). 990, pp [4] Mnstry of Defence, Procurement Executve, Drectorate of Procurement Polcy MoD-PE-DPP.99. Rsk Management n Defence Procurement., Document ref. D/DPP (PM)///, Whtehall, 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 the DoT., HAPTER3.htm. [7] Feylzadeh, M.R., Hendalanpour, A., Bagherpour, M., A Fuzzy Neural Network to Estmate at Completon Costs of Constructon Projects. Internatonal Journal of Industral Engneerng Computatons, do: 0.567/j.jec [8] Abdelgawad, M., Fayek, A.R., Rsk Management n the Constructon Industry usng Combned Fuzzy FMEA and Fuzzy AHP. Journal of Constructon Engneerng and Management. 36(9). 00, pp [9] Lu, J.Y.a., Low, S.P., He, X.a, Current Practces and Challenges of Implementng Enterprse Rsk Management (ERM) n Chnese Constructon Enterprses. Internatonal Journal of Constructon Management, (4). 0, pp [0] Creedy. G., Sktmore. M., Wong. J., Evaluaton of Rsk Factors Leadng to Cost Overrun n Delvery of Hghway Constructon Projects. Journal of Constructon Engneerng and Management. 36(5). 0, pp [] Jannad, O., Almshar, S., Rsk Assessment n Constructon. ASCE Journal of Constructon Engneerng and Management, 9(5), 003, pp [3] Touran, A., Probablstc Model for Cost Contngency. ASCE Journal of Constructon Engneerng and Management, 9(3), 003, pp [5] Zadeh, L.A., Fuzzy Sets. Informaton and control. 8(3): 965, pp [6] Wang, M. and Chou, H., "Rsk Allocaton and Rsk Handlng of Hghway Projects n Tawan", J. of Mgmt. n Engrg. ASCE., 003, pp [7] Herrera-Vedma, E., Herrera F., Chclana F., A Consensus Model for Multperson Decson Makng wth Dfferent Preference Structures, Systems, Man and Cybernetcs, Part A, IEEE Transactons on, v 3(3), 00, pp [8] Chclana, F., Herrera, F., Herrera-Vedma, E., Integratng Three Representaton, Models n Fuzzy Multpurpose Decson Makng Based on Fuzzy Preference Relatons, Fuzzy Sets Systems., Vol. 97, 998, pp [9] Zadrozny S., An Approach to the Consensus Reachng Support n Fuzzy Envronment. Consensus Under Fuzzness, Kluwer, Norwell, MA, 997. [0] Choudhurya, A.K., Shankarb, R., Twar, M.K., Consensus-Based Intellgent Group Decson-Makng Model for the Selecton of Advanced Technology. J. Decson Support Systems, , pp [] Yager, R.R., On Ordered Weghted Averagng Aggregaton Operators n Mult-Crtera Decson Makng, IEEE Trans.Systems, Man Cybernet. Vol. 8, 988, pp [] Yager, R.R., Famles of OWA Operators, Fuzzy Sets and Systems, Vol. 59, 993, pp [3] Yager, R.R., Aggregaton Operators and Fuzzy Systems Modelng, Fuzzy Sets and Systems, Vol. 67, pp [4] Yager, R.R., Quantfer Guded Aggregaton Usng OWA Operators. Internatonal Journal of Intellgent Systems,, 996, pp [5] Lee, Y.W., Bogard, I., Stansbury, J., "Fuzzy Decson Makng n Dredged-Materal Management", J. Envr. Engrg. ASCE., 7(5). 99, pp Internatonal Journal of Industral Engneerng & Producton Research, March 03, Vol. 4, No.

10 F. Nasrzadeh, M. Khanzad & H. Manabad A Fuzzy Group Decson Makng Approach Downloaded from at 4: IRST on Wednesday January nd 09 [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 [7] Chen, S.J., Hwang, C.L., "Fuzzy Multple Attrbute Decson Makng, Methods and Applcatons.", Sprnger, Berln, 99. [8] Chen, S.H., "Rankng Fuzzy Sets wth Maxmzng Set and Mnmzng Set", Fuzzy Sets and Systems, 7(), 985, pp [9] Sobe, O., Ardt, D., "Managng Owners Rsk of Contractor Default.", J. Constr. Engrg. and Mgmt. ASCE , pp Internatonal Journal of Industral Engneerng & Producton Research, March 03, Vol. 4, No. 80