Risk Analysis for Critical Infrastructures Using Fuzzy TOPSIS

Transcription

1 Rsk Analyss for Crtcal Infrastructures Usng uzzy TOPSIS Morteza Yazdan (Correspondng Author) MSc of Economy, aculty of Economy, Isfahan Unversty, Isfahan, Iran E-mal: Al Aldoost MSc of Mechanc Engneerng, Malek-e-Ashtar Unversty of Technology, Tehran, Iran E-mal: Mohammad Hossen Basr Assstant Professor of Tarbat Modares Unversty, Engneerng aculty, Tehran, Iran E-mal: Receved: September 20, 2011 Accepted: October 19, 2011 Publshed: January 1, 2012 do: /jmr.v URL: Abstract Crtcal nfrastructures are the most mportant sector n countres because of the essentalty of naton securty, publc safety, socoeconomc securty, and way of lfe. Accordng to the mportance of nfrastructures, t s a necessty to analyze the potental rsks to do not allow these rsks convert nto events. The man purpose of ths paper s to provde a developed framework wth the am to overcome lmtatons of the classcal approach to buld a more secure, safer, and more reslent crtcal nfrastructures n order to develop, mplement, control. The proposed framework extends conventonal RAMCAP (Rsk Analyss and Management for Crtcal Asset Protecton) through ntroducng new parameters the effects on rsk value. Accordng to the complexty of problem and the nherent uncertanty, ths research adopts the fuzzy TOPSIS as a fuzzy mult crtera decson makng technque to determne the weghts of each crteron and the mportance of alternatves wth respect to crtera. Case analyss s mplemented to llustrate the capablty and effectveness of the model for rankng the rsk of crtcal nfrastructures. The proposed model demonstrates a sgnfcant 1

2 mprovement n comparson wth conventonal RAMCAP. Keywords: Crtcal Infrastructures, uzzy TOPSIS, RAMCAP, Rsk Rankng 2

3 1. Introducton The countres of all around the world were recently faced wth several events generated by varous causes n the crtcal nfrastructures sector. They have led to a lot of casualtes and major damage to human, machnery, and envronment. That s demonstrated by many events whch rsk connected wth securty, safety, health, and envronment cannot be perfectly avoded. Therefore, mscellaneous methodologes were developed n order to analyze and rank the exstng rsks. Rsk Analyss and Management for Crtcal Asset Protecton (RAMCAP) methodology s one the most well-known methods n ths feld that were presented by the Department of Homeland Securty. The RAMCAP method s a functon of three components threat (T), vulnerablty (V), and consequence (C) (Brashear et al., 2007; ASME-ITI, 2006; Cox, 2009). Regardless of the relatve mportance weghts of the evaluaton crtera, t appears to be an urgent need for crtcal nfrastructures to develop a rsk assessment methodology to manage the effectve components. TOPSIS s one of the most applcaton mult crtera decson makng (MADM) methods, whch assgns the best alternatve among a pool of feasble alternatves by calculatng the dstances from the postve and negatve deal solutons. Ths technque s crtczed due to neglect uncertanty. On the other hand, fuzzy logc s able to model the uncertanty. Ths technque uses lngustc varable nstead of tradtonal quanttatve expresson, whch s a very helpful concept for dealng wth stuatons whch are too complex or not well-defned enough (Zadeh, 1965). Therefore, fuzzy TOPSIS s developed n order to solve dfferent aspects of prorty ssues. Jola et al. (2011) proposed a two-phase approach for suppler selecton and order allocaton problem under fuzzy envronment. The proposed model n ths paper contan of two phases, n the frst phase of the approach, a fuzzy multple crtera decson makng method s used to obtan the overall ratngs of alternatve supplers, and to select the most qualfed ones for further evaluatons, n the second phase, a mult-objectve mxed nteger lnear programmng (MOMILP) model to determne the order quanttes of each selected suppler for each product n each perod s constructed. Kaya & Kahraman (2011) proposed a modfed fuzzy TOPSIS methodology for the selecton of the best energy technology alternatve. Kelemens et al (2011) extend fuzzy TOPSIS for support managers selecton. rass et al (2009) proposed an ntegrated estmatve approach based on the fuzzy logc theory, whch permts more coherence n the evaluaton process, producng a very sutable fnal rank of hazardous actvtes. Yu & Hu (2010) developed an ntegrated mult crtera decson makng approach that combnes the votng method and the fuzzy TOPSIS method to evaluate the performance of multple manufacturng plants n a fuzzy envronment. Sad-Nezhad & Damghan (2010) presented a TOPSIS approach based on preference rato and an effcent fuzzy dstance measurement n assessment of traffc polce centers performance. Torlak et al (2011) used fuzzy TOPSIS mult-methodologcal approach n the Turksh 3

