Research on complex system evaluation based on fuzzy theory

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1 Avlble onlne Journl of Chemcl nd Phrmceutcl Reserch, 214, 67: Reserch Artcle ISSN : CODENUSA : JCPRC5 Reserch on complex system evluton bsed on fuzzy theory Yongqng Chen 1,2 1 College of Economcs & Mngement, Huzhong Agrculturl Unversty, Wuhn, Chn 2 Busness School, Jngngshn Unversty, J n, Chn ABSTRACT Complex system evluton les n the core poston of system engneerng theory nd methodology nd s lso reserch hotspot nd dffculty n system engneerng theory nd prctce reserch. The pper, tkng performnce evluton of ntegrtes wth grculture bse nd supermrket for exmple, dvnces n evluton ndctor system nd fuzzy comprehensve evluton lgorthm. Frstly, performnce evluton ndctor system of ntegrtes wth grculture bse nd supermrket s desgned through nlyzng the smlrtes of generl performnce evluton nd the specltes of the evluton object; Secondly, the prncple of nlytc herrchy process nd fuzzy comprehensve evluton lgorthm re nlyzed nd the two methods re combned to dvnce new lgorthm to evlute complex system wth dynmcs, subjectve nd trnstonl evluton ndctors nd mprove evluton ccurcy; Thrdly, three ntegrtes re tken for expermentl exmples nd the results llustrte tht the mproved lgorthm cn be used for evlutng the performnce of ntegrtes wth grculture bse nd supermrket fesbly nd effectvely nd cn provde reference for evlutng other complex systems. Keywords: Complex system evluton, fuzzy comprehensve evluton, nlytc herrchy process, ntegrtes wth grculture bse nd supermrket. INTRODUCTION Wth the development of scence nd technology, the humn socety hs moved nto mterl nd extremely complex mmterl network socety. Under ths condton, more nd more ttentons hve been pd on the study of complex systems. System evluton hs been ppled to the ech lyer from the orgnl sngle engneerng system evluton to vrous spects n the nturl scence nd humn 1fe. Therefore the evluton for the complex system seems to hve gret prctcl sgnfcnce[1]. The trdtonl evluton methods nclude fuzzy comprehensve evluton, nlytc herrchy process technque nd the evluton method bsed on the neurl network,etc. The wdely pplcton of evluton des hs been dvnced nd the trdtonl nd new evluton methods come to emergence contnuously whch deeply rchens the pplcton of system evluton. In ths pont, people cn nlyze nd understnd the system by certn mens n broder rnge. When t comes to complex systems, ther own complexty determnes tht the evluton of complex systems cn not be sngle evluton method. Therefore, synthetcl evluton method should be estblshed n complex system evluton. EXPERIMENTAL SECTION Lterture Revew Followng methods re wldly used n the complex system evluton. Anlytc herrchy processahp effectvely combnes qulttve nlyss wth quntttve nlyss, not only ble to gurntee the systemtcness nd rtonlty of 2554

2 Yongqng Chen J. Chem. Phrm. Res., 214, 67: model, but lso ble to let decson mkers mke full use of vluble experence nd judgment, so s to provde powerful decson-mkng support for lots of regultory decson mkng problems. The method hs such strengths s cler structure nd smple computton, but due to ts strong subjectve judgment, the method lso hs shortcomngs lke low evluton ccurcy[2]. Mult-herrchy comprehensve evluton of fuzzy mthemtcs, ts prncple of s to frstly evlute vrous knds of fctors of the sme thng, dvdng nto severl bg fctors ccordng to certn ttrbute; Then crry out ntl herrchcl comprehensve evluton on certn bg fctor, nd crry out hgh herrchcl comprehensve evluton on the result of ntl herrchcl comprehensve evluton bsed on tht. The key of successful pplcton les n correctly specfyng the fctor set of fuzzy evluton nd resonbly form fuzzy evluton mtrx, obtnng evluton result ccordng to mtrx clculton result. Mke use of fuzzy comprehensve evluton method cn obtn the vlue grde of evluted object or mutul precedence reltonshp; however, the method requres to estblsh pproprte evluton mtrx of evluton object, whch wll obtn dfferent evluton mtrxes due to the nconformty of dfferent experts, ledng to the nconformty of fnl evluton results[3]. Dt envelopment nlyss DEA, strtng from the perspectve of reltve effcency, evlutes ech decson-mkng unt, nd the ndctors selected re only reled on nput nd output. As t doesn t rely on specfc producton functon, t s effectve for delng wth the evluton wth vrous