ERP System Flexibility Measurement Based on Fuzzy Analytic Network Process

Transcription

1 JOURNAL OF SOFTWARE, VOL. 8, NO. 8, AUGUST 20 4 ERP System Flexblty Measuremet Based o Fuzzy Aalytc Netork Process Xaoguag Zhou ad Bo Lv Doglg School of Ecoomcs ad Maagemet, Uversty of Scece ad Techology Beg, Beg, Cha Emal: [email protected], [email protected] M Lu Dept. of Electrcal ad Computer Egeerg, Texas A&M Uversty, College Stato, TX, USA Emal: [email protected] Abstract To meet the chages of teral ad exteral evromet, Eterprse Resources Plag (ERP) system eeds to have a good flexblty. Flexblty s a dspesable request ad s also a ay that must be take durg the establshmet process of ERP. Flexblty measuremet s a mportat tem for the mplemetato of ERP flexblty. Accordg to the characterstcs of ERP system, a dex system for flexblty measuremet of ERP system s preseted th the terdepedece ad feedback relatoshps amog crtera ad/or dces beg take to accout. Due to the vagueess ad ucertaty formato durg the process of flexblty measuremet, tragular fuzzy umbers are used to dcate the preferece opos of experts ad decso makers. A flexblty measuremet model of ERP system based o fuzzy aalytc etork process (FANP) s proposed. The local eghts of crtera ad dces are derved by fuzzy preferece programmg (FPP) method. A ueghted supermatrx based o the etork structure of dex system s developed, ad the lmt supermatrx s geerated. The flexblty level of ERP system ca be measured by the eghts ad scores of ERP. Fally, a case s gve by the proposed method. Idex Terms fuzzy aalytc etork process, ERP, flexblty measuremet, fuzzy preferece programmg I. INTRODUCTION Although ERP mplemetato has bee oe of the most sgfcat challeges of the last decade, t comes th a surprsgly hgh falure rate due to ts hgh rsk ature ad lo flexblty. The rsks of ERP, hch volve both techcal ad socal ucertates, must to be effectvely maaged ad cotrolled. Tradtoal ERP practces address the mplemetato of ERP as a statc process. Such practces focus o structure, ot o ERP as somethg that ll meet the eeds of a chagg orgazato. As a result, may relevat ucertates that caot be predefed are ot accommodated, ad cause the mplemetato fal the form of proect delay ad cost overrus, ad so o. Dfferet flexblty deftos ad measuremets have bee proposed the lteratures. Flexblty s defed as "a ready capablty to adapt to e, dfferet, or chagg requremets" the Webster s Dctoary []. Flexblty s the ablty to accommodate, thstad or hadle ucertaty as ell. It descrbes the level of capablty a system ca hadle or absorb ucertates or chages. May categores, such as mache flexblty, operato flexblty, ad process flexblty, have bee adopted as ma strateges for mprovg market resposveess ucerta demad. I systems egeerg, flexblty s the characterstc of the terface betee a system ad ts exteral evromet [2]. Flexblty has bee dely researched the feld of maufacturg. The typcal reaso that maufacturg dustres have adopted flexblty s to speed up the etre product cycles. Flexblty of the trasportato system s oe of the mportat performace measures. ERP flexblty s a capablty to adapt the chages of eterprse's teral ad exteral evromet. Flexblty measuremet has alays played a role plag ad maagg complex systems. Che ad Kasktat provded a quattatve assessmet of capacty flexblty for the passeger trasportato etork usg b-level etork capacty models []. Fred ad Sugadha proposed a geeral model of flexblty measuremet based o Data Evelopmet Aalyss [4]. Gachett et al. preseted a measuremet frameork to aalyze the structural propertes of the eterprse system [5]. The frameork ca provde a cosstet bass for specfyg ad usg measures, hch ll empoer system desgers to better corporate desrable structural propertes to alg system desg th eterprse strategy. Koste et al. dscussed the lack of o-dustry specfc measures for maufacturg flexblty, ad poted out that gve the mult-dmesoal complexty assocated th ths cocept, "Churchll paradgm" as a approprate frameork [6]. Hldegard proposed a complexty measuremet hch addresses the fuctoal flexblty of etorks []. It s coectured that the fuctoal flexblty s reflected a topologcal dversty of the assged graphs, resultg from a resoluto of ther vertces ad a rerg of ther edges uder certa costrats. Cadl ad Whtley explored the terpretatve flexblty of ERP systems through the study of a proect to mplemet a hosted system for the Cetral Accoutg Departmet of a large multatoal [8]. They questoed the extet to hch techologcal features of the e system fluece the perceved do:0.404/s