4 domestc arlne ndustry. Sngh & Benyoucef (2011) proposed a fuzzy TOPSIS based methodology along wth a mechansm for determnaton of fuzzy lngustc value of each attrbute. They utlzed entropy method to enumerate the weghts of varous attrbutes automatcally wthout nvolvement of decson makers. Lao & Kao (2011) proposed ntegrated fuzzy TOPSIS and mult-choce goal programmng (MCP) approach to solve the suppler selecton problem. They stated the advantage of ths method s that t allows decson makers to set multple aspraton levels for suppler selecton problems. Based on fuzzy TOPSIS Krohlng & Campanharo (2011) proposed a fuzzy TOPSIS for group decson makng, whch s appled to evaluate the ratngs of response alternatves to a smulated ol spll. Sun & Ln (2009) used fuzzy TOPSIS as the analytcal tool that determnes the weghts of each crteron, from ther research results, the securty and trust are the most mportant factors for mprovng the compettve advantage of shoppng webste. It s clear that fuzzy TOPSIS has demonstrated ts capabltes and effcences as a practcal engneerng and problem-solvng tool. In ths paper, we extend the approach of TOPSIS to develop a rsk-based methodology under fuzzy envronment. uzzy TOPSIS s adopted because of ts capablty and effcency n handlng uncertanty, smultaneous consderaton of the postve deal and the negatve solutons, smple computatons, and logcal concepts. The rest of the paper s organzed as follows: In Sectons 2, the basc structure of the RAMCAP methodology s ntroduced. Secton 3 descrbes fuzzy TOPSIS technque. The proposed framework s summarzed n Secton 4, ncludng rsks dentfcaton, selecton of crtera, rsk evaluaton usng fuzzy TOPSIS procedure, and senstvty analyss. In Secton 5, study for rsk evaluaton n an llustratve case s presented. The comparson of the proposed model wth the conventonal RAMCAP s mplemented and results are dscussed n Secton 6. Conclusons are dscussed and some shortages of the conventonal RAMCAP are lsted n Secton The Basc Concepts of RAMCAP Methodology The RAMCAP methodology provdes a systematc process to dentfy and analyze the sgnfcance of potental events assocated wth crtcal nfrastructures. The RAMCAP process s comprsed of seven steps as follows (ASME-ITI, 2006; Brashear et al., 2007): (1)Asset characterzaton and screenng, (2) Threat characterzaton, (3) Consequence analyss, (4) Vulnerablty analyss, (5) Asset attractveness and threat assessment, (6) Rsk assessment, and (7) Rsk management. Ths steps are depcted n gure 1. gure 1. Process of RAMCAP technque 4

5 The benefts of conventonal RAMCAP, but are not lmted to, nclude (Brashear & Jones, 2010): () More effcent management of captal and human resources, () Ablty to dentfy the assets wth the greatest need and value of mprovement, () ratonal allocaton of resources to maxmze the securty and reslence enhancement wthn a fnte budget. Accordng to the conventonal RAMCAP technque, rsk (R) s determned by the ntersecton of consequences of the attack (C), the threats of the attack (T) and vulnerabltes to the attack (V). More specfcally, rsk s formulated as Eq. (1): 3. uzzy TOPSIS 3.1 uzzy Theory R= C T V (1) Adequate knowledge and comprehensve data base on a number of dfferent problems are requested to analyze crtcal nfrastructures. There are a close relatonshp between complexty and certanty, so that; ncreasng the complexty lead to decrease the certanty. uzzy logc ntroduced by Zadeh (1965) - can take nto account uncertanty and solve problems where there are no sharp boundares and precse values. uzzy logc provdes a methodology for computng drectly wth words (Zadeh, 1996). uzzy set s a powerful mathematcal tool for handlng the exstng uncertan n decson makng. A fuzzy set s general form of a crsp set. A fuzzy number belong to the closed nterval 0 and 1, whch 1 addresses full membershp and 0 expresses non-membershp. hereas, crsp sets only allow 0 or 1. There are dfferent types of fuzzy numbers that can be utlzed based on the stuaton. It s often convenent to work wth trangular fuzzy numbers (TNs) because they are computed smply, and are useful n promotng representaton and nformaton processng n a fuzzy envronment (Torlak et al, 2011). A fuzzy number A on R can be a trangular fuzzy number (TN) f ts membershp functon ( ): R [0,1] be defned as follows: A x 0, x a ( x a) / ( ba), a xb A ( x) ( c x) / ( c b), b x c 0, otherwse (2) 3.2 uzzy TOPSIS Approach TOPSIS s based on the concept that the chosen alternatve should have the shortest dstance from the postve-deal soluton and the longest dstance from the negatve-deal soluton (Seçme et al, 2009; umus, 2009; Sun, 2010; Yue, 2011). The postve deal soluton s a soluton that maxmzes the beneft crtera and mnmzes the cost crtera smultaneously, whereas the negatve deal soluton maxmzes the cost crtera and mnmzes the beneft 5

