A METHODOLOGY FOR RATING AND RANKING HAZARDS IN MARITIME FORMAL SAFETY ASSESSMENT USING FUZZY

Transcription

1 Doumas N. Geogos, Nktakos V. Nñtas, ambou A. aa A ETODOOGY FOR RATING AND RANKING AZARDS IN ARITIE FORA SAFETY ASSESSENT USING FUZZY OGIC A ETODOOGY FOR RATING AND RANKING AZARDS IN ARITIE FORA SAFETY ASSESSENT USING FUZZY OGIC Doumas N. Geogos, Nktakos V. Nñtas, ambou A. aa Unvesty of the Aegean, Dept. of Shppng Tade and Tanspot, Chos, Geece Keywods decson makng, Fomal Safety Assessment, hazad dentfcaton, mane safety, fuzzy logc Abstact Fomal safety assessment of shps has attacted geat attenton ove the last few yeas. Ths pape, followng a bef evew of the cuent status of mane safety assessment s focused on the hazads dentfcaton (AZID) and potsaton pocess. A multctea decson makng famewok, whch s based on expets estmaton, s then poposed fo hazads evaluaton. Addtonally n ths pape many aspects of the evaluaton famewok ae pesented ncludng the synthess of evaluaton teams, the assessment of the mpotance of ctea, the evaluaton of the consequences of the altenatve hazads and the fnal ankng of the hazads. The poposed methodology has the nnovatve featue of embodyng technques of fuzzy logc theoy nto the classcal multctea decson analyss. The pape concludes by explong the potentalty of the above methodology n povdng a obust and flexble evaluaton famewok sutable to the chaactestcs of a hazad evaluaton poblem.. Intoducton azad dentfcaton (AZID) s the fst and n many ways the most mpotant step n a sk assessment. Ths pape, followng a bef evew of the cuent status of mane safety assessment s focused on the hazads dentfcaton and potsaton pocess. azad Identfcaton s the pocess of systematcally dentfyng hazads and assocated events that have the potental to esult n a sgnfcant consequence. The am of AZID s fst to poduce a lst of all possble hazads and second to evaluate them n ode to potse them. In ode to suppot the evaluatng pocedue we popose as a tool the ultctea Decson Analyss (CDA). The eason s that the fnal decson depends on ctea, whch coelate the potental hazadous scenaos wth dffeent consequences. CDA deals wth the poblem of ankng vaous altenatves n the pesence of multple ctea. Up to now, thee ae a vaety of methods that one can choose fom solvng a multctea decson poblem, the most famous beng the maxmn, the weghted aveage, the multctea utlty evaluaton and the Analytcal eachcal Pocess [3]. All the afoementoned methods assume that the decson make s able to povde exact assessments on the mpotance of the mpotance of evaluaton ctea on the mpact of altenatves. oweve, owng to the avalablty and subjectvty of nfomaton, t s vey dffcult to obtan exact assessment data as concens the fulflment of the equements of the ctea o the elatve mpotance of each cteon. Classcal decson-makng methodologes ae thus ctczed fo ove-smplfyng the decson-makng pocess by focng the expets to expess the vews on pue numec scales. It s common evdence that assessments made by expets ae mostly of subjectve and qualtatve natue. Fuzzy sets theoy, ognally poposed by. A. Zadeh [22], s an effectve means to deal wth the vagueness of human judgement. Ths theoy offes us tools to handle lngustc tems as the ones

2 Doumas N. Geogos, Nktakos V. Nñtas, ambou A. aa A ETODOOGY FOR RATING AND RANKING AZARDS IN ARITIE FORA SAFETY ASSESSENT USING FUZZY OGIC mentoned above by convetng them to sutable fuzzy sets and numbes. Fuzzy multctea decson analyss methods allow us to ntegate lngustc assessments and weghts n a multctea decson analyss settng [], [4]. Afte fuzzy sets geneal methodology pesentaton ths pape poposes an applcaton to evaluate and ank a numbe hazads. We assume a mult-ctea decson makng famewok, whee sets of geneal and doman-specfc ctea ae used to judge the elatve mpact of evaluatng hazads. The poposed methodology has the nnovatve featue of embodyng technques of fuzzy logc theoy nto the classcal multctea decson analyss. 