2 44 JOURNAL OF SOFTWARE, VOL. 8, NO. 8, AUGUST 20 flexblty of the system. Namabad et al. poted out hardare flexblty of automato systems s addressed through the troducto of three ma parametrc flexblty measures fuctoal, structural, ad throughput []. They proposed a e quattatve measuremet method for these parameters the realm of the Axomatc Theory. Kermoglu et al. defed orgazatoal adopto of ERP systems through buldg a frameork hch has the core techology acceptace model varables, satsfacto ad commo actors of a ERP proect: techology, user, orgazato ad proect maagemet [0]. Results of ther study revealed that orgazatoal adopto ca oly be accomplshed f the satsfacto th the ERP system s acheved by competecy ad flexblty of the techology alog th the specal efforts of proect maagemet durg proect mplemetato. Wu et al. proposed a actve ERP mplemetato maagemet perspectve to maage ERP rsks based o the Real Optos theory, hch addresses ucertates over tme, resolves ucertates chagg evromets that caot be predefed []. By actvely maagg ERP mplemetato, maagers ca mprove ther flexblty, take approprate acto to respod to the ofte-chagg ERP evromet, ad acheve a more successful ERP mplemetato. Özogul et al. troduced a real optos-based methodology hch overcomes the lmtatos of tradtoal valuato methods ad eables decso-makers to value a ERP system vestmet corporatg multple optos [2]. The opto valuato model developed ther study exteds the bomal lattce frameork to model a hosptal formato system vestmet opportuty th compoud optos. We ad L proposed a tutostc trapezodal fuzzy model to select a optmal ERP system accordg to the dstace betee the overall value of the alteratves ad deal soluto []. Zheg preseted a method for eterprse accoutg process reegeerg based o ERP system, ad t ould mprove the effcecy of accoutg process ad ERP system as ell [4]. L et al. aalyzed the basc codto for medum ad small publshers to carry out EPR system ad proposed the gudeles for remedyg other shortfalls by creasg the flexblty of system [5]. They specfcally aalyzed fve custom fuctos that ERP system should have hch ca dramatcally crease the flexblty of ERP system ad effectvely solve may o-stadard ad ufxed busess problems order to better meet actual eeds. Although some scholars have researched ad dscussed the flexblty measuremet method of ERP system, hoever, the teracto ad feedback relatoshps amog crtera ad/or dces are ot take to accout exstg research results. Furthermore, durg the process of ERP flexblty measuremet, there are a good deal of ucertaty ad vague formato. The crsp values seem to be suffcet ad mprecse to dcate the rght preferece opos of experts ad decsomakers. Cosequetly, the obectve of ths paper s to propose a e method based o fuzzy aalytc etork process to make up for the defcecy of covetoal ERP flexblty measuremet. II. FUZZY ANALYTIC NETWORK PROCESS A. Tragular Fuzzy Number I geeral, a tragular fuzzy umber (TFN) s deoted smply as (l, m, u). The parameters l, m ad u, respectvely, represet the loer boudary, the most promsg value, ad the upper boudary that descrbe a fuzzy probablty, as sho Fgure. Each TFN has lear represetatos o ts left ad rght sde such that ts membershp fucto ca be defed as, 0, x < l; x l, l x m; m l u M ( x) = () u x, m x u; u m 0, x > u. u M (x) 0 l m u x Fgure. Tragular fuzzy umber Assume to tragular fuzzy umber A = (l, m, u ) ad A 2 = (l 2, m 2, u 2 ), the A A2 = ( l, m, u) ( l2, m2, u2) = ( l + l2, m + m2, u + u2), (2) A A2 = ( l, m, u) ( l2, m2, u2) = ( l l2, m m2, u u2), () A A2 = ( l, m, u) ( l2, m2, u2) = ( l l2, m m2, u u2), (4) A A2 = ( l, m, u) ( l2, m2, u2) = ( l / u2, m / m2, u / l2), (5) A = l, m, u ) = (/ u,/ m,/ ). (6) ( l B. Fuzzy Aalytc Netork Process The Aalytc Netork Process (ANP), troduced by Saaty [6], s a geeralzato of Aalytc Herarchy Process (AHP). The basc characterstc of the AHP s to decompose the decso makg process to a herarchcal structure here the relatoshps of elemets dfferet levels are depedet. Ufortuately, a lot of decso-makg problems caot be structured herarchcally, or there ould have strog teractos ad depedeces amog crtera ad/or dces. To meet more practcal decso makg propertes, the ANP exteds the AHP to problems th depedeces ad feedback by usg a supermatrx approach.