6 crtera smultaneously. In the conventonal TOPSIS technque, expert judgments are represented wth precse values. In real world problems, t s often dffcult for a decson maker to determne precse weghts for crtera and alternatves wth respect to the crtera under consderaton. The mert of usng a fuzzy approach s to determne the mportance or preference of crtera and alternatves usng fuzzy numbers nstead of crsp numbers to be more adapted to the real world cases. or ths reason, fuzzy TOPSIS was developed to solve the real world problems under fuzzy envronment (Kuo et al, 2007; Yang, Hung, 2007; Chen, Tsao, 2008; Ashtan et al, 2009; Ebrahmnejad et al, 2009; Roghanan et al, 2010; Aydogan, 2011; Jola et al, 2011; Awasth et al, 2011). Ths technque helps decson-makers carry out analyss and comparsons n rankng ther preference of the alternatves wth vague or mprecse data (Yu & Hu, 2010). The mathematcs concept of uzzy TOPSIS can be descrbed as follows: Step 1: Choose the lngustc ratngs for crtera and alternatves wth respect to crtera. In ths step, the mportance weghts of evaluaton crtera and the ratngs of alternatves are consdered as lngustc terms to assess rsk under fuzzy envronment as shown n Table 1 and Table 2. Table 1. Lngustc terms for crtera Lngustc terms uzzy number Very low (VL) (0.0,0.0,0.25) Low (L) (0.0,0.25,0.5) Medum (M) (0.25,0.5,0.75) Hgh (H) (0.5,0.75,1.0) Very Hgh (VH) (0.75,1.0,1.0) Table 2. Lngustc ratng for alternatves Lngustc terms uzzy ratng Very Poor (VP) (0.0,0.0, 2.5) Poor (P) (0.0,2.5,5.0) ar () (2.5,5.0,7.5) ood () (5.0,7.5,10.0) Very ood (V) (7.5,10.0,10.0) Step 2. Construct the fuzzy decson matrx. If assume that the number of crtera s n and the count of alternatves s m, fuzzy decson matrx wll be obtaned wth m rows and n columns as followng matrx: 6

7 C1 C2 Cn x x x A x x x A D xm1 xm2 xmna n n 2 m (3) And crtera are constructed as follows: (,,..., ) (4) w1 w2 w n Step 3. After constructng fuzzy decson matrx, the normalzaton of fuzzy decson matrx s accomplshed usng lnear scale transformaton. The calculatons are done usng formulas (5), (6) to convert the dfferent crtera scales nto a comparable scale. aj bj cj r (,, ) and c maxc c c c, for maxmzaton objectve (5) j j j j j j aj aj aj r (,, ) and a mn a c b a j j j j j j, for mnmzaton objectve (6) The normalzed fuzzy decson matrx can be represented by Eq. (7): R rj, 1, 2,..., m; j 1,2,..., n. mn (7) here the r j s the normalzed value of xj ( aj, bj, cj ). Step 4. Calculate the weghted normalzed fuzzy decson matrx. The weghted normalzed value v s calculated by multplyng the weghts ( w ) of crtera j j wth the normalzed fuzzy decson matrx r j. The weghted normalzed decson matrx V for each crteron s calculated through the followng relatons: V [ v ], 1, 2,..., n, j 1, 2,..., J, j n j (8) here v r () w (9) j j Step 5. Then the fuzzy postve-deal soluton (PIS A ) and fuzzy negatve-deal soluton 7