2. azad dentfcaton azad dentfcaton (AZID) s the fst and n many ways the most mpotant step n a sk assessment. An ovelooked hazad s lkely to ntoduce moe eo nto the oveall sk estmate than an naccuate consequence model o fequency estmate. The am of the AZID s to poduce, theefoe, a compehensve lst of all hazads. The lst should nclude all foeseeable hazads, but t should also avod double countng by ncludng the same hazad unde moe than one headng. In ode to dstngush between hazads and consequences, t s advsable to stat wth defnng a hazad. In fomal shp safety assessment, a hazad s defned as a physcal stuaton wth potental fo human njuy, damage to popety, damage to the envonment o some combnaton [2]. Theefoe, shp goundng s consdeed as a possble consequence of hazads elated, fo example, to navgaton eo/falue, and not as a hazad tself. Smlaly, navgaton shp manoeuvng, etc. ae consdeed as hazadous opeatons because a component falue could lead to a chan of unwanted outcomes. AZID s concened wth usng banstomng technque nvolvng taned and expeenced pesonnel to detemne the hazads. AZID s, most of the tme a qualtatve execse stongly based on expet judgement. any dffeent methods ae avalable fo hazad dentfcaton and some of them have become standad fo patcula applcatons. Expeence poved that thee s no need to specfy whch technque should be used n patcula cases. Typcally, the system beng evaluated s dvded nto pats and the team leade chooses the methodology, whch can be standad technque, a modfcaton of one of these o, usually, a combnaton of seveal. In othe wods, the technque used s not that mpotant snce each goup can follow a methodology of combned technques. The most mpotant thng s that the AZID has to be ceatve n ode to obtan compehensve coveage of hazads skppng as fewe aeas as t could pactcably be. Also, t s vey mpotant that the conclusons of AZIDs wll be dscussed and documented dung a fnal sesson, so that they epesent the vews of the goup athe than of an ndvdual. Vaous scentfc safety assessment appoaches such as Pelmnay azads Analyss (PA), Falue ode, Effects and Ctcalty Analyss (FECA) and azad and Opeablty (AZOP) study can be appled n ths step [2]. 3. azad analyss azad analyss appoach s consdeed a sutable tool fo shp safety assessment. In ths appoach t s assumed that each specfc hazad can be epesented by one o seveal theats that have the potental to lead to an ncdent o top (ntatng) event [8]. A theat can be a specfc hazad o a moe detaled epesentaton of a specfc hazad. Each accdental event may lead to unwanted consequences. If a azad s eleased, the accdental event can escalate to one of the seveal possble consequences. To pevent escalaton, the mtgaton measues, emegency pepaedness and escalaton contol measues need to be n place to stop chan of events popagaton and/o to mnmze the consequences of escalaton [9]. At the table ae descbed some geneal hazads, whch ae analysed n moe detaled hazads.

3 Doumas N. Geogos, Nktakos V. Nñtas, ambou A. aa A ETODOOGY FOR RATING AND RANKING AZARDS IN ARITIE FORA SAFETY ASSESSENT USING FUZZY OGIC Table. st of hazads 4. The buldng blocks Geneal azad Impacts and collson Shp elated Navgaton anoeuvng Fe/exploson oss of contanment Specfc azad Vessel collson Stkng whle at beth Floodng oadng/oveloadng Navgaton eo Vessel not unde command Fne manoeuvng eo Bethng/unbethng eo Cago tank fe/exploson Fe n accommodaton Othe fes Release of flammables Release of toxc mateal The evaluaton settng assumed though out the pape eflects a athe epesentatve stuaton faced by hazad evaluatos. Ths s manly chaactezed by the followng: Thee s a numbe of hazads and the objectve s to evaluate the elatve mpact fo each hazad and fnally to povde an odeng fom the hghest (hghest scoe) to the lowest (lowest scoe) of the set of the hazads. The hghest hazad s that one whch causes the wost consequences. Fo the evaluaton pocess a set of ctea s used, whch follows a tee-lke stuctue. The depth of the ctea tee, whch somehow eflects the depth of the analyss, s usually not constant but vaes wth the thematc