knds of nput nd output ndctors, sutble for the nlyss of beneft, scle economy nd ndustry dynmcs. But t s complcted n computtonl method, subject to certn lmttons n pplcton[4]. BP neurl network method; BP neurl network lernng lgorthm dopts grdent serch technology so s to mnmze the error men squre vlue between ctul output vlue nd desred output vlue; the method s dept n the processng of uncertn nformton. If the nput mode s close to trnng smple, the evluton system s ble to provde correct resonng concluson. The method hs such dvntges s wde pplcblty nd hgh evluton ccurcy, but t lso hs some dsdvntges lke esy to fll nto locl mnmum n the computton, low rte of convergence, nd etc[5]. AHP nd fuzzy evluton lgorthm re wldly used n complex system evluton for ther own dvntges, but they lso hve ther own dsdvntges n prctce. The pper tkes some mesures nd ntegrtes AHP nd fuzzy evluton lgorthm to overcome ther own questons nd brng ther superortes nto full ply. In dong so new lgorthm for evlutng complex system s dvnced. Evluton Indctor System Estblshment Here tkes performnce evluton of ntegrte wth grculture bse nd supermrket for exmple to estblsh n evluton ndctor system. As performnce evluton of ntegrte wth grculture bse nd supermrket needs to focus on frmer vlue whch s specl nd complcted fctors, the smlrty of generl performnce evluton nd the speclty of the topc n ths pper shll be combned to estblsh evluton ndctor system of performnce. Integrtng the generl de of performnce evluton, nd combnng exstng reserch lterture[7,8], ths pper wll, from such four spects s evluton of nternl nd externl performnce, estblsh the evluton ndctor system of the performnce of ntegrte wth grculture bse nd supermrket, whch ncludes 3 herrches, 4 ctegores, 15 second-grde ndctors; see tble 1 for detls. Tble 1 Performnce evluton ndctor system of ntegrtes wth grculture bse nd supermrket Trget herrchy Frst -clss ndctor Second -clss ndctor Customer stsfcton Consumer vlue performnce Repet purchse rte Customer complnt rte Hndlng tme of the complnt Return rte of nvestment Supermrket vlue performnce Supply stblty Rte of qulty montorng coverge Mrket recton force Performnce of ntegrtes wth grculture bse nd supermrket Frmer vlue performnce Vlue performnce of professonl frmers coopertves Rte of frmer s return Improved vretes of grculture products Ablty of nt rsk blty Trnsportton convenence Coordnton degree Extenson rte of grculture technology Own brnd promoton Constructng Fuzzy Comprehensve Evluton Model Whle evlutng complex system, there re lots of problems dffcult to be smply descrbed wth ponts; for exmple, whle evlutng customer, fctors nfluencng evluton result re mnly eductonl bckground of the customer, hs ncome, workng experence, nd etc. Therefore, dfferent people ncludng students, peers nd experts my hve dfferent evlutons, the evluton results of whom re lso dffcult to be quntzed. So the evluton results shll 2555

3 Yongqng Chen J. Chem. Phrm. Res., 214, 67: express specfc concepts wth fuzzy lnguge. Besdes, n prctcl pplcton, the dscussed objects re ffected by lot of uncertnty fctors, mong whch fuzzness fctor s one of the mn nfluencng fctors. Such knd of combnton of clsscl comprehensve evluton theory wth fuzzy theory ppers to be logcl to evlute courses. For ths reson, the fuzzy comprehensve evluton method dopted n ths thess hs good rtonlty, scentfcty nd operblty, ble to obtn reltvely correct, fr nd resonble evluton results. The most frequently used n fuzzy decson s fuzzy comprehensve evluton method, whch tres to deduce comprehensve evluton model of fuzzy mthemtcs bsed on fuzzy evluton theory, nd crres out roundly comprehensve evluton on techers course techng wth ths, lso very effectve n specfc utlzton. To correctly nd resonbly stpulte the domn of dscourse of fuzzy evluton nd estblsh fuzzy evluton mtrx s the key to successfully pply fuzzy comprehensve evluton model. Determnton method of membershp functon. The bsc thought of fuzzy theory s the thought of the membershp degree ttrbute towrds subject; s prevously mentoned, the key to pply fuzzy evluton model les n estblshng resonble fuzzy evluton model, whle the key to buld fuzzy comprehensve evluton model s to resonbly buld membershp functon conformng to the fcts. The method of determnng the membershp functon of certn fuzzy set remns dffculty needng to be solved up tll now. Accordng to the