8 (NIS A ) are determned as descrbed n followng part n A ( v, v, v,..., v ) max v ( 1, 2,..., n) (10) n A ( v, v, v,..., v ) mn v ( 1, 2,..., n) j j Based on the weghted normalzed fuzzy decson matrx, the ranges belong to the closed nterval [0,1]. Therefore, the PIS and NIS can be defned as (1,1,1) and (0,0,0) respectvely. Step 6. After assgnng the PIS and NIS, the dstance of each alternatve from A + and A - are calculated by Eqs. (12) and (13): n j j j1 (11) d d( v, v ), 1,2,..., m (12) n j j j1 d d( v, v ), 1,2,..., m (13) here the dstance measurement between two fuzzy number a ( a1, a2, a3) and b b1 b2 b3 can be calculated by Vertex method as follows: (,, ) dv ( a, b ) ( a1b1) ( a2 b2) ( a3 b3) 3 (14) Step 7. Calculate the closeness coeffcent. The closeness coeffcent ( CC ) takes nto account the dstance of the PIS, d and the NIS, d smultaneously. The closeness coeffcent of each alternatve s obtaned through Eq. (15): d CC d d (15) Step 8. Rank preference order. The rankng of the alternatves can be determned accordng to the closeness coeffcent n descendng order. 4. The Proposed ramework The proposed framework for rankng rsk n crtcal nfrastructures has followng four phases: 8

9 1. Identfy the exstng rsks. 2. Select the evaluaton crtera. 3. Evaluate the dentfed rsks usng fuzzy TOPSIS procedure. 4. Senstvty analyss 4.1 Rsks dentfcaton In the rsk dentfcaton phase, threats and hazards whch could dsrupt the crtcal servces and products should be dentfed. One of the smplest method of dentfyng and analyzng the rsks n a nfrastructure s by askng questons such as whch assets are most crtcal, whch assets are more exposed to danger, and gettng the rght answers. 4.2 Selecton of crtera Selecton of crtera s the frst step for evaluatng rsk of crtcal nfrastructures. The parameters of the RAMCAP methodology were dentfed as a part of evaluaton crtera. Snce these crtera are not enough to cover all aspects of rsks; new crtera for a more precse, accurate, and sure rsk analyss are developed. These crtera are presented n Table 3. As shown n Table 3, the frst three crtera (.e. C1, C2, and C3) are the cost type crtera (the lower, the better). The remanng crtera are the beneft type crtera (the hgher, the better). Table 3. Evaluaton crtera for analyze rsk Crtera Defnton Type of crteron Threat (C1) Threat s defned as an event wth an undesred mpact Cost Vulnerablty Any weakness of an asset that can convert t nto an event Cost (C2) or dsaster by one or more threats Consequence Consequence s defned as the effect of an event or ncdent Cost (C3) Detectablty The capablty and potental for dentfcaton and Beneft (C4) elmnaton of the weakness Reacton aganst event (C5) The capablty of an approprate response n order to reduce or lmt the effect of an event after happenng or prevent aganst the development of casualtes, damage, and loss Beneft 4.3 Evaluatng the exstng rsks usng fuzzy TOPSIS procedure In the thrd phase, evaluatng rsks s determned by usng fuzzy TOPSIS. Lngustc terms are utlzed for evaluatng the ratngs and mportance weghts of alternatves and crtera. The defnton of lngustc terms and trangular fuzzy numbers are presented n Tables (1) and (2). 4.4 Senstvty analyss Senstvty analyss s a useful tool n the present of uncertanty n the defnton of the relatve mportance of evaluaton crtera. Ths technque s appled to determne the effect of crtera weghts on decson makng. 9