aea unde consdeaton. The totalty of evaluaton ctea s dvded n two clustes: the goup of geneal and thematc ctea. As the name ndcates, the ctea of the thematc class vay wth the hazad doman, wth the geneal ctea can be natually appled to geneal stuatons accodng to type of effects (e.g. safety, popety damage, msson nteupton, envonmental effects e.t.c.). A panel of expets s used to evaluate hazads by means of the evaluaton ctea heachy. Geneally, both thematc aea and evaluaton heachy ae gven n advance and expets ae asked ethe to gve the opnon usng lngustc tems on the elatve mpotance of the ctea to the oveall objectve o to the degee at whch evey hazad appeals to the equements set by each cteon. 5. ethodology usng fuzzy logc 5.. Fuzzy numbes and athmetc When dealng wth numec evaluaton data, fndng the weghted aveage of ndvdual scoes and aggegatng acoss the heachy s moe o less a tval task. oweve, when dealng wth fuzzy quanttes t s not clea at all what s the outcome of cetan expessons, such as vey good o vey mpotant. One needs an athmetc that could sutably genealst basc numbe opeatons such as addton o multplcaton. The theoy of fuzzy sets offes a moe systematc famewok fo handlng expet lngustc assessments. Ths scentfc aea attempts to captue the vagueness that s an nheent chaactestc of qualtatve appasals [2], [7], [], [23]. A fuzzy numbe s consdeed as a fuzzy set ove the set of all eal numbes. Geneally, thee s much feedom n choosng between dffeent shapes fo the membeshp functon (efes to the degee of membeshp fo a fuzzy numbe, vayng fom no to full membeshp and takes ates fom 0 to ) of a fuzzy numbe. oweve, smple ones, such as a tangula o tapezodal, ae fequently moe convenent to handle. A tapezodal (tangula) fuzzy numbe s a fuzzy numbe whose membeshp functon foms a tapezum (tangle). Thoughout ths pape, tapezodal fuzzy numbes ae denoted by (α, α 2, α 3, α 4 ), whee

4 Doumas N. Geogos, Nktakos V. Nñtas, ambou A. aa A ETODOOGY FOR RATING AND RANKING AZARDS IN ARITIE FORA SAFETY ASSESSENT USING FUZZY OGIC α, α 2, α 3, α 4 coespond to the tapezum s angle ponts (α α 2 α 3 α 4 ). Note that a tangula fuzzy numbe s a specal case of tapezodal wth α 2 =α 3. Athmetc smla to that of eal numbes can be also developed by fuzzy numbes by extendng the basc algebac opeatons of addton, subtacton, multplcaton and dvson. The applcaton of the above opeatons to fuzzy numbes yelds always a new fuzzy numbe [6]. In the case of tapezodal fuzzy numbes computatons ae geatly smplfed. et A ~ = (α, α 2, α 3, α 4 ) and B ~ = (b, b 2, b 3, b 4 ) be any two stctly postve tapezodal fuzzy numbes (t s custom n fuzzy sets lteatue to use ~ above lettes to dscmnate fuzzy fom csp quanttes). Then, t can be poven that coespondng algebac opeatos {,,, } fo fuzzy sets ae as follows [3]: A ~ B ~ = (α +b, α 2 +b 2, α 3 +b 3, α 4 +b 4 ) A ~ B ~ = (α -b, α 2 -b 2, α 3 -b 3, α 4 -b 4 ) A ~ B ~ = (α xb, α 2 xb 2, α 3 xb 3, α 4 xb 4 ) A ~ B ~ = (α /b 4, α 2 /b 3, α 3 /b 2, α 4 /b ) whee the ccle s used to notfy that the opeato apples to fuzzy and not odnay numbes Defuzzfcaton pocedue Gong back to the poblem of ankng e-sevces, we see that fuzzy numbes and the athmetc povde us wth a convenent tool fo easonng wth qualtatve lngustc assessments. In patcula, one could easly epesent each lngustc tem, such as poo, fa, etc., by a fuzzy numbe on a pedefned numec scale (e.g. 0-, 0-0). In such a way, one gves se to a set of fuzzy weghts and fuzzy ates, upon whch an assessment scheme can be based. oeove, the algeba of fuzzy numbes, pesented above and n patcula the extended opeatons of addton and multplcaton, povde us wth a tool fo calculaton-weghted aveages of lngustc data. As seen, the oveall pefomance of e-sevces s gven n tems of a fuzzy set, whch s somehow expected as any algebac opeaton on two abtay fuzzy numbes yelds always a new one. Ths vague pctue of the oveall pefomances geneally hndes the task of ankng altenatves, snce the odeng of fuzzy numbes s not as obvous as that of eal numbes. To