COTS evaluation using modified TOPSIS and ANP

Transcription

1 Appled Mathematcs and Computaton 177 (2006) COTS evaluaton usng modfed TOPSIS and ANP Huan-Jyh Shyur Department of Informaton Management, Tamkang Unversty, Tawan 151 Yng-Chuan Rd., Tamsu, Tape 25137, Tawan Abstract Ths paper models the COTS evaluaton problem as an MCDM problem and proposes a fve-phase COTS selecton model, combnng the technque of ANP (analytc network process) and modfed TOPSIS (technque for order performance by smlarty to dea soluton). Ths artcle dscusses usng the ANP to determne the relatve weghts of multple evaluaton crtera. The modfed TOPSIS approach s used to rank competng products n terms of ther overall performance. To llustrate how the approach s used for the COTS evaluaton problem, an emprcal study of a real case s conducted. The case study demonstrates the effectveness and feasblty of the proposed evaluaton procedure. Ó 2005 Elsever Inc. All rghts reserved. Keywords: COTS; TOPSIS; ANP; Multple crtera decson makng 1. Introducton Gven the hgh nterest n motvaton to the use of commercally avalable software, the evaluaton and selecton of commercal-off-the-self (COTS) products s an mportant actvty n the software development projects. Selectng an approprate COTS product s often a non-trval task n whch multple crtera need to be careful consderaton. Accordng to our observaton, many decson makers select COTS products accordng to ther experence and ntuton. Ths approach s obvously subjectve and ts weakness has been addressed n several prevous studes [8 10,12]. Alternatvely, multple crtera decson makng (MCDM) approach s used n rankng or selectng one or more COTS products from a set of avalable alternatves wth respect to multple evaluaton crtera. MCDM provdes an effectve framework for COTS products comparson nvolvng the evaluaton of multple crtera. For example, Konto [8] developed a systematc approach called OTSO (off-the-self-opton) to demonstrate that MCDM can be effectvely used to compare varous COTS products from multple dmensons. The OTSO approach uses the analytc herarchy process (AHP) to consoldate the evaluaton data for decson makng process. The AHP method s now wdely used by both researchers and practtoners n COTS selecton problems [5,6,8,11]. The methodology s only useful when the decson makng framework has a undrectonal herarchcal relatonshp among decson levels. However, Carney and Wallnau [2] ponts out the evaluaton E-mal address: shyur@mal.m.tku.edu.tw /$ - see front matter Ó 2005 Elsever Inc. All rghts reserved. do: /j.amc

2 252 H.-J. Shyur / Appled Mathematcs and Computaton 177 (2006) crtera for COTS product are not always ndependent of each other, but often nteract. An nvald result can be made n the face of ths complexty. Moreover, AHP s not practcally usable f the number of alternatves and crtera s large snce the repettve assessments may cause fatgue n decson makers [1]. The pror proposed MCDM technques for COTS product evaluaton are useful but have restrcted applcaton. Another popular method for solvng MCDM problems s the TOPSIS (technque for order performance by smlarty to dea soluton) whch was frst developed by Hwang and Yoon [7]. The TOPSIS bases upon the concept that the optmal alternatve should have the shortest dstance from the postve dea soluton (PIS) and the farthest dstance from the negatve dea soluton (NIS). Although the concept of TOPSIS s ratonal and understandable, and the computaton nvolved s uncomplcated, the nherent dffculty of assgnng relable subjectve preferences to the crtera s worth of note. Ths paper models the COTS evaluaton problem as an MCDM problem and proposes a fve-phase COTS selecton model, combnng the technque of analytc network process (ANP) and modfed TOPSIS. The ANP method s used n obtanng the relatve weghts of crtera but not the entre evaluaton process to reduce the large number of parwse comparson. As for the performance correspondng to each alternatve, the modfed TOPSIS approach usng a new defned weghted Eucldean dstance s conducted to rank competng products n terms of ther overall performance on multple evaluaton crtera. The method presents here does not account for dervng the evaluaton crtera for COTS selecton. However, the proposed model may provde organzatons a way to devse and refne adequate crtera and allevate the rsk of selectng sub-optmal solutons. The rest of ths paper s structured as follows: In the next secton, the proposed COTS evaluaton procedure s presented and an overvew of the technques used n our model s gven. Secton 3 wll dscuss the procedure and results of an emprcal study. In Secton 4, we present our conclusons on the results reported n ths paper. 2. Proposed model The evaluaton procedure of ths study conssts of several steps as shown n Fg. 1. The frst step s to dentfy the multple crtera that are consdered n the decson makng process for the decson makers to make an objectve and unbased decson. Brand [1] ponts out that the selecton of approprate crtera s context Crtera for COTS Selecton Identfy Relatonsh p Between Crtera ANP Weghts of Crtera Create Decson Matrx TOPSIS Rankng of COTS Fg. 1. Selecton framework of COTS.

3 H.-J. Shyur / Appled Mathematcs and Computaton 177 (2006) dependent and cannot be part of a general COTS selecton methodology. Then a relatonshp between crtera that shows the degree of nterdependence relatonshp s determned by group expert dscusson n general. After constructng the relatonshp of a crtera network structure, the crtera weghts can be calculated by applyng ANP. Fnally, we conduct a modfed TOPSIS approach to acheve the fnal rankng results. The detaled descrptons of each step are elaborated n each of the followng subsecton Evaluaton crtera and ther nterdependence relatonshp The large number of crtera to be usually consdered n the COTS evaluaton process makes t very dffcult for the evaluators to make an objectve, unbased decson. These crtera nvolve both the requrements that a company may currently have and wll also need when they mplement the COTS and those requrements that they currently do not need but wll requre when they mplement and mantan the system. Konto [8] presents a crtera defnton process that essentally decomposes a goal nto a herarchcal crtera set and each branch n ths herarchy ends n an evaluaton attrbute. The formal group management technque we have been usng to determne the herarchcal crtera set s called nomnal group technque (NGT) [3]. The process forces everyone to partcpate and no domnant person s allowed to come out and control the proceedngs. In NGT all deas have equal stature. Seven potental evaluaton crtera are determned through a NGT process n our emprcal study. To smplfy the process and avod any msunderstandng, the nteracton between any of these crtera s not consdered n the frst nstance. Table 1 presents the proposed crtera and ther related attrbutes. The seven crtera may not nclude all of the decson factors n COTS evaluaton. However, they are the most meanngful measures n our case and have been stressed n many leadng artcles and books. In order to reflect the nterdependence property among the evaluaton crtera, we need to dentfy the exact relatonshp n the network structure frst. Another NGT process n our study constructed the relatonshp based on the followng recogntons. (a) Good ntegrated soluton, one-stop servce, educaton support, and techncal support wll reduce the technologcal rsk and make mplementaton process easer. (b) The hgher charged prce for mplementaton and mantenance may let suppler tend to place more emphass on customer care. (c) A system wth hgher ntegraton level nduces lower technologcal rsk snce less customer development s needed. Table 1 Proposed crtera and ther related attrbutes Selecton crtera Cost (CO) SupplerÕs support (SS) Technologcal rsk (TR) Closeness of ft to the companyõs busness (FB) Easy of mplementaton (EI) Flexblty to easy change as the companyõs busness changes (FC) System ntegraton (SI) Evaluaton attrbutes Lcense fee, modular prcng, mantenance, documentaton, consultant fee, resource utlzaton, converson cost Vendor responsveness, consultng, hot lne, tranng, techncal support personnel, contnung enhancement, tme sharng access, warranty, documentaton, fnancal stablty, local branch offce, thrd vendor support, growth of customer base, actve R&D Nonrobust and ncomplete packages, complex and undefned COTS-to-legacy-system nterfaces, mddleware technology bugs, poor custom code, and poor system performance, software maturty, hardware maturty Man target, ncluded functonalty Shorter mplementaton tme, user frendlness, multste mplementaton Adaptablty, openness for customer development, openness for workng wth other systems Internal connectvty, external connectvty

4 254 H.-J. Shyur / Appled Mathematcs and Computaton 177 (2006) SI TR FC CO SS EI FB Fg. 2. Relatonshp among crtera. (d) A system s flexble whch means t s desgned more openness for customer development and workng wth other systems. It reduces some technologcal rsks such as a system wth a complex and undefned COTS-to-legacy-system nterface. Fg. 2 represents the type of nterdependency network. The sngle arrows mply a one-way relatonshp. For example, the arrow that leaves from SI and feeds nto TR nfers that the attrbutes of crteron SI nfluence crteron TR Determne the weghts of crtera To determne the relatonshp of the degree of nterdependence, the analytc network process (ANP) technque, an extenson of AHP, s used to address the relatve mportance of the evaluaton crtera. The ANP s developed by Saaty [14 16] to generate prortes for decsons wthout makng assumptons about a undrectonal herarchy relatonshp among decson levels. To take the place of a lnear top-to-bottom form of strctly herarchy, the ANP model provdes a looser network structure makes possble the representaton of any decson problem. The relatve mportance or strength of the mpacts on a gven element s measured on a rato scale smlar to AHP. The major dfference between AHP and ANP s that ANP s capable of handlng nterrelatonshps between the decson levels and attrbutes by obtanng the composte weghts through the development of a supermatrx. The supermatrx s a parttoned matrx, where each submatrx s composed of a set of relatonshps between two components or clusters n a connecton network structure. Saaty [15] explans the concept correspondng to the Markov chan process. For our dscusson, we use the matrx manpulaton based on the concept of Saaty and TakzawaÕs [14] n place of SaatyÕs supermatrx, whch s much easer to understand. Due to the characterstcs of COTS evaluaton presented here we explore the approprateness of ANP to allow for the explct consderaton of nteractons n the decson makng process. The remanng procedure nvolves three substeps and shown as follows: Step 1: Wthout assumng the nterdependence among crtera, the decson makers are asked to evaluate all proposed crtera parwse. They responded questons such as: whch crtera should be emphaszed more n a COTS product, and how much more? The responses were presented numercally and scaled on the bass of SaatyÕs proposed 1 9 scale [13], where 1 represents ndfference between the two crtera and 9 s extremely preferred of the crteron under consderaton over the comparson crteron. Each par of crtera s judged only once. A recprocal value wll be automatcally assgned to the reverse comparson. Once the parwse comparsons are completed, the local prorty vector w 1 s computed as the unque soluton to Aw 1 ¼ k max w 1 ; ð1þ where k max s the largest egenvalue of parwse comparson matrx A. The obtaned vector s further normalzed by dvdng each value by ts column total to represent the normalzed local prorty vector w 2. Step 2: Next to resolve the effects of the nterdependence that exsts between the evaluaton crtera. The decson makers examne the mpact of all the crtera on each other by usng parwse comparsons as well. Questons such as: whch crteron wll nfluence crteron TR more: SI or FC? and how much more?

5 are answered. Varous parwse comparson matrces are constructed for each of the crteron. These parwse comparson matrces are needed to dentfy the relatve mpacts of crtera nterdependent relatonshps. The normalzed prncpal egenvectors for these matrces are calculated and shown as column component n nterdependence weght matrx of crtera B, where zeros are assgned to the egenvector weghts of the crtera from whch a gven crteron s gven. Step 3: Now we can obtan the nterdependence prortes of the crtera by syntheszng the results from prevous two steps as follows: w c ¼ Bw T 2. ð2þ 2.3. The rankng process The evaluaton procedure calculates the mportance weghts of varous crtera by ANP. Once the weghts of crtera are determned, a modfed TOPSIS rankng approach s proceeded to conduct the remanng evaluaton procedure. The full ANP soluton s only practcally usable f the number of crtera and alternatves s suffcently low so that the number of parwse comparsons performed by evaluator must reman below a reasonable threshold. For example, f there are n crtera whch have been assgned the mportance weghts and m alternatves, then to run a full ANP soluton there are n Æ m Æ (m 1)/2 parwse comparsons remanng to be performed. The number of alternatve COTS on the market ncreases rapdly [1]. To avod unreasonably large number of parwse comparsons, we conduct TOPSIS to acheve the fnal rankng result and replace the full ANP soluton. The basc TOPSIS technque conssts of the followng steps: 1. Establsh a decson matrx for alternatve performance. The structure of the matrx can be expressed as follows: F 1 F 2 F j F n 2 A 1 f 11 f 12 f 1j f 3 1n A 2 f 21 f 22 f 2j f 2n.. D ¼.... A f 1 f 2 f j f ; n A m f m1 f m2 f mj f mn where A denotes the possble alternatves, =1,...,m; F j represents attrbutes or crtera relatng to alternatve performance, j =1,...,n; and f j s a crsp value ndcatng the performance ratng of each alternatve A wth respect to each crteron F j. 2. Calculate the normalzed decson matrx R (=[r j ]). The normalzed value r j s calculated as f j r j ¼ q ffffffffffffffffffffffffffffff P ; j ¼ 1;...; n; ¼ 1;...; m. ð3þ n j¼1 f j 2 3. Calculate the weghted normalzed decson matrx by multplyng the normalzed decson matrx by ts assocated weghts. The weghted normalzed value v j s calculated as v j ¼ w j r j ; j ¼ 1;...; n; ¼ 1;...; m; ð4þ where w j represents the weght of the jth attrbute or crteron. 4. Determne the deal and negatve-deal solutons. V þ ¼fv þ 1 ;...; vþ n g¼fðmax V ¼fv 1 ;...; v n g¼fðmn H.-J. Shyur / Appled Mathematcs and Computaton 177 (2006) v j jj 2 JÞ; ðmn v j jj 2 J 0 Þg; v j jj 2 J 0 Þg; v j jj 2 JÞ; ðmax where J s assocated wth beneft crtera, and J 0 s assocated wth cost crtera. ð5þ

6 256 H.-J. Shyur / Appled Mathematcs and Computaton 177 (2006) Calculate the separaton measures, usng the m-dmensonal Eucldean dstance. The separaton of each alternatve from the deal soluton ðd þ Þ s gven as vffffffffffffffffffffffffffffffffffffffffffffffffffffff ux n ¼ t ðv j v þ j Þ 2 ; ¼ 1;...; m. ð6þ D þ j¼1 Smlarly, the separaton of each alternatve from the negatve-deal soluton ðd Þ s as follows: vffffffffffffffffffffffffffffffffffffffffffffffffffffff ux n ¼ t ðv j v j Þ 2 ; ¼ 1;...; m. ð7þ D j¼1 6. Calculate the relatve closeness to the dea soluton and rank the preference order. The relatve closeness of the alternatve A wth respect to V + can be expressed as D C ¼ D þ þ D ; ¼ 1;...; m; ð8þ where the C ndex value les between 0 and 1. The larger the ndex value means the better the performance of the alternatves. In the aggregaton process, a set of alternatve COTS s to be compared wth respect to predefned crtera. The performance ratng of each alternatve for each crteron s assgned and formed as a decson matrx. Furthermore, the normalzaton formula as shown n formula (1) s used to transform the varous scale nto a comparable scale. The normalzed decson matrx s weghted by multplyng each column of the matrx by ts assocated crtera weght n the above process. The overall performance of an alternatve s then determned by ts Eucldean dstance to V + and V. However, Shpley et al. [17] ponts out that ths dstance s nterrelated wth the crtera weghts and should be ncorporated n the dstance measurement. Ths s because all alternatves are compared wth V + and V, rather than drectly among themselves. Deng et al. [4] presents the weghted Eucldean dstances to nstead of creatng a weghted decson matrx. In ths process, we defne the postve deal soluton (R + ) and the negatve-deal soluton (R ), whch are not depended on the weghted decson matrx, as R þ ¼fr þ 1 ;...; rþ n g¼fðmax R ¼fr 1 ;...; r n g¼fðmn r j jj 2 JÞ; ðmn r j j j 2 J 0 Þg; r j jj 2 JÞ; ðmax r j jj 2 J 0 Þg. The weghted Eucldean dstances, between A and R +, and between A and R, are calculated, respectvely, as vffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff vffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff X n u ux ¼ t w j ðr j r þ j Þ 2 n ; D ¼ t w j ðr j r j Þ 2 ; ¼ 1;...; m; ð10þ D þ j¼1 j¼1 where the value of w j (j =1ton) s the element of vector w c whch s calculated by formula (2). Then we can obtan closeness coeffcent for each alternatve based on formula (8). Fnally, a set of alternatve can be preference ranked accordng to the descendng order of closeness coeffcent. 3. Illustratve example To llustrate the proposed COTS evaluaton process, an applcaton based on practcal experence and mplementaton n an electronc company s presented n ths sesson. A team of four s been charged n an off-lne producton data analyss system selecton project. All the team members have prevous experence n nformaton systems evaluaton. To conduct the emprcal study, we spent more than two weeks to gather enough nformaton through ntervews wth users and managers, observaton of current operaton process, and analyss of the systemõs documentaton to develop some general deas for the to-be system. Next, the screenng crtera were created ð9þ

7 H.-J. Shyur / Appled Mathematcs and Computaton 177 (2006) to conduct a market research ntatve lookng for sutable work flow systems and narrow the feld, where screenng crtera are the mnmum requrements about canddate systems. In our practcal example, we brng nto budget lmt as the major screenng crtera, and four systems (A 1,A 2,A 3,A 4 ) were selected nto the canddate lst. After the ntal screenng process wth respect to a few rgorous cutoff crtera, the decson problem faced by the evaluaton team was to determne the prorty of each canddate and select the fnalsts. The phase composes of a seres of complex revew and decson but short of an explct approach. In ths study, the proposed method was appled to solve ths problem and the computatonal procedure s summarzed as follows: Step 1: The team members were asked to evaluate all proposed crtera (Table 1) parwse wthout assumng the nterdependence among them. The result s presented n Table 2. The normalzed egenvector s lke w 2 = (CO, EI,SS,FB,FC, TR, SI) = (0.242,0.360,0.042, 0.102,0.030, 0.157, 0.067) whch represents the related local prorty of these crtera. Step 2: In addton we consdered and analyzed the dependence among the selecton crtera. The team members examned the mpact of all the crtera on each by usng parwse comparson. Totally, seven parwse comparson matrces were developed. The normalzed egenvectors for these matrces are calculated and shown as seven columns n Table 3, where zeros are assgned to the egenvector weghts of the crtera from whch a gven crteron s gven. The data of Table 3 mean seven crteraõs degree of relatve mpact for each seven crtera. For example, the COÕs degree of relatve mpact for SS s Step 3: The relatve mportance of the crtera consderng nterdependence now can be obtaned by syntheszng the results from Steps 1 and 2 as follows: CO 1 0: :242 0:301 SS 0 0:835 0: : :360 0:332 EI 0 0 0: :042 0:026 w c ¼ FB ¼ 0 0 0: :102 ¼ 0:112. FC : :030 0: TR : : :097 5 SI : :067 0:091 Table 2 Crtera parwse comparson matrx CO SS EI FB FC TR SI Vector weghts CO 1 1/ SS EI 1/5 1/7 1 1/3 2 1/5 1/ FB 1/3 1/ / FC 1/7 1/8 1/2 1/4 1 1/4 1/ TR 1/2 1/ SI 1/4 1/5 2 1/2 3 1/ Table 3 Degree of relatve mpact for evaluaton crtera CO SS EI FB FC TR SI CO SS EI FB FC TR SI

8 258 H.-J. Shyur / Appled Mathematcs and Computaton 177 (2006) Table 4 Normalzed decson matrx CO SS EI FB FC TR SI A A A A Table 5 Fnal rankng of COTS products Rank Alternatve Closeness coeffcent 1 A A A A Accordng to what we calculated, SS, CO, and FB were three of the most mportant consderng factors relatng to the system evaluaton n ths company, whch was confrmed by the decson team. Step 4: At the next level of the decson procedure, the team members were asked to establsh the decson matrx by comparng canddates under each of the crtera separately. The crtera were assumed to be beneft crtera and all the members were asked to gve a set of crsp values wthn the range from 1 to 10 to represent the performance of each alternatve wth respect to each crteron. After the decson matrx was determned, we normalzed the matrx by usng formula (1). Table 4 shows the result. Step 5: The fnal rankng procedure starts at the determnaton of the deal and negatve-deal solutons. The deal and negatve-deal solutons are defned by formula (9) as R þ ¼ð0:64; 0:70; 0:63; 0:64; 0:61; 0:69; 0:63Þ; R ¼ð0:28; 0:35; 0:39; 0:32; 0:30; 0:30; 0:39Þ. Snce the crtera weghts (w c ) have been obtaned from ANP, the weghted Eucldean dstances, between A and R +, and between A and R, can be calculated by formula (10). Fnally, usng formula (8) the relatve closeness to the dea soluton of each alternatve are then calculated. The evaluaton results can be seen n Table 5. Accordng to the closeness coeffcent, the rankng order of the four canddates s A 4, A 1, A 2, and A 3. Obvously, the best selecton s canddate A 4. In ths emprcal study, a refnement process was performed to confrm the result whch was obtaned by our proposed approach. The decson team revewed and refned the applcaton of the lst of crtera to each fnal canddate system. Each system provder was requested to demonstrate the system, to help the decson team to obtan a much deeper knowledge on ts functonalty and adaptablty to the company. The decson team vsted two reference stes of the wnnng software as well, to see the software n actual use n a company. In ths case, alternatve A 4 was selected as the fnal wnner after the refnement process. 