10 5. Case analyss The proposed model s utlzed to rank the exstng rsk n a crtcal nfrastructure n order to demonstrate the potental applcatons of the model. A ral transportaton example s adopted from API & NPRA (2004). The example s of a fcttous hydrocarbon tank truck transportaton system, whch ncludes the tank truck, nventory of flammable lquds and the route specfc varables such as the type of road, populaton centers and envronmental receptors, and any stops. 5.1 Rsks Identfcaton In our case, eght crtcal assets were dentfed as rsky assets to be analyzed by the model. These assets nclude 25 ralcars of petroleum products (RPP), rural secton of track to swtch yard - 25 mles from shpper's ste (RST), manlne secton of track n rural area mles (MST-200), swtch yard (SY), rver crossng (RC), manlne secton of track n urban area mles (MST-300), sdng n Urban Area (SUA), and tunnel n Urban Area (TUA). 5.2 Selecton of Crtera rom above dscusson, evaluaton crtera to utlze n the proposed model comprse Threat (C1), Vulnerablty (C2), Consequence (C3), Detectablty (C4), and Reacton aganst event (C5). Thus, the decson herarchy s structured as depcted n gure 2. The decson problem conssts of three levels: the objectve of the problem s stuated at the hghest level, whle n the second level, the crtera are presented, and the last level belongs to the alternatves. Rankng rsks C1 C2 C3 C3 C5 RPP RST MST-200 SY RC MST-300 SUA TUA gure 2. The structure of decson 5.3 Evaluatng the Exstng Rsks Usng uzzy TOPSIS Procedure Regardng the evaluaton of the dentfed rsks, 8 decson makers wth mnmum 5 years experence were nvted to evaluate the weghts of crtera and alternatves wth respect to each crteron by usng lngustc varables gven n Table 1 and Table 2. or achevng the am, two questonnares are desgned; one of them s to obtan the weghts of crtera and other s to acqure the mportance of alternatves wth respect to crtera. To determne the 10

11 fuzzy weght of each crteron, lngustc varables are converted nto trangular fuzzy numbers as shown n the thrd column of Table 4. Table 4. uzzy weghts of crtera Crtera Lngustc term uzzy number C1 M (0.25,0.5,0.75) C2 H (0.5,0.75,1.0) C3 VH (0.75,1.0,1.0) C4 L (0.0,0.25,0.5) C5 M (0.25,0.5,0.75) Then, decson makers were asked to form fuzzy evaluaton matrx by lngustc varables presented n Table 2. It s constructed by comparng eght potental rsks under fve crtera separately. The fuzzy decson matrx s presented n Table 5. Based on the fuzzy TOPSIS procedure, the decson matrx formed n Table 5 needs to be normalzed by usng Eqs. (5) and (6). Then, the fuzzy weghted decson matrx for the exstng alternatves s calculated by multplyng the weghts of crtera wth the normalzed fuzzy decson matrx as depcted n Table 6. Table 5. uzzy decson matrx RPP RST MST-200 SY RC MST-300 SUA TUA C1 C2 C3 C4 C5 V (5.0,7.5,10.0) (2.5,5.0,7.5) (5.0,7.5,10.0) (7.5,10.0,10.0) (2.5,5.0,7.5) P P (2.5,5.0,7.5) (5.0,7.5,10.0) (2.5,5.0,7.5) (0.0,2.5,5.0) (0.0,2.5,5.0) P V (2.5,5.0,7.5) (2.5,5.0,7.5) (0.0,2.5,5.0) (7.5,10.0,10.0) (5.0,7.5,10.0) VP P V (5.0,7.5,10.0) (0.0,0.0, 2.5) (0.0,2.5,5.0) (2.5,5.0,7.5) (7.5,10.0,10.0) P V (2.5,5.0,7.5) (5.0,7.5,10.0) (0.0,2.5,5.0) (2.5,5.0,7.5) (7.5,10.0,10.0) V P (7.5,10.0,10.0) (2.5,5.0,7.5) (2.5,5.0,7.5) (0.0,2.5,5.0) (5.0,7.5,10.0) VP P V (0.0,0.0, 2.5) (0.0,2.5,5.0) (5.0,7.5,10.0) (7.5,10.0,10.0) (5.0,7.5,10.0) P (5.0,7.5,10.0) (5.0,7.5,10.0) (2.5,5.0,7.5) (0.0,2.5,5.0) (2.5,5.0,7.5) 11