ovecome dffcultes of that knd, seveal appoaches have been poposed n the fuzzy lteatue, the most common beng the defuzzfcaton. Defuzzfcaton s the pocedue of selectng the most epesentatve among all membes of a fuzzy set. By means of defuzzfcaton we attempt to elmnate the fuzzness fom a fuzzy set, povdng thus a csp esult. Pobably, the smplest defuzzfcaton technque that one can thnk of s to choose among all membes of a fuzzy set the one wth the hghest degee of membeshp. oweve, a moe sophstcated method, whch takes nto account all the nfomaton ncluded n the membeshp functon, s the cente of aea o centod. Ths s smply the cente of aea fomed unde the membeshp functon. The followng equaton gves the geneal fomula fo calculatng the centod x of an abtaly shaped membeshp functon μ (x) xμ( x) dx X x = μ( x) dx. () X In the fomula above, X denotes the efeental of the fuzzy set, whch n the case of fuzzy numbes s dentfed wth the eal lner. Fo the tapezodal fuzzy numbe (α, α 2, α 3, α 4 ) the above fomula educes to [4]:

5 Doumas N. Geogos, Nktakos V. Nñtas, ambou A. aa A ETODOOGY FOR RATING AND RANKING AZARDS IN ARITIE FORA SAFETY ASSESSENT USING FUZZY OGIC x = (α +α 2 +α 3 +α 4 )/4 (2) 6. Evaluaton famewok We use two vaatons of the evaluaton pocess, denoted by V. and V.2 whose man dffeence lays n the way the vaous atng and mpotance assessments ae aggegated to povde a ankng of the altenatve hazads. The sepaaton of the atng fom the mpotance assessment s a means of makng the evaluaton of hazads as fa and objectve as possble. In ode to avod dsageement o dscepances among evaluaton commttee s membes we selected to follow Delph method. Geneally speakng, the Delph method s an teatve pocedue, whch ams at the convegence of vaous subjectve opnons nto a moe wdely acceptable vew. In geneal, a set of assumptons fom the bass of ou evaluaton plan: All people beng nvolved n the assessment pocedue agee to categozaton of hazads, evaluaton ctea and assessment tems. Thee ae a numbe of hazads, whch ae to be odeed fom the hghly to the least ecommended. 6.. Assessment of ctea mpotance In ou hazads evaluaton poject a panel of expets has to evaluate the ctea mpotance by answeng a questonnae. Despte the numeous books and atcles that have been wtten on the subject, questonnae desgn lacks untl today a coheent theoy [5]. Fo moe detals about the topc the nteested eade could be efeed to bblogaphy [8], [9], [0], [7]. Evaluato s task s to debate on the lngustc weghts of the geneal and thematc ctea, whch have been pedetemned. Each expet s asked to assgn weghts: To evey pa of geneal-thematc tees and At each node of the heachcal stuctue, movng fom the lowest to the hghest-level ctea. The mpotance of evey sngle cteon s evaluated by a closed-fomat queston (o descpton of the cteon n geneal), whose answe set ncludes the fve lngustc values: vey low (V), low (), medum (), hgh (), vey hgh (V). Fom a methodologcal pont of vew, those values coespond to a sutably chosen tapezodal (and tangula) fuzzy numbes on the numec scale 0- (see Table 2). Afte the assessment has been completed fo the totalty of thematc aeas, a Delph study s caed out fo each thematc aea sepaately, n ode that an acceptable level of consensus s acheved. Table 2. The lngustc ates of ctea mpotance 6.2. Ratng of hazads Vey ow (V) (0.0, 0.0, 0., 0.3) ow () (0., 0.3, 0.3, 0.5) edum () (0.3, 0.5, 0.5, 0.7) gh () (0.5, 0.7, 0.7, 0.9) Vey gh (V) (0.7, 0.9,.0,.0) Evaluatos ae asked to gve the opnon on the mpact of each hazad wth espect to the ctea set by the patcula evaluaton poblem. Rates ae only gven at the lowest level of the geneal and thematc heachy. Ratng questonnaes could be vey smla (o even the same) n desgn to those descbed n the pevous secton. In ode to efe n a subjectve attbute of hazad mpact we use lngustc tems of consequence assgnment (see Table 3). The mpact fo evey sngle cteon s assessed by means of closedfomat questons wth the answe set: catastophc (CA), ctcal (CR), sgnfcant (SI), mno (I), neglgble (NE).