specfc fetures of comprehensve evluton of PE course techng effect, ths thess dopts fuzzy sttstcl method to determne the membershp functon of fuzzy evluton model. Determnng membershp functon of ttrbute towrds object wth fuzzy sttstcl method s reltvely objectve method, whch s lso wdely used. Ths method, n the specfc operton, through fuzzy sttstcl test, ccordng to the ctul exstence of membershp of ttrbute, determnes specfc membershp. Fuzzy sttstcl test generlly ncludes four fctors whch re domn of dscourse U, fxed element x n U, common set A formed by rndom A s elstc boundry, nd restrctng the chnge of A. Among the vrbles n U, fuzzy set A n U tkng bove four elements, x A, thus, the membershp functon of x towrds A s unble to be fxed nd determned. Now suppose tht expermenter does n tmes of fuzzy sttstcl test, he/she cn crry out clculton ccordng to Formul 1 s follows. A Tmesofx n = A 1 In specfc clculton, wth the ncrese of test tmes n, membershp frequency s grdully stble; the stble frequency vlue s clled membershp of Tmesofx x = lm n n A x towrds A n fuzzy mthemtcs,.e. Formul 2. µ A 2 Estblshment of fuzzy comprehensve evluton mtrx. The second key to successfully use fuzzy comprehensve evluton model s to resonbly buld fuzzy comprehensve evluton mtrx. Now use U = u, u, u... u } to { express n knds of ndctors or nfluencng fctors of study object, whch cn be clled ndctor set or fctor set. Use V = v, v, v... v } to express evluton set lso clled evluton set, decson set, etc., formed by m knds { m of evluton ndctors of ll the ndctors.e. fctors. Indctors number nd nme of ndctors cn be generlly determned ccordng to decder s specfc demnd n specfc evluton. As prevous sd, n the prctcl prctce of evluton, the evluton set of ndctors fctors of mny problems s not tht cler, nsted, t s reltvely fuzzy. So comprehensve evluton result s fuzzy subset on V, s shown n formul 3. B = b, b, b... bk F V In Formul 3, membershp of evluton v = b k 1,2,3,... m B k k = b towrds fuzzy subset B s obtned through the clculton of k µ, whch cn reflect the role of the k th evluton v k plyed n comprehensve evluton. Comprehensve evluton set B reles on the weght vlues of ech ndctor,.e. B shll be the fuzzy 2556

4 Yongqng Chen J. Chem. Phrm. Res., 214, 67: subset on ndctor set U, A =,,... n F, nd meetng tht the sum of ndctor weght s 1; n whch U ndctes the weght of the th ndctor. Hence, whle the weght set A s set, correspondng comprehensve evluton set B cn be determned. Generl steps to determne fuzzy comprehensve evluton mnly nclude the followng ones. Determne ndctor set u, u, u... u } { V = { v1, v2, v3... vm ; R = r j n m U = ; Clculte determnton evluton set } Clculte determnton fuzzy evluton mtrx R = r j n m, frst, crry out evluton of f u = 1,2,3... n ;Whle determnng fuzzy evluton mtrx = on ech ndctor ndctor set U to evluton set V cn be obtned; the mppng s s shown n formul 4. u, fuzzy mppng f from f : U F U u f u = r 1, r 2, r 3... rm F V 4 Then, deduce fuzzy relton R f F U V ccordng fuzzy mppng f, s shown n formul 5[3]. R u, v f u v = r = = 1,2,3... n; j 1,2,3... m 5 f j j j = As result, fuzzy evluton mtrx evluton; U V, R R = r j n m cn be clculted,, V, R, re generlly clled the necessry elements of the model. Comprehensve evluton: s to set n whch weght,,... U s the model of fuzzy comprehensve A = n, through model, F U M, tke compostonl operton of mxmum mnmum, then obtn fnl comprehensve evluton mtrx, s shown n Formul 6. B n = A R bj = rj, j = = 1 1,2,3,... m o 6 A = n evluton set Accordng to the bove, we cn know tht the correct determnton of weght,,... V plys crtcl role n fnl comprehensve evluton. A =,,... s generlly determned by model desgner by vrtue of self relevnt experence, but ths s often subjectve. If the weght set s to reflect ctul stuton, to objectvely nd fthfully reflect ctul stuton, weghtng sttstcs, experts evluton or fuzzy relton cn be dopted to determne,,... ; for prctcl pplcton, dfferent determnton methods cn be chosen A = ccordng to dfferent stutons[7,8]. Specfc Evluton Step Fuzzy overll evluton n ths pper s conducted ccordng to the followng fve steps. 1 Estblshng vluton element set. Evluton element set s n ordnry set consttuted by ll the elements nfluencng evluton object; suppose there re n evluton ndctor elements expressed by,,..., un u 1, u2 u3 respectvely, then the set consttuted by these n evluton elements s clled evluton element set,.e. =,. U u u u,... 