12 Table 6. eghted normalzed fuzzy decson matrx C1 C2 C3 C4 C5 RPP (0.12,0.37,0.75) (0.12,0.37,0.75) (0.37,0.75,1.0) (0.0,0.0,0.25) (0.06,0.25,0.56) RST 0.06,0.25,0.56) (0.25,0.56,1.0) (0.19,0.5,0.75) (0.0,0.0,0.12) (0.0,0.12,0.37) MST ,0.25,0.56) (0.12,0.37,.075) (0.0,0.25,0.5) (0.0,0.0,0.25) (0.12,0.37,.075) SY 0.12,0.37,.075) (0.0,0.0, 0.25) (0.0,0.25,0.5) (0.0,0.0,0.19) (0.19,0.5,0.75) RC 0.06,0.25,0.56) (0.25,0.56,1.0) (0.0,0.25,0.5) (0.0,0.0,0.19) (0.19,0.5,0.75) MST-300 (0.19,0.5,0.75) (0.12,0.37,0.75) (0.19,0.5,0.75) (0.0,0.0,0.12) (0.12,0.37,0.75) SUA (0.0,0.0,0.19) (0.0,0.19,0.5) (0.37,0.75,1.0) (0.0,0.0,0.25) (0.12,0.37,.075) TUA 0.12,0.37,.075) (0.25,0.56,1.0) (0.19,0.5,0.75) (0.0,0.0,0.12) (0.06,0.25,0.56) Then for the eght alternatves, the fuzzy postve deal soluton (PIS, A ) and the fuzzy negatve deal solutons (NIS, A ) are calculated usng Eqs. (10), (11). As a result, PIS and NIS are defned as v (1,1,1) v (1,1,1) and v (0,0,0) for beneft crteron, and v (0,0,0) and for cost crteron. As mentoned above, C1, C2, and C3 are cost crtera whereas C4 and C5 are beneft crtera. Then, the dstance of each alternatve from the fuzzy postve deal soluton and fuzzy negatve deal soluton are calculated through Eqs. (12) and (13). or example, the dstances of the PIS and NIS for alternatve A1 are calculated as follows: d 1 ( ) ( ) ( ) ( ) ( ) ( ) 1 1 ( ) ( ) (0.0 1) ( ) (1 0.0) ( ) ( ) 2 (1 0.25) 2 ( ) And d 1 ( ) ( ) ( ) ( ) ( ) ( ) 1 1 ( ) ( ) (1.0 1) ( ) ( ) ( ) ( ) 2 ( ) 2 ( ) Then, d 1 CC1 d 1 d

13 Smlar calculatons are fulflled for the other alternatves and the results are presented n Table 7. Table 7. uzzy TOPSIS result d d CC Rank base on securty RPP RST MST SY RC MST SUA TUA Accordng to CC values, the rsk rankng n descendng order s SY, MST-200, SUA, RC, RPP, TUA, RST and MST-300. Therefore, the rskest asset s MST-300 and the securest asset s SY. 5.4 Senstvty analyss Senstvty analyss plays a sgnfcant role n complex decson makng because of nherent nstablty. Ths technque generates dfferent scenaros that may change the prorty of alternatves and be needed to reach a consensus. If the rankng order be changed by ncreasng or decreasng the mportance of the crtera, the results are expressed to be senstve otherwse t s robust. In ths study, senstvty analyss s mplemented to see how senstve the alternatves change wth the mportance of the crtera. Ths tool graphcal exposes the mportance of crtera weghts n selectng the optmal alternatve among the feasble alternatves. The man goal of senstvty analyss s to see whch crtera s most sgnfcant n nfluencng the decson makng process. or ths reason, twenty fve experments were conducted as presented n Table 8. g. 3 shows how the prorty of each alternatve can be changed wth ncreasng or decreasng the mportance of the crtera. 13

14 Table 8. Senstvty analyss No. eghts of crtera Rankng 1 C1, C5 (0.25,0.5,0.75), C2 (0.5,0.75,1), C3 (0.75,1,1), C4 (0, 0, 0.25) SY> MST-200> SUA> RC> MST-300> RPP> TUA> RST (0.5,0.75,1), (0.75,1,1), (0,0,0.25) SY> SUA> MST-200> RC> MST-300> RST > RPP> TUA 2 C1, C2 C3 C4, C5 (0.5, 0.75,1), (0, 0, 0.25) SY> SUA> MST-200> RC> MST-300> RPP > RST > TUA 3 C1, C2, C3 C4, C5 (0.5, 0.75,1), (0.25, 0.5, 0.75) SUA> MST-200> SY> RC> RPP MST-300 > RST > TUA 4 C1, C2, C3, C4 C5 (0.5, 0.75,1), (0.25, 0.5, 0.75) SUA> SY> MST-200> RC> RPP MST-300 > TUA> RST 5 C2, C3, C4, C5 C1 (0.5,0.75,1), (0.25,0.5,0.75) SUA> MST-200> SY> RC> RPP MST-300 > TUA> RST 6 C3, C4, C5 C1, C2 (0.5, 0.75,1), (0.25, 0.5, 0.75) SUA> MST-200> SY> RC> RPP MST-300 > TUA> RST 7 C4, C5 C1, C2, C3 (0.5, 0.75,1), (0.25, 0.5, 0.75) SUA> SY> MST-200> RC> RPP MST-300 > TUA> RST 8 C5 C1, C2, C3, C4 9 C1, C2, C3, C4, C5 (0.25,0.5,0.75) SUA> MST-200> SY> RC> RPP MST-300 > TUA> RST (0,0,0.25), (0.25,0.5,0.75) SUA> MST-200> SY> RC> RPP > RST> MST-300 > TUA 10 C5 C1, C2, C3, C4 (0,0,0.25), (0.25,0.5,0.75) SUA> SY> MST-200 > RC> RST> MST-300> RPP > TUA 11 C4, C5 C1, C2, C3 (0,0,0.25), (0.25,0.5,0.75) SY> SUA> MST-200 > MST-300> RPP> RC > TUA> RST 12 C1, C3, C4, C5 C2 (0,0,0.25), (0.25,0.5,0.75) SY> MST-200 > SUA> RC >MST-300> RPP> TUA> RST 13 C1, C4, C5 C2, C3 (0,0,0.25), (0.25,0.5,0.75) SY> MST-200 > SUA> RC >MST-300> RPP> TUA> RST 14 C1, C4 C2, C3, C5 (0,0,0.25), (0.25,0.5,0.75), (0.5,0.75,1) SY> MST-200 > SUA> RC >MST-300> RPP> RST> TUA 15 C1, C4, C5 C3 C2 (0,0,0.25), (0.25,0.5,0.75), (0.75,1,1) SY> SUA> MST-200 > RC >MST-300> RPP> RST> TUA 16 C1, C4 C3, C5 C2 (0,0,0.25), (0.25,0.5,0.75), (0.75,1,1) SY> SUA> MST-200 > RC >MST-300> RPP> RST> TUA C (0,0,0.25), C C (0.25,0.5,0.75), C (0.5,0.75,1), SY> SUA> MST-200 > RC >MST-300> RPP> RST> TUA C 2 (0.75,1,1) C (0, 0, 0.25), C C (0.25, 0.5, 0.75), C C (0.75,1,1) SY> SUA> MST-200 > RPP> RC> MST-300> RST> TUA C (0,0,0.25), C (0.25,0.5,0.75), C C (0.75,1,1) SY> SUA> MST-200 > RPP> RC> MST-300> RST> TUA C 5 (0.5,0.75,1) (0, 0, 0.25), (0.25, 0.5, 0.75), (0.75,1,1) SY> SUA> MST-200 > RC> RPP> MST-300> RST> TUA 17 C1 C3, C4, C5 C , , 5 2, , 4 21 C1 C3 C2, C4, C5 (0,0,0.25), (0.5,0.75,1), (0.75,1,1) SY> MST-200 > SUA> RC> RPP> MST-300> RST> TUA 22 C1 C3 C2, C4, C5 (0,0,0.25), (0.75,1,1) SY> MST-200 > SUA> RC> RPP> MST-300> RST> TUA 23 C1 C2, C3, C4, C5 (0.25, 0.5, 0.75), (0.75,1,1) SY> MST-200 > SUA> RC> RPP> MST-300> RST> TUA 24 C1 C2, C3, C4, C5 (0.25, 0.5, 0.75), (0.75,1,1), (0.5, 0.75,1) SY> SUA> MST-200 > RC> RPP> MST-300> RST> TUA 25 C1 C3 C2, C4, C5 14

15 RPP RST MST-200 SY RC MST SUA TUA As depcted n Table 8 and g. 3, asset SY has top rank among all assets n 17 experments out of 25 ones. In the rest of the experments (experment numbers 4-11), the asset SUA s located n the top level as the wnner. As a result, asset SY s the securest asset. 6. Compare the Proposed Model wth the Conventonal RAMCAP In ths subsecton, n order to show the capablty and sutablty of the rsk evaluaton model proposed n ths paper, a comparson of the model wth conventonal RAMCAP s presented. or ths am, we fulfll the rsk analyss by usng the conventonal RAMCAP for prevous case. Based on RAMCAP, rsk s a functon of only three components threat, vulnerablty, and consequence magntude. An evaluaton scale wth fve judgments {1, 2, 3, 4, and 5} was appled, where 1 represents mnmum judgment level and 5 means the maxmum as depcted n Table 8. The results of evaluator team for assets are presented n Table 9. or the am of comparson, the output of fuzzy TOPSIS s shown n the last column of Table 9. 15

16 Table 8. Defnton of the RAMCAP components Components Ratng Threat (C1) Vulnerablty (C2) Consequence (C3) 1 Very Poor (VP) Very Poor (VP) Very Poor (VP) 2 Poor (P) Poor (P) Poor (P) 3 ar () ar () ar () 4 ood () ood () ood () 5 Very ood (V) Very ood (V) Very ood (V) Table 9. RAMCAP matrx C1 C2 C3 Rsk value Rank based on securty RAMCAP result uzzy TOPSIS result RPP RST MST SY RC MST SUA TUA As can be easly seen, the fnal classfcaton shows sgnfcant dfferences between the results of RAMCAP and fuzzy TOPSIS. Accordng to the output of RAMCAP, the rsk value belong to a lmted set and never takes nto account values such as 7, 11, 13, 14, 17, 19, 21. urthermore, from a computatonal pont of vew, there s a reducton n the capablty of the conventonal RAMCAP methodology to defne a precse and accurate rank, then groupng the crtcal assets nto a few categores and allocatng smlar rank to dfferent assets. Ths should be consdered that organzatons are forced wth two man lmtatons fnance and tme. The allocaton of resources for unnecessary actvtes leads to waste opportuntes. Besdes dfferent sets of vulnerablty, threat, and consequence may generate an dentcal value of rsk; however, the rsk mplcaton may not necessarly be the same. or example, two assets RPP and TUA have values of 4, 3, 4 and 4, 4, 3 for C1, C2 and C3 respectvely. Both these assets wll have a rsk value of 48; however, the rsk mplcatons of these two assets may be completely varous. Other example s two assets SUA and SY, whch have values of 1, 2, 4 and 4, 1, 2 for C1, C2 and C3 respectvely, wth smlar rsk value 8; nevertheless, the rsk mplcatons of these two assets may be entrely dfferent. nally, the relatve mportance among C1, C2 and C3 are not consdered. Ths may not be accurate n real world problems. Therefore, the outputs of proposed model are more accurate. Ths may result a more precse, accurate and sure rsk analyss for protecton. 7. Concluson In response to the rapd growth of mltary ndustres and ncreasng the capablty of 16

17 terrorsts to carry out destructve work, partcularly for the crtcal nfrastructures, the need for assets controls and rsk measures has caught much tme and attenton of governments and responsble sectors. On the other hand, the measurement of rsk s dffcult for decson makers to be precsely and accurately measured because of the ntangble nature of dangerous and threats. Most prevous studes only used the RAMCAP parameters to evaluate rsk. In ths paper, a new framework for evaluatng rsk n crtcal nfrastructures s ntroduced and developed. The model proposed extends the conventonal RAMCAP through ntroducng new parameters the effects on rsk level to obtan a more precse classfcaton of the exstng rsks. Accordng to the complexty of the proposed model due to exst dfferent crtera, whch are n conflctng wth each other, a mult-crtera decson makng method based on the fuzzy logc theory s descrbed to also handle the uncertanty of decson makng problem. Ths technque helps decson maker to specfy relatve mportance of crtera and to determne judgments by means of lngustc varables. A case study s presented n order to demonstrate the potental applcatons of ths methodology. Then a comparson between the proposed model and conventonal RAMCAP s fulflled. The results of the comparson show some shortages of the conventonal RAMCAP as lsted n the followng: (1) The values of rsk evaluaton belong to a lmted set, (2) roupng the assets nto a few categores, (3) Allocatng smlar rank to dfferent assets, (4) Neglectng the relatve mportance of crtera. References Amercan Petroleum Insttute (API) and Natonal Petrochemcal Refners Assocaton (NPRA), Securty Vulnerablty Assessment Methodology for the Petroleum and Petrochemcal Industres (2nd ed.), (Appendx C1). Avalable at Ashtan, B., Haghghrad,., Maku, A., & Montazer,. (2009). Extenson of fuzzy TOPSIS method based on nterval-valued fuzzy sets. Appled Soft Computng, 9: ASME Innovatve Technologes Insttute (ASME-ITI), (2006). RAMCAP (Rsk Analyss and Management for Crtcal Asset Protecton); the ramework, ASME Innovatve Technologes Insttute, LLC (Chapter 1). Avalable at age.pdf Awasth, A., Chauhan, S. S., & Omran, H. (2011). Applcaton of fuzzy TOPSIS n evaluatng sustanable transportaton systems. Expert Systems wth Applcatons, 38 (10): Aydogan, E. K. (2011). Performance measurement model for Turksh avaton frms usng the rough-ahp and TOPSIS methods under fuzzy envronment. Expert Systems wth 17

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