6 Doumas N. Geogos, Nktakos V. Nñtas, ambou A. aa A ETODOOGY FOR RATING AND RANKING AZARDS IN ARITIE FORA SAFETY ASSESSENT USING FUZZY OGIC Table 3. ngustc tems of hazad mpacts ngustc tem Neglgble no Sgnfcant Ctcal Catastophc azad mpact Injuy not equng fst ad, no cosmetc vessel damage, no envonmental mpact, no mssed voyages Injuy equng fst ad, cosmetc vessel damage, no envonmental mpact, no mssed voyages Injuy equng moe than fst ad, vessel damage, some envonmental damage, a few mssed voyages o fnancal loss Sevee njuy, majo vessel damage, majo envonmental damage, mssed voyages oss of lfe, loss of vessel, exteme envonmental mpact Each of the above lngustc tems coesponds to a fuzzy numbe on the numec atng scale 0-0. Detals of the coespondence ae gven n Table 4. Afte the assessment has been completed fo the totalty of evaluatos, a Delph study s caed out fo each hazad sepaately. The nfomaton descbed above togethe wth the pope ctea weghts s used n the next phase of the evaluaton poblem: the heachy aggegaton. Table 4. The lngustc ates of hazads mpact 6.3. eachy aggegaton Neglgble (NE) (0, 0,, 3) no (I) (, 3, 3, 5) Sgnfcant (SI) (3, 5, 5, 7) Ctcal (CR) (5, 7, 7, 9) Catastophc (CA) (7, 9, 0, 0) All have dscussed by fa efe to the fst stage of methodology, the acquston data. In that pat, pocedues wee less standadzed and automated, due to the stong nvolvement of human expetse. Fom ths stage onwads, tasks tend to be of moe algothmc natue, whch defntely calls fo the use of specally desgned compute pogams fo pefomng the equed computatons. The steps followng the data acquston could be summazed n two phases: Phase I: The evaluaton of the aggegate pefomance of each hazad. Phase II: The ankng of hazads wth espect to the oveall ate. Those ae, accodng to. J. Zmmeman, the two typcal stages of a multctea decson-makng poblem n whch fuzzy sets ae used n the assessment pocess [8]. It s woth mentonng that n most classcal (non-fuzzy) multctea methods, the esults of phase I ae numec scoes. ence, phase II becomes a tval task, as fo the ankng of hazads all that s needed s the pa wse compason of scoes. oweve, n fuzzy multctea analyss, the stuaton s moe peplexed. Usually, the oveall mpact of hazads s descbed by a fuzzy numbe o a fuzzy set n geneal, whch calls fo an addtonal technque fo emovng the fuzzness and povdng a csp esult. Geneally, many appoaches have been poposed n the lteatue that addesses the ssues of the oveall atng and ankng of altenatves when fuzzy sets ae nvolved n the decson-makng pocess. Fo an ovevew of dffeent appoaches the eade could efe to seveal extensve suveys [5]. In the poposed methodology s used a technque that s based on the dea of weghted aveagng, popely adjusted to fuzzy numbes [4], [5], [7], [20]. Is poposed the mplementaton of two vaatons of the weghted-aveage scheme (efeed V. and V.2), whose dffeence manly les at the stage whee defuzzfcaton s appled. Those vaatons ae descbed below n detal. Vaaton V. In the fst vaaton, s appled a fuzzy weghted aveagng scheme fo evaluatng the aggegate mpact of hazads. Fo each hazad we compute a weghted aveage of fuzzy lngustc ates, whee each ate

7 Doumas N. Geogos, Nktakos V. Nñtas, ambou A. aa A ETODOOGY FOR RATING AND RANKING AZARDS IN ARITIE FORA SAFETY ASSESSENT USING FUZZY OGIC s multpled by a sutable fuzzy lngustc weght. In vaaton V. the aggegate mpact of hazads s gven n tems of a fuzzy scoe. Theefoe, defuzzfcaton s appled to obtan a sngle numec value fom each fuzzy scoe. Those values ae then used fo ankng hazads. To gve a moe concete pesentaton of the method, let us assume that fo the abtay thematc aea (say XYZ), the evaluaton ctea heachy s gven, consstng of both the geneal and the XYZ ctea tee. et the oveall evaluaton heachy compse K banches n total, whch s also the numbe of both endctea and ates pe hazad. Then, the followng algothm s followed:. Fom the evaluaton matx: 2 m B ~ 2 m B2 ~ 2 22 m2 O B K K 2K ~ mk Whee by B K, k=,2,,k we denote the banches of the ctea tee and by, =,2,,m the hazads to be evaluated. Evey element ~ k of the matx coesponds to the ate acheved by hazad fo the patcula sub-cteon that les at the end of banch B k. The entes of the evaluaton matx ae chosen fom the set of lngustc ates ( vey poo (VP), poo (P), fa (F), good (G), vey good (VG) ), whch coespond, to the tapezodal fuzzy numbes pesented n Table Fo obtanng the weght ~ ω k that coesponds to ate ~ k, tace down the evaluaton ctea tee by followng the k banch. Fo evey node of the banch that s vsted, adjust ~ ω k by multplyng wth the fuzzy weght assgned to ths node. 3. The aggegated fuzzy ates s~, =,2,,m ae obtaned by multplyng the evaluaton matx wth the vecto of fuzzy weghts: ~ s ~ s ~ 2 s~ = = ~ s ~ m m m2 O K 2K mk ~ ω ~ ω2 ~ ω Κ whee denotes the poduct opeaton fo fuzzy matces, whch woks exactly the same as n odnay matx algeba. Note that evey s~, =,2,,m s a tapezodal fuzzy numbe. 4. In ode to obtan an odeng on the set of hazads, apply the defuzzfcaton fomula fo tapezodal membeshp functons (eq. 2). The defuzzfcaton values ae used fo ankng hazads fom the hghest to the lowest mpactng. Vaaton V.2 In the second vaaton, the vaous fuzzy lngustc assessments (ates and weghts) ae a po defuzzfed by usng the cente of gavty technque. The aggegate mpact of each hazad s found by computng weghted aveages of defuzzfed ates. The numec scoes obtaned ae used fo ankng puposes. oe pecsely, let us agan assume that the oveall evaluaton ctea tee conssts of K banches, B, B 2,, B K. Suppose that thee ae also m hazads,, =,2,,m to be evaluated. Then, the pocedue followed s:. Gven the fuzzy ates of each e-sevce, apply the cente of gavty defuzzfcaton technque to obtan a set of numec ates k, =,2,,m and k=,2,,k ( ~ k denotes the numec scoe acheved by hazad

8 Doumas N. Geogos, Nktakos V. Nñtas, ambou A. aa A ETODOOGY FOR RATING AND RANKING AZARDS IN ARITIE FORA SAFETY ASSESSENT USING FUZZY OGIC fo the sub-cteon that les at the end of banch evaluaton matx: B k ). Use these ates to fom the followng 2 m B 2 m B m2 O B K K 2K mk 2. Gven the fuzzy weghts, applyng to the patcula evaluaton heachy, use the cente of gavty to obtan numec weghts fo each node of the evaluaton tee. Tacng down each banch k=,2,,k and multplyng the numec weghts assgned to each node, fnd the value of ω k that multples each of k, =,2,,m. 3. A csp aggegate scoe s fo each hazad, s obtaned by computng the weghted aveage of k, k=,2,,k. In matx fom: s s2 s = = s m m m2 O K ω 2 K ω2 mk ω K 4. azads, =,2,,m ae anked by means of the aggegate scoe. 7. Concluson In ths pape we pesent an nnovatve methodologcal appoach to the evaluaton, ankng and selecton of hazads. The poposed methodology ntoduces a heachcal analyss of the decson-makng poblem, n whch geneal and doman specfc ctea compose the evaluaton stuctue. The adopted fuzzy appoach povdes us wth a sutable tool fo modellng and pocessng lngustc assessments and subjectve vews n a smple and athe ntutve way. Apat fom methodologcal ssues, ths pape also dscusses many pactcal aspects of the evaluaton famewok and gves multple gudelnes on how such an evaluaton pocedue could be mplemented. Nevetheless, s obvous that the poposed famewok s of moe geneal use. ost mpotant t gves enough flexblty n modellng an evaluaton poblem, snce t affectvely emans nsenstve to changes n many ndvdual components of the methodology. Refeences [] Baas, S. & Kwakenaak,. (977). Ratng and ankng of multple-aspect altenatves usng fuzzy sets. Automatca 3, [2] Bellman, R. & Zadel,. (970). Decson-makng n a fuzzy envonment. anagement Scence 7, 4, [3] Chen, C. (998). A study of fuzzy goup decson-makng method. In th Natonal Confeence on Fuzzy Sets and Its Applcatons, vol. 42, pp [4] Cheng, C. & n, Y. (2002). Evaluatng the best man battle tank usng fuzzy decson theoy wth lngustc ctea evaluaton. Euopean Jounal of Opeatonal Reseach 42, [5] Dong, W., Shah,. & Wong, F. (985). Fuzzy computatons n sk and decson analyss. Cvl Engneeng Systems 2, [6] Dubos, D. & Pade,. (978). Opeatons on fuzzy numbes. Int. J. Syst. Sc.9, 3,

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