3 JOURNAL OF SOFTWARE, VOL. 8, NO. 8, AUGUST The frst phase of ANP compares the measurg crtera the overall system to form a supermatrx. Ths ca be accomplshed usg parse comparsos. The relatve mportace-values of parse comparsos ca be categorzed from to order to represet pars of equal mportace to extreme equalty mportace. AHP/ANP has bee dely used as a decso makg tool may felds, but the AHP/ANP-based method seems to be effectve dealg th the fuzzess or ucertaty for the udgmets durg the parse comparso process. I real-lfe decso-makg stuato, ucerta huma udgmets th teral cosstecy obstructg the drect applcato of the ANP are frequetly foud. Such codtos ll also occur durg the process of measurg ERP flexblty. Therefore, t s more approprate to measure ERP flexblty uder fuzzy codto. To cope th ths problem, Mkhalov ad Sgh preseted fuzzy aalytc etork process method []. FANP has bee used may felds, such as commodty acqusto [8], rsk evaluato [] ad koledge maagemet [20]. The geerato of prorty vectors from parse comparso matrces s a essetal part of the FANP. A umber of methods have bee suggested to acqure the local eghts of fuzzy matrces. For stace, Csutora ad Buckley brought forard a Lambda-Max method, hch s the fuzzfcato of kmax method [2]. Mkhalov came up th a fuzzy preferece programmg (FPP) method, hch ca obta crsp eghts from fuzzy udgmet matrces [22]. Srdevc developed a mult-crtera approach for combg prortzato methods for AHP, such as least-squares, goal programmg, egevector ad fuzzy preferece programmg [2]. Wag et al. proposed a modfed fuzzy logarthmc least square method to derve the local eghts [24]. Yu ad Cheg preseted a multple obectve programmg approach to acqure the local prortes for crsp or terval udgmets smultaeously [25]. Huo et al. developed e parametrc prortzato methods to determe prorty eghts AHP [26]. Grzybosk preseted e optmzato techques for dervg prorty vectors va computer smulatos, ad the e approach provdes a meagful dex that ca be cosdered as a atural exteso of the CI to all types of matrces [2], ad so o. C. Fuzzy Preferece Programmg Method I ths study, FPP method s adopted because the method has the follog advatages over other approaches. The most mportat advatage s the acquremet of cosstecy dex for fuzzy parse comparso matrces. It s mpossble to obta the cosstecy ratos thout coductg a addtoal study other methods. Aother mportat aspect s that the models developed to determe the local eghts ca be easly solved th the help of Matlab softare. The ma theory of Mkhalov s approach s sho as follos [22]. Suppose a prortzato problem th elemets, here the parse comparso matrces are deoted by fuzzy umbers. Assume the decso-maker ca provde a set F = {ã } of m (-)/2 fuzzy comparso udgmets, =, 2,, -; = 2,,, ; >, represeted as tragular fuzzy umbers ã = (l, m, u ). The problem s to develop a prorty vector = (, 2,, ) T, such that the prorty ratos / are approxmately th the scopes of fuzzy udgmets, or l ~ ~ u, () here the symbol " ~ " deotes the statemet "fuzzy less or equal to". Whe the cosstet udgmet occurs, the doublesde equaltes () represet to satsfy all udgmets as much as possble. The, the prorty vector ca be measured by a membershp fucto, lear th respect to the uko rato /, ( ) l, m, m l u ( ) = (8) u ( ), m. u m The membershp fucto (8) s learly creasg over the terval (-, m ) ad learly decreasg over the terval (m, ). The fucto has a maxmum value u =. Over the rage (l, u ), the membershp fucto (8) cocdes th the fuzzy tragular udgmet (l, m, u ). FPP method s based o to ma assumptos. The frst oe requres the exstece of o-empty fuzzy feasble area P o the (-) dmesoal smplex Q - Q = {(,, K ) > 0, = }. () 2 = The membershp fucto of the fuzzy feasble area s gve by u ( ) = m{ u ( ) =,2, K, ; = 2,, K, ; }. (0) P > The secod assumpto specfes a selecto rule, hch determes a prorty vector, havg the hghest degree of membershp (0). It ca easly be proved that u p () s a covex set, so there s alays a prorty vector * Q - that has a maxmum degree of membershp, λ = u ( ) = max m{ u ( ) }. () P Q The maxmum prortzato problem () ca be represeted the follog ay: Max λ λ u ( ), =,2, K, ; = 2,, K, ; >, (2) =, > 0, k =,2, K,. k= k k Cosderg the specfc form of the membershp fuctos (8), the prortzato problem (2) ca be further trasformed to a o-lear program Max λ ( m l ) + l 0, ( u k = λ m ) λ k =, k =,2, K, ; = 2,, K, ; >. + u > 0, k =,2, K,. 0, ()