1, 2 3 u n Confrmng vluton set. Evluton set s lso clled judgment set, whch s comprsed of ll the evluton results of evlutor on evluton object, s n ordnry set formed by ll the possble evluton results of evlutors on evluton object. Evluton results cn be dvded nto m herrches ccordng to ctul demnd of specfc cses, whch cn be expressed by v 1, v2, v3,... vm, respectvely, then evluton set cn be consttuted s =, ; V v v v,... 1, 2 3 v m 3Confrm the weght of evluton ndctor. The resonble confrmton of ndctor weght embodes the dfferent weght reltons mong ll the evluton ndctors n the system, ncreses the comprblty mong ll the evluton 2557

5 Yongqng Chen J. Chem. Phrm. Res., 214, 67: ndctors nd the effectveness of evluton result. AHP s objectve wth such merts s prctcblty, concseness nd systemtcness. Thus, ths pper dopts AHP to confrm the weghts of ll the evluton ndctors, obtnng the weght w of ech evluton ndctor u. The set consttuted by ech weght w s clled weght set W, s shown n formul 7[9]; CI = λ mx n / n 1 8 In formul 8, λmx s the mxmum egenvlue of judgment mtrx, n s the number of comprson ndctor. λ mx s clculted s follows: respectvely multply elements n ech lne of judgment mtrx by vector component of weght W, then dd, obtnng A w ; dvde A w respectvely by w, obtnng vlue A w / w. λ mx s the verge vlue of A w / w. In order to confrm the llowed rnge of nconsstency degree, the correspondng verge rndom consstency ndctor RI of n cn be looked for tble 2. At lst, judge whether the mtrx s consstent through consstency rto CR, =. If p. 1, the consstency of judgment mtrx s cceptble. Wheres, f CR. 1, the consstency of judgment mtrx s uncceptble; judgment mtrx should be properly mended to keep the consstency of judgment mtrx to certn extent. Tble 2 Averge rndom consstency ndctor Order RI CR CI / RI CR 4 Sngle-fctor fuzzy evluton. Suppose tht evluton object crres out evluton ccordng to the th fctor n fctor set U, u = 1,2,3... n, the subordnton of whch s to the jth V v j j = 1,2,3... m s expressed s j fctor n evluton set r, formul 3 cn be used to show the evluton result of the th fctor RESULTS AND DISCUSSION Expermentl Results nd Anlyss Expermentl dt come from dtbse of three ntegrtes wth grculture bse nd supermrkets, cll A,B nd C respectvely. For dt of customer prt, consumers of ntegrtes re selected s the bss for dt trnng nd expermentl verfcton n the pper, totlly 15 consumers dt for study dt tht come from prctcl nvestgton nd vst. In order to mke the selected consumers dt representtves, 3 frmers 1 frmers from ech supermrket wth more thn 2 yers, 3 frmers wth 1 yer ntegrte experence, 3 frmers wth less thn 1 yer ntegrte experence. Lmted to pper spce, the evluton of ntermedte results s omtted here, only provdng secondry evluton results nd fnl comprehensve evluton results, see tble 3. Tble 3 Prt evluton results of dfferent ntegrtes Consumer vlu Supermrket vlu Frmer vlue Coopertves Vlue Fnl evluton e e A B C As for the performnce of the presented lgorthm, ths pper lso relzes the pplcton of the DEA[4] nd ordnry fuzzy evluton lgorthm[1], evluton performnce of dfferent lgorthms s shown n Tble 4. In tble 4 evluton results of trnng effects of dfferent ntegrtes re selected nd compred wth rtfcl evluton to clculte the evluton ccurcy. u. 2558

6 Yongqng Chen J. Chem. Phrm. Res., 214, 67: Tble 4 Evluton performnce comprson of dfferent lgorthms Algorthm n the pper Ordnry fuzzy lgorthm DEA lgorthm Evluton ccurcy 92.66% 79.54% 75.86% CONCLUSION Comprehensve evluton of complex system s n effectve method for nlyzng complex system nd les n the core sttus of the entre evluton system of system engneerng. Thus, there s fvorble pplcton prospect for the nlyss nd compettveness evluton of complex system performnce bsed on the prncple of fuzzy nlyss. Ths pper mkes use of mult-herrchy fuzzy evluton method to estblsh comprehensve evluton model for performnce evluton of ntegrte wth grculture bse nd supermrket, lso crres out cse study tkng the dt of three ntegrtes s n exmple. Menwhle, the mult-herrchy fuzzy evluton method bult n ths pper cn be reference for the nlyss nd evluton of other complex system nlyss. REFERENCES [1] CS Shrm; RK Nem; SN Meyynthn. Acdemc J. Cncer Res., 29, 21, [1] JH Toms; ZW Thle. J. Comp. App., 213, 11, [2] YF Yueh; SH Jnnu. Indus. Eng. J., 212, 189, [3] YS Y; SH Jnst. J. