ERP Software Selecton Usng The Rough Set And TPOSIS Methods Under Fuzzy Envronment Informaton Management Department, Hunan Unversty of Fnance and Economcs, No. 139, Fengln 2nd Road, Changsha, 410205, Chna smon5115@163.com Abstract Improperly selected ERP software may have an mpact on the tme requred, and the costs and market share of a company, selectng the best desrable ERP software has been the most crtcal problem for a long tme. On the other hand, selectng ERP software s a multple-crtera decson-makng (MCDM) problem, and n the lterature, many methods have been ntroduced to evaluate ths knd of problem, whch has been wdely used n MCDM selecton problems. In ths paper, an ntegrated approach of ERP software selecton analytc herarchy process mproved by rough sets theory (Rough-AHP) and fuzzy TOPSIS method s proposed to obtan fnal rankng. Keywords: Enterprse Resource Plannng ; Software Selecton ; Rough Set ; TOPSIS 1. Introducton Any ERP software n market cannot fully meet the needs and expectatons of companes, because every company runs ts busness wth dfferent strateges and goals. ERP vendors use dfferent hardware platforms, databases, and operaton systems, and some ERP software s only compatble wth some companes databases and operaton systems. Therefore, one of the most crtcal ssues n mplementaton of an ERP system s the selecton of the approprate software to be used. The mportance of the actual software selecton Influental factors must not be underestmated. In our study, These dentfed fve mportant dmensons of performance are Rsk, Qualty, Effectveness, Effcency, and customers satsfacton degree. 2. Analytc herarchy process mproved by rough set theory (Rough-AHP) AHP, developed by Saatty (1980), addresses how to determne the relatve mportance of a set actvtes n dfferent decson-makng processes. The AHP method s based on three prncples: structure of the herarchy, the matrx of parwse comparson ratos and the method for calculatng weghts. But, AHP s strongly connected to human udgment and parwse comparsons n AHP may cause evaluator s assessment bas whch stuaton makes the comparson udgment matrx nconsstent. In ths paper the concept of attrbute sgnfcance n rough sets theory s utlzed to solve evaluaton bas problem n AHP. Condtonal entropy and attrbute sgnfcance concepts n rough sets theory are utlzed n AHP to mprove the udgment consstency. Formally, a data table s the 4-tuple S=(U,R,V,f) where U s a fnte set of obects (unverse);r = C D s a set of attrbutes, subsets C and D are the condton attrbute set and the decson attrbute set,respectvely; Vr s doman of the attrbute r, V= Vr A and f:u A V s a total functon such that f(x, r) Vr for each r R, x U, called nformaton functon. Defnton 1.Entropy H(P) of knowledge P (attrbutes set) s defned as n H ( p) p( X)log p( X) 1 (1) Advances n nformaton Scences and Servce Scences(AISS) Volume4, Number3, February 2012 do: 10.4156/AISS.vol4.ssue3.15 111
X px ( ) U Where and p(x)donates the probablty of X when p s on the partton X { X1, X2,, X n } of unverse U, =1,2,,n. H ( QP) QU ( INDQ ( )) { Y Defnton 2. condtonal entropy whch knowledge 1, Y2,, Y m } s QU ( INDP ( )) { X1, X2,, X } relatve to knowledge n s defned as n m HQP ( ) px ( ) py ( X)log py ( X) 1 1 (2) p( Y X ) Where s condtonal probablty, =1,2,,n,=1,2,,m. Defnton 3.Suppose that decson table S=(U,R, V, f), R = C D, subsets C and D are the condton attrbute set and the decson attrbute set, respectvely, attrbute subset A C. The attrbute sgnfcance Sg(a, A, D) of attrbute a C/A s defned as H( D A) H( D A{ a}) Sg(a, A, D)= (3) Gven attrbute subset A,the greater the value of Sg(a, A, D),the more mportant attrbute a s for decson D. 3. Fuzzy TOPSIS TOPSIS method s a technque for order performance by smlarty to deal soluton from a fnte set of ponts. The man rule s that the best alternatve would be the shortest dstance from the postve deal soluton and the furthest dstance from the negatve deal soluton. But n real lfe, measurement by usng crsp values s not always possble. For ths reason, the fuzzy TOPSIS method s very sutable for solvng real lfe applcaton problems under a fuzzy envronment. a ( a Defnton 4.Let 1, a2, a3) b ( b and 1, b2, b3) be two trangular fuzzy numbers then the vertex method s defned to calculate the dstance between them dab (, ) [( ab) ( ab) ( ab) ] 1 2 2 2 3 1 1 2 2 3 3 (4) Defnton 5. Consderng the dfferent mportance values of each crteron, the weghted normalzed fuzzy-decson matrx s constructed as. V [ v ] Where v X () W A set of performance ratngs of A,(=1,2,,J)wth respect to crtera X ( x, 1, 2,, n, 1, 2,, J) C,(=1,2,,n)called A set of mportance weghts of each crteron W(=1,2,,n). n,=1,2,,n,=1,2,,j, (5) 112
Fuzzy TOPSIS steps can be outlned as follows: ( x, 1, 2,, n, 1, 2,, J) Step1:choose the lngustc ratng for alteratves wth respect to crtera. The fuzzy lngustc ratn( x ) preserves the property that the ranges of normalzed trangular fuzzy numbers belong to [0,1];thus, thers s no need for normalzaton. Step 2:calculate the weghted normalzed fuzzy decson matrx. the weghted normalzed value caluated by eq.(5). Step 3:nentfy postve-deal (A) and negatve deal (A-) solutons. The fuzzy postve-deal soluton(fpis, A)and the fuzzy negatve-deal soluton(fnis, A-)are shown n the followng equatons: A { v 1, v 2,..., v } max v I mn v I A { 1, 2,..., } mn max v v v v I v I =1,2,,n,=1,2,,J, =1,2,,n,=1,2,,J, v (6) (7) where I s assocated wth beneft crtera and I s assocate wth cost crtera. Step 4:caluate the dstance of each alternatve from A and A usng the followng equatons: n 1 D dv (, v ) =1,2,,J (8) n 1 D dv (, v ) =1,2,,J (9) Step 5:caluate smlartes to deal soluton D D D (10) Step 6:rank preference order choose an alternatve wth maxmum to n descendng order. 4. A new methodology for ERP software selecton 4.1. Defne the crtera for ERP system selecton or rank alternatves accordng If there are more ERP alternatves n the lst than expected, a pre-selecton process should be used to reduce the number of alternatves to an acceptable level (three or four) so that the selecton process wll 113
not be too lengthy. We selected four ERP system selecton frms(such as CA-MANMAN/X, BAAN, SSA-BPCS and SAP R/3),to evaluate ther selecton ndcators and ther weghts n total score, so we ntervewed wth ERP users, the frms s and corporaton s senor management cadre. Expectatons from a ERP software selecton scale nclude partcularly low rsk, hgh qualty, flawless product, relablty, delvery on tme. To develop fuzzy envronment selecton model, we frst dentfed varous Influental factors of ERP system selecton and the correspondng ndcators, that are used to evaluate those frms under aforementoned expectatons. These dentfed fve mportant Influental factors of software selecton are Rsk, Qualty, Effectveness, Effcency, and users satsfacton degree. We arranged the herarchy structure of the selecton ndcators n Fg.1. 4.2. Calculate the weghts of crtera After formng the herarchy of the problem, decson table s bult. In decson table (.e. Table 1) rows ndcate the dstnct obects, and columns ndcate the dfferent attrbutes(.e. selecton ndcators) consdered. Intally decson column s empty. The rsk, qualty, effectveness, effcency and users satsfacton degree crtera are rated usng the 1, 2, 3 values. Only for the Rsk crtera 1 means low, 2 means medum and 3 means hgh whereas these mean the contrary for other crtera; 1 hgh, 2 medum and 3 low. Secondly, we can make a table that lsts dfferent combnatons of crtera rates before evaluaton process. In Table 1, we lst 24 dfferent combnatons. Then the table s gven to evaluaton team to make a decson. The number 1 n decson column represents selecton approves and the number 0 represents selecton dsapproves. Selecton of the best ERP frms Rsk Qualty Effectveness Effcency Users satsfacton Frm-1 (F1) Frm-2 (F2) Frm-3 (F3) Frm-4 (F4) Fgure 1. The herarchy of the study. 114