4 46 JOURNAL OF SOFTWARE, VOL. 8, NO. 8, AUGUST 20 The optmal soluto to the above o-lear problem ( *, λ * ) s a vector hose frst compoet represets the prorty vector that maxmzes the degree of membershp the fuzzy feasble area, hereas ts secod compoet gves the value of the maxmum achevemet level λ * of the terval udgmet cosderg the cosstet pheomeo, hch s a cosstecy dex. A greater value λ * dcates greater cosstecy of the decso maker s udgmets, ad vce versa. Ⅲ. PROPOSED ERP FLEXIBILITY MEASUREMENT FRAMEWORK A e approach based o FANP s proposed to assst the flexblty measuremet of ERP system ths study. The measuremet dex system s frst detfed, ad the measuremet model s preseted the follog secto. A. Idex System of ERP Flexblty Measuremet To market competto, the ERP system eeds to meet the chages of exteral evromet ad teral busess. O the bass of exstg research results, a mproved ERP flexblty measuremet dex system s developed. The dex system s made up of fve parts: archtecture flexblty (C ) archtecture flexblty, fucto flexblty, trasacto processg flexblty, resposveess flexblty ad clet flexblty, as sho Fgure 2. Archtecture flexblty: the capablty of ERP structure adapts system evromet chages, cludg four subcrtera: degree of structurg, adaptablty, structure expasblty ad kerel stablty. Fucto flexblty: the ablty of ERP system meets the fuctoalty, cludg four dces: module couplg degree, parametrc desg, matchg degree ad the flexblty of cofgurato. If the module couplg degree s hgher, the the fucto flexblty of ERP system s loer. If the degree of parametrc desg, or matchg degree, or the flexblty of cofgurato s hgher, the the fucto flexblty of ERP system s hgher. Trasacto processg flexblty: the capablty of ERP hadles the umbers of busess ad adapts the chages of busess. It s a mportat tem to measure the flexblty of ERP system, cludg the follog three aspects: compoet-based busess, busess adaptablty ad busess recofgurato. The hgher of busess compoet s, the hgher of busess recofgurato has ad the better adaptablty of ERP system gets. degree of structurg (C ) adaptablty (C 2 ) structure expasblty (C ) kerel stablty (C 4 ) module couplg degree (C 2 ) Flexblty measuremet of ERP system fucto flexblty (C 2 ) trasacto processg flexblty (C ) clet flexblty (C 4 ) parametrc desg (C 22 ) matchg degree (C 2 ) flexblty of cofgurato (C 24 ) compoet-based busess (C ) busess adaptablty (C 2 ) busess recofgurato (C ) redefto of process documets (C 4 ) redefto of put ad output (C 42 ) redefto of terface (C 4 ) ole ob respose tme (C 5 ) resposveess flexblty (C 5 ) task stchg speed (C 52 ) accuracy (C 5 ) Fgure 2. Idex system of flexblty measuremet for ERP System

5 JOURNAL OF SOFTWARE, VOL. 8, NO. 8, AUGUST 20 4 Clet flexblty: the ablty of clet adapts busess chages, or the capablty of ERP meets customer requremets, cludg three factors: redefto of process documets, redefto of put ad output ad redefto of terface. Resposveess flexblty: the capablty of ERP resposes dfferet evromets. It s made up of three factors: ole ob respose tme, task stchg speed ad accuracy. There are teracto ad feedback relatoshps amog crtera ad/or dces the above dex system. For example, archtecture flexblty has a effect o the flexblty of other four crtera; coversely, fucto flexblty, trasacto processg flexblty ad clet flexblty ll affect archtecture flexblty, ad so o. Hoever, these teracto ad feedback relatoshps are ot cosdered exstg lteratures. It s obvous that the lack of formato ould lead to devato or rog results durg the flexblty measuremet process of ERP system. Therefore, ths paper presets a dex system th depedece ad feedback relatoshps amog the crtera ad/or dces. If archtecture flexblty (C ) has a effect o fucto flexblty (C 2 ), the a le th arro from C to C 2 s added. If the sub-crtera of archtecture flexblty (C ) have teracto tself, the C s er depedece, ad a arc th arro s added to C, as sho Fgure 2. B. Tragular Fuzzy Lgustc Varables The lgustc approach s a approxmate techque, hch represets qualtatve aspects as lgustc values by meas of lgustc varables. Accordg to lgustc scale, lgustc preferece relato s a effectve tool for expressg decso makers prefereces decso makg. For a ERP flexblty measuremet problem, let E = (e, e 2,, e m ) be a set of the experts volved the decso process, X = (x, x 2,, x ) be a set of cosdered alteratves. I the process of flexblty measuremet, a expert geerally eeds to provde hs/her prefereces for each par of dces or alteratves th respect to each crtero by the lgustc terms. TABLE Ⅰ. TRIANGULAR FUZZY LINGUISTIC SCALES FOR RELATIVE IMPORTANCE OF PAIRWISE COMPARISON Lgustc scales for relatve mportace Tragular fuzzy umbers Tragular fuzzy recprocal umbers Equally mportat(ei) (,, ) (,, ) Itermedate(IM ) (, 2, ) (/, /2, ) Moderately mportat(mi) (2,, 4) (/4, /, /2) Itermedate2(IM 2 ) (, 4, 5) (/5, /4, /) Importat(I) (4, 5, 6) (/6, /5, /4) Itermedate(IM ) (5, 6, ) (/, /6, /5) Very mportat(vi) (6,, 8) (/8, /, /6) Itermedate4(IM 4 ) (, 8, ) (/, /8, /) Absolutely mportat(ai) (,, ) (/, /, /) There are some kds of lgustc scales. The tragular fuzzy lgustc scale s effectve oe hch s ofte used to express the subectve preferece of experts. Varables descrbg the experts prefereces ca be dvded to umerous lgustc crtera, such as equally mportat, moderately mportat, mportat, very mportat ad absolutely mportat. A -pot scale of tragular fuzzy umbers ad ther recprocals s preseted for the relatve mportace of parse comparso, as sho Table Ⅰ. C. FANP-based Approach for Flexblty Measuremet of ERP System The approach of FANP-based that combes the FPP ad the ANP has the follog steps: Step. Costruct a etork structure accordg to the decso goal ad lst the depedeces amog all compoets of the etork structure ad defe the mpact betee each. A three-level measuremet dex system s preseted: the frst level s the comprehesve flexblty measuremet of ERP system; the secod level s crtera, cludg fve parts: archtecture flexblty, fucto flexblty, trasacto processg flexblty, clet flexblty ad resposveess flexblty; the thrd level s sub-crtera, cludg dces, as sho Fgure 2. Step 2. Buld parse comparso matrces of the compoets by a decso commttee usg the tragular fuzzy lgustc scales gve Table Ⅰ. The experts or decso makers are asked to respod to a seres of parse comparso th respect to the crtera/dces Fgure 2. For stace, to dces adaptablty (C 2 ) ad structure expasblty (C ) are compared usg the questo Ho mportat s adaptablty (C 2 ) he t s compared th structure expasblty (C ) at the dmeso of degree of structurg (C ) uder the crtero archtecture flexblty (C )? ad the aser s termedate mportat (IM ), so ths lgustc scale s placed the relevat cell agast the tragular fuzzy umbers (, 2, ). All the tragular fuzzy comparso matrces are produced the same maer. Step. Perform the FPP method o each comparso matrx dvdually to derve each set of local prortes. Accordg to equato (), local eghts ad cosstecy dces of the tragular fuzzy matrces are calculated th the help of a Matlab program. Step 4. Establsh a ueghted supermatrx th the derved local prortes from Step. The supermatrx s a parttoed matrx, here each sub-matrx s made up of a set of relatoshps amog crtera ad dces. Step 5. Geerate a eghted supermatrx th colum stochastc property. The reaso s that each colum of the ueghted supermatrx cossts of several egevectors, ad hece the etre colum of the matrx may sum to a teger greater tha oe. Step 6. Derve a lmt supermatrx th a suffcetly large poer umber to coverge to a stable supermatrx. The e ca choose ay colum from the lmt supermatrx as the global eghts of the dces.

6 48 JOURNAL OF SOFTWARE, VOL. 8, NO. 8, AUGUST 20 W = lmw t. (4) t Step. Measure the flexblty of ERP system. The comprehesve flexblty level V of ERP system s calculated by the follog equato: V = ( V ), (5) = here =, 2,, ; s the global eght of dex, ad V s the score of ERP system hch s gve by the decso commttee based o the measuremet dex system. The flexblty level of ERP system s gve Table Ⅱ. flexblty level of ERP TABLE Ⅱ. THE FLEXIBILITY LEVEL OF ERP SYSTEM bad poor geeral good Excellet score < ~ ~ ~0.85 >0.85 IV. CASE STUDY I order to have a better developmet ad market competto, a medum-szed techology compay ould lke to adopt a e ERP system through pre-test. To uderstad hether the ERP system adapts the surroudgs of eterprse's teral requremet ad exteral evromet, the decso makers of the compay at to have a flexblty measuremet of the system. Therefore, a cross-fuctoal decso commttee cosstg of varous departmets orks to measure the flexblty of the e ERP system. The flexblty measuremet process based o FANP s as follos. Step. Accordg to the decso goal ad the teracto relatoshps amog crtera ad/or dces, a three-level measuremet dex system s preseted, as sho Fgure 2. TABLE Ⅳ. THE UNWEIGHTED SUPERMATRIX Step 2. Buld parse comparso matrces of the compoets by the decso commttee usg the tragular fuzzy lgustc scales gve Table Ⅰ, ad the scores of the ERP system are determed as ell. For stace, the decso commttee eeds to establsh four matrces for measurg archtecture flexblty as the dces of t have er teracto ad feedback relatoshps. Table Ⅲ s the parse comparso matrx for adaptablty (C 2 ), structure expasblty (C ) ad evrometal kerel stablty (C 4 ) at the dmeso of degree of structurg (C ) uder the crtero of archtecture flexblty (C ). Experts' opos are frst dcated by fuzzy lgustc scales. The they ll be coverted to the correspodg tragular fuzzy umbers accordg to Table Ⅰ, as sho Table Ⅲ. All the tragular fuzzy comparso matrces are produced the same ay. TABLE Ⅲ. COMPARISON MATRIX AT THE DIMENSION OF DEGREED OF STRUCTURING UNDER THE CRITERION OF ARCHITECTURE FLEXIBILITY C C 2 C C 4 C 2 (,,) (,2,) (/,/2,) C (,,) (/6,/4,/2) 0.42 C 4 (,,) 0.54 λ= Step. Perform the FPP method o each comparso matrx dvdually to derve the local eghts. For example, accordg to formulato (), the local eghts of Table Ⅲ ca be acqured by solvg the follog o-lear programmg. C C 2 C C 4 C 2 C 22 C 2 C 24 C C 2 C C 4 C 42 C 4 C 5 C 52 C 5 C C C C C C C C C C C C C C C C C

7 JOURNAL OF SOFTWARE, VOL. 8, NO. 8, AUGUST 20 4 Max λ λ ; λ ; (/6)λ - + (/) 0; (/2)λ + - 0; (/2)λ (/6) 0; (/4)λ (/2) 0; = ;, 2, 0. It ca be solved by a Matlab program, ad the optmal solutos are =0.285, 2 =0.42, =0.54, as sho Table Ⅲ. Cosstecy dex λ s, hch meas that the experts opos have a good cosstecy, ad the local eghts are acceptable. All the local eghts of tragular fuzzy comparso matrces are calculated the same maer. Step 4. Accordg to the local eghts derved from step, a ueghted supermatrx s geerated, as sho Table Ⅳ. Step 5. The eghted supermatrx s derved by radomzg the ueghted supermatrx. Step 6. Accordg to formulato (4), the lmt supermatrx s obtaed by multplyg the eghted supermatrx by tself utl the supermatrx s ro values coverge to the same value for each colum of the matrx. We ca select ay colum from the lmt supermatrx as the global eghts of the dces, as sho Table Ⅴ. The fal comprehesve eghts of the dces are: W * =(0.080,, 0.04, 0.06, 0.06, , 5, 0.04, 0.06, 25, 0.04, , 0.066, 25, 0.06, 0.044, 0.068). Step. Accordg to formulato (5), the flexblty level of the ERP system ca be calculated, as sho Table Ⅵ. The flexblty score of the ERP system s TABLE Ⅴ. THE LIMIT SUPERMATRIX 0.25, ad t dcates that the flexblty level of the ERP system s good accordg to Table Ⅱ. V. CONCLUSIONS Takg to accout the teracto ad feedback relatoshps amog crtera ad/or dces, a dex system for measurg the flexblty of ERP system s proposed. Takg to cosderato the ucertaty ad the accuracy formato, a flexblty measuremet model for ERP system based o fuzzy aalytc etork process s developed. The local eghts of dces are determed by fuzzy preferece programmg method. A ueghted supermatrx s geerated based o the etork structure of dex system. The coverget lmt supermatrx s acqured by multplyg the eghted supermatrx, hch s the radomzg of the ueghted supermatrx. Accordgly, the comprehesve eghts of dces ad fal flexblty score of the ERP system ca be calculated. A umercal example s gve by the proposed method, ad the result s sho that t ca deal ell th ths kd of problem. C C 2 C C 4 C 2 C 22 C 2 C 24 C C 2 C C 4 C 42 C 4 C 5 C 52 C 5 C C 2 C C C C C C C C C C C C C C C

8 50 JOURNAL OF SOFTWARE, VOL. 8, NO. 8, AUGUST 20 TABLE Ⅵ. SCORE OF INDICES AND FLEXIBILITY LEVEL OF ERP SYSTEM dces C C 2 C C 4 C 2 C 22 C 2 C 24 C C 2 C C 4 C 42 C 4 C 5 C 52 C 5 sum eghts scores eghted scores Compared th the exstg research results, the proposed method s fully cosderg the teracto ad feedback relatoshp amog dmesos ad/or attrbutes. The usg of tragular fuzzy umbers helps to make more accurate ad reasoable decsos uder ucerta ad fuzzy codtos. ACKNOWLEDGMENT Ths ork as supported by "the Natoal Natural Scece Foudato of Cha (No. 022)" ad "the Fudametal Research Fuds for Chese Cetral Uverstes (No. FRF-BR--00A)". REFERENCES [] Merram-Webster, "Webster's Thrd Ne Iteratoal Dctoary," Uabrdged Merram-Webster, Sprgfeld, Massachusetts, [2] H. L. Correa, "Lkg Flexblty, Ucertaty ad Varablty Maufacturg Systems," Ashgate Publshg Lmted, Avebury, Eglad, 4. [] A. Che ad P. Kasktat, "Modelg capacty flexblty of trasportato etorks," Trasportato Research Part A, vol., pp. -, 200. [4] Phlps Fred ad D. Tuladhar Sugadha, "Measurg Orgazatoal Flexblty-A Explorato ad Geeral Model," Techologcal Forecastg ad Socal Chage, vol. 64, pp. 2 8, [5] R. E. Gachett, L. D. Martez, O. A. Saez ad C. S. Che, "Aalyss of the structural measures of flexblty ad aglty usg a measuremet theoretcal frameork," It. J. Producto Ecoomcs, vol. 86, pp. 4-62, 200. [6] Lor L. Koste, Mao K. Malhotra ad Subhash Sharma, "Measurg dmesos of maufacturg flexblty," Joural of Operatos Maagemet, vol. 22, pp. 6, [] M. O. Hldegard, "Fuctoal complexty measure for etorks," Phasca A, vol., pp. 6-60, [8] S. Cadl ad E. A. Whtley, "O the terpretatve flexblty of hosted ERP systems," Joural of Strategc Iformato System, vol. 4, pp. 6-5, [] P. Namabad, A. A. Goldeberg ad A. Eml, "Hardare Flexblty of Laboratory Automato Systems: Aalyss ad Ne Flexble Automato Archtectures," Clcs Laboratory Medce, vol. 2, o., 28, 200. [0] O. Kermoglu, N. Basoglu ad T. Dam, "Orgazatoal adopto of formato techologes: Case of eterprse resource plag systems," The Joural of Hgh Techology Maagemet Research, vol., o., pp. 2-5, [] Lag-Chua Wu, Chorg-Shyog Og ad Yao-We Hsu, "Actve ERP mplemetato maagemet: A Real Optos perspectve," Joural of Systems ad Softare, vol. 8, o. 6, pp , [2] C. Oka Özogul, E. Ertugrul Karsak ad Ethem Tolga, "A real optos approach for evaluato ad ustfcato of a hosptal formato system," Joural of Systems ad Softare, vol. 82, o. 2, pp , 200. [] Guu We, Ru L, "Models for selectg a ERP system th tutostc trapezodal fuzzy formato," Joural of Softare, vol. 5, o., pp. 25-2, 200. [4] Jgl Zheg, "The research o the eterprse accoutg process reegeerg based o the ERP evromet," Joural of Computers, vol. 6, o. 6, pp. 0-6, 20. [5] Ju L, Tagtag Xe ad Shuag Du, "Requremets aalyss o flexblty of ERP system of medum ad small publshers," Proceda Egeerg, vol. 5, pp , 20. [6] T. L. Saaty, "Decso Makg th Depedece ad Feedback: The Aalytc Netork Process," RWS Publcatos, Pttsburgh, PA, 6. [] L. Mkhalov ad M. G. Sgh, "Comparso aalyss of methods for dervg prortes the AHP," Proceedgs of IEEE Coferece o Systems, Ma ad Cyberetcs, Tokyo, Japa, pp ,. [8] Semra Bora ad Kerm Goztepe, "Developmet of a fuzzy decso support system for commodty acqusto usg fuzzy aalytc etork process," Expert Systems th Applcatos, vol., pp. -45, 200. [] Xaoguag Zhou ad M Lu, "Rsk evaluato of dyamc allace based o fuzzy aalytc etork process ad fuzzy TOPSIS," Joural of Servce Scece ad Maagemet, vol. 5, pp , 202. [20] Qglg Lu, "Eterprse koledge maagemet applcato evaluato based o cloud gravty ceter model ad fuzzy exteded AHP," Joural of Softare, vol., o. 0, pp , 202. [2] R. Csutora ad J. J. Buckley, "Fuzzy herarchcal aalyss: The Lamda-Max method," Fuzzy Sets ad Systems, vol. 20, pp. 8-5, 200. [22] L. Mkhalov, "Dervg prortes from fuzzy parse comparso udgmets," Fuzzy Sets ad Systems, vol. 4, pp , 200. [2] B. Srdevc, "Combg dfferet prortzato methods the-aalytc herarchy process sythess," Computers & Operatos Research, vol. 2, pp. 8-, [24] Y. M. Wag, T. M. S. Elhag ad Z. S. Hua, "A modfed fuzzy logarthmc least squares method for fuzzy aalytc herarchy process," Fuzzy Sets ad Systems, vol. 5, pp , [25] J. R. Yu ad S. J. Cheg, "A tegrated approach for dervg prortes aalytc etork process," Europea Joural of Operatoal Research, vol. 80, pp , 200. [26] L. A. Huo, J. B. La ad Z. X. Wag, "Ne parametrc prortzato methods for a aalytcal herarchy process based o a parse comparso matrx," Mathematcal ad Computer Modelg, vol. 54, pp , 20. [2] Adrze Z. Grzybosk, "Note o a e optmzato based approach for estmatg prorty eghts ad related cosstecy dex," Expert Systems th Applcatos, vol., pp. 6-08, 202.

9 JOURNAL OF SOFTWARE, VOL. 8, NO. 8, AUGUST 20 5 Xaoguag Zhou receved hs PhD degree Maagemet Scece ad Egeerg from Beg Isttute of Techology Cha. He s curretly orkg at Uversty of Scece ad Techology Beg the Departmet of Maagemet Scece ad Egeerg as a Assocate Professor. He has publshed more tha 0 papers coferece proceedgs ad ourals. Hs research terests clude maagemet formato system, fuzzy decso-makg, as ell as operatos research. Bo Lv receved hs master degree Maagemet Scece ad Egeerg from Uversty of Scece ad Techology Beg Cha. He s curretly orkg at sosoft Co., Ltd as a egeer. Hs research terests clude maagemet formato system, computer etorks ad data mg. M Lu receved her MS ad PhD degrees electrcal egeerg from Rce Uversty, Housto, 84 ad 8, respectvely. She oed the Departmet of Electrcal Egeerg at Texas A&M Uversty 8, ad s curretly a professor. Her research terests clude parallel computg, dstrbuted processg, computer etorks ad computer arthmetc. She has publshed over 20 techcal papers cludg books these areas. She s a Seor Member of the IEEE. She also served as some coferece charma ad as a assocate edtor for several mportat refereed ourals computer scece.