4. Conclusons The purpose of ths paper s to present an effectve framework usng both ANP and modfed TOPSIS methods for performng COTS evaluaton. To address the crtera nterdependence problem, ANP method s used n obtanng the relatve weght of crtera. As the results shown n the emprcal study, we fnd that the proposed method s practcal for rankng competng COTS products n terms of ther overall performance wth respect to multple nterdependence crtera. Whle we beleve that the approach presented there s room for future enhancements and valdaton. For example, how to extend the current proposed approach to handle the nherent uncertanty and mprecson of the human decson makng process should be examned. The ANP whch s used n determnng the crte-

9 ron weghts requres complex matrx operatons on real number, tradtonal fuzzy concept cannot be drectly used n the matrx calculatons of the ANP [10]. Ths may be a new drecton n future development. In concluson, the underlyng concept of ths method s ratonal and comprehensble. The consderaton of relatonshps among COTS evaluaton crtera presented n ths paper provdes organzatons a way to devse and refne adequate crtera and allevate the rsk of selectng sub-optmal solutons. References H.-J. Shyur / Appled Mathematcs and Computaton 177 (2006) [1] L.C. Brand, COTS evaluaton and selecton, n: Proceedngs of the Internatonal Conference on Software Mantenance, vol. 1998, 1998, pp [2] D.J. Carney, K.C. Wallnau, A bass for evaluaton of commercal software, Informaton and Software Technology 40 (1998) [3] A.L. Delbecq, V.A.H. Ven, D.H. Gustafson, Group Technques for Program Plannng, Scott, Foresman and Company, IL, [4] H. Deng, C.H. Yeh, R.J. Wlls, Inter-company comparson usng modfed TOPSIS wth objectve weghts, Computers and Operatons Research 27 (2000) [5] G.R. Fnne, G.E. Wttg, D.I. Petkov, Prortzng software development productvty factors usng the analytc herarchy process, Journal of Systems and Software 22 (1995) [6] S. Hong, R. Ngam, Analytc herarchy process appled to evaluaton of fnancal modelng software, n: Proceedngs of the 1st Internatonal Conference on Decson Support Systems, Atlanta, [7] C.L. Hwang, K. Yoon, Multple Attrbute Decson Makng: Methods and Applcatons, A State of the Art Survey, Sprnger-Verlag, New York, [8] J. Konto, A case study n applyng a systematc method for COTS selecton, n: IEEE Proceedngs of ICSE-18, 1996, pp [9] K.R.P.H. Leung, H.K.N. Leung, On the effcency of doman-based COTS product selecton method, Informaton and Software Technology 44 (2002) [10] L. Mkhalov, M.G. Sngh, Fuzzy analytc network process and ts applcaton to the development of decson support systems, IEEE Transactons on Systems, Man, and Cybernetcs Part C: Applcatons and Revews 33 (1) (2003) [11] H. Mn, Selecton of software: the analytc herarchy process, Internatonal Journal of Physcal Dstrbuton and Logstcs Management 122 (1) (1992) [12] C. Rolland, Requrement engneerng for COTS based systems, Informaton and Software Technology 41 (14) (1999) [13] T.L. Saaty, The Analytc Herarchy Process, McGraw-Hll, New York, [14] T.L. Saaty, M. Takzawa, Dependence and ndependence: from lnear herarches to nonlnear networks, European Journal of Operatonal Research 26 (1986) [15] T.L. Saaty, The Analytc Network Process, RWS Publcatons, Pttsburgh, [16] T.L. Saaty, Fundamentals of the Analytc Network Process, ISAHP, Kobe, Japan, [17] M.F. Shpley, D.K. Korvn, R. Obt, A decson makng model for mult-attrbute problems ncorporatng uncertanty and bas measures, Computers and Operatons Research 18 (1991)