Table 1. Decson table about rsk, qualty, effectveness, effcency and occupatonal satsfacton U Rsk (a) Qualty (b) Effectveness (c) Effcency (d) Occupatonal Satsfacton(e) 1 2 3 1 3 2 0 2 1 2 2 3 3 1 3 3 1 1 2 2 0 4 1 2 1 1 3 1 5 2 3 3 2 2 0 6 2 3 2 2 3 0 7 1 3 3 3 2 0 8 1 2 2 2 2 1 9 2 1 2 3 3 1 10 3 2 1 1 3 0 11 1 2 2 1 3 1 12 3 2 2 2 2 0 13 2 2 3 3 3 0 14 1 3 1 3 2 1 15 2 2 2 2 2 1 16 2 2 3 2 3 0 17 2 2 2 2 3 1 18 2 2 2 3 3 0 19 2 1 3 2 2 1 20 2 1 1 2 2 1 21 2 2 2 1 3 1 22 2 3 1 2 2 0 23 2 2 3 2 1 1 24 2 1 3 3 3 0 Decson (D) For the decson table of table 1,we can get crtera sgnfcances of rsk, qualty, effectveness, effcency, and occupatonal satsfacton by the followng process: U\IND{a,b,c,d,e}={{1},{2},{3},{4},{5},, {20},{21},{22},{23},{23}}, U\IND{D}={{2,4,8,9,11,14,15,17,19,20,21,23},{1,3,5,6,7,10,12,13,16,18,22,24}}={D1,D2}, U\IND{b,c,d,e}={{4,10},{8,12,15},{3,20},{2,18},{1,14}} ={X1,X2,X3,X4,X5}, P(X1)=2/24,P(D1\ X1)=1/2, P(D2\ X1)=1/2; P(X2)=3/24,P(D1\ X2)=1/3, P(D2\ X2)=1/2; P(X3)=2/24, P(D1\ X3)=1/2, P(D2\ X3)=1/2; P(X4)=2/24, P(D1\ X4)=1/2, P(D2\ X4)=1/2; P(X5)=2/24, P(D1\ X5)=1/2, P(D2\ X5)=1/2; Sg(a,{b,c,d,e},{D})=H({D}\{b,c,d,e})-H({D}\{a,b,c,d,e}) 2 1 1 1 1 3 1 1 2 2 ( log log ) 4 ( log log ) 24 2 2 2 2 24 4 3 3 3 = =0.135 We obtan the sgnfcance of attrbute a (.e. rsk crteron) s 0.135.By the smlar process, we also can get the sgnfcance of attrbute b(.e. qualty crteron)s 0.100 and the sgnfcance of attrbute c(.e. effectveness crteron) s 0.075 and the sgnfcance of attrbute d(.e. effcency crteron) s 0.035 and the sgnfcance of attrbute e (.e.users satsfacton degree) s 0.025,respectvely. For rsk, qualty, effectveness, effcency and users satsfacton degree crtera, the udgement matrx J s constructed accordng crtera sgnfcance as follows: 115
1 1.345 1.792 3.899 5.375 0.744 1 1.332 2.899 3.996 J 0.558 0.751 1 2.176 3 0.256 0.345 0.459 1 1.387 0.186 0.250 0.333 0.725 1 Ths matrx s then translated nto the largest egenvalue problem and resultng prorty weghts of rsk, qualty, effectveness, effcency, occupatonal satsfacton are found as 0.364,0.271,0.203,0.093 and 0.068,respectvely.The largest egenvalue max s 5.The consstency ndex(ci) s defned as max n CI n 1, (11) where n s the rank of udgment matrx. Accordng to the formula of CI, we know that CI=0 for matrx J. Ths result shows that parwse comparson matrx constructed by rough sets method possesses complete consstency. 4.3. Evaluate the alternatves wth fuzzy TOPSIS and determnate the fnal rank Durng the decson procedure, the evaluaton users were asked to establsh the decson matrx by comparng alternatves under each of the crtera one by one. Fuzzy Evaluaton Matrx formed by the evaluaton of alternatve s shown n lngustc varables n Table 2.The fuzzy evaluaton matrx constructed by lngustc varables s converted to trangular fuzzy numbers, whch are equvalent to lngustc varables, as seen n Table 3.After the determnaton of fuzzy evaluaton matrx the next acton s to obtan a fuzzy weghted decson table. By usng the crtera weghts obtaned from rough-ahp n ths level, the Weghted Evaluaton Matrx s establshed wth Eq. (5). The consequent fuzzy weghted decson matrx s presented n Table 4. Table 2. Lngustc values and fuzzy numbers. Lngustc values Fuzzy numbers Very low(vl) (0,0,0.2) Low (L) (0,0.2,0.4) Medum (M) (0.2,0.4,0.6) Hgh (H) (0.4,0.6,0.8) Very hgh (VH) (0.6,0.8,1) Excellent (E) (0.8,1,1) v In relaton to (Table 4) the elements are normalzed postve trangular fuzzy numbers and ther ranges are assocated wth the closed nterval [0,1]. Thus, we can determne the fuzzy postve deal soluton(fpis, A (1,1,1) ) and the fuzzy negatve-deal soluton (FNIS,A-) as (0,0,0) (1,1,1) (0,0,0) for beneft crteron, and and for cost crteron. All along the study, rsk crtera s defned as cost crtera, whereas qualty, effectveness, effcency and users satsfacton degree are defned as beneft crtera. For the thrd phase, the dstance of each alternatve from D and D can be calculated by usng Eqs. (8) and (9).The last phase elucdates the smlartes to an deal soluton by Eq.(10).In order to llustrate steps 3 and 4 calculaton, calculaton s used as an example as follows: D1 1.163 = =0.232 D D 3.860 1.163 1 1 and 116
Smlar calculatons are done for the other alternatves and the results of fuzzy TOPSIS analyses are summarzed n Table 5. Based on values, the rankng of the alternatves n descendng order are ERP system selecton frm 4,2,1,3. These results ndcate that ERP system selecton frm 4 has the best choce. Table 3. Fuzzy evaluaton matrx for the alternatve ERP system selecton. C1 C2 C3 C4 C5 A1 (0.6,0.8,1) (0.6,0.8,1) (0.4,0.6,0.8) (0.2,0.4,0.6) (0.8,1,1) A2 (0.4,0.6,0.8) (0.6,0.8,1) (0.4,0.6,0.8) (0.8,1,1) (0.2,0.4,0.6) A3 (0.8,1,1) (0.4,0.6,0.8) (0.6,0.8,1) (0,0.2,0.4) (0,0.2,0.4) A4 (0.2,0.4,0.6) (0.4,0.6,0.8) (0.4,0.6,0.8) (0.6,0.8,1) (0.4,0.6,0.8) weght 0.364 0.271 0.203 0.093 0.068 Table 4. Weghted evaluaton for the alternatve ERP system selecton C1 C2 C3 C4 C5 A1 (0.218,0.291,0.364) (0.163,0.217,0.271) (0.081,0.122,0.162) (0.019,0.037,0.056) (0.054,0.068,0.068) A2 (0.146,0.218,0.291) (0.163,0.217,0.271) (0.081,0.122,0.162) (0.074,0.093,0.093) (0.014,0.027,0.041) A3 (0.291,0.364,0.364) (0.108,0.163,0.217) (0.122,0.162,0.203) (0.000,0.019,0.037) (0.000,0.014,0.027) A4 (0.073,0.146,0.218) (0.108,0.163,0.217) (0.081,0.122,0.162) (0.056,0.074,0.093) (0.027,0.041,0.054) A 1=(0,0,0) 2=(1,1,1) 3=(1,1,1) 4=(1,1,1) 5=(1,1,1) A- -1=(1,1,1) -2=(0,0,0) -3=(0,0,0) -4=(0,0,0) -5=(0,0,0) 5. Concluson and suggestons Table 5. Rough AHP-fuzzy TOPSIS results. Alternatves D D- A1 3.680 1.163 0.232 A2 3.776 1.248 0.248 A3 3.968 1.037 0.206 A4 3.760 1.269 0.252 For evaluatng performance of the ERP system selecton frm, rough-ahp and fuzzy TOPSIS are appled. Despte the fact that AHP and Fuzzy TOPSIS have been utlzed n many places due to ther easy-to-apply features and effectveness n mult-crtera decson makng there has not been any study n the lterature about the applcaton and theory of combned rough-ahp and fuzzy TOPSIS. However, n rough-ahp, the qualtatve udgment can be quantfed to make more ntutonstc comparsons and reduce or elmnate assessment bas n parwse comparson process. The proposed method s mportant, because t can be mplemented to structures and other areas. References [1] Ta Chung Chu., Ychen Ln. Improved extensons of the TOPSIS for group decson makng under fuzzy envronment. Journal of Informaton and Optmzaton Scences, vol.23, no.2, pp.273 286..2002 [2] Salvatore Greco, Benedetto Matarazzo, Roman Slownsk. Rough sets methodology for sortng problems n presence of multple attrbutes and crtera. European Journal of Operatonal Research, vol.138.no.2,pp 247 259. 2002 [3] L Lng Hsu, Robert S.Q. La, Yu Te Weng. Understandng the crtcal factors effect user satsfacton and mpact of ERP through nnovaton of dffuson theory. Internatonal Journal of Technology Management, vol.43, no13, pp. 30-47,2008 [4] Huang, Y. F., Wu, W. W., Lee, Y. T. Smplfyng essental competences for Tawan cvl servants by usng the rough set approach. The Journal of the Operatonal Research Socety, vol.59.no2,pp 259 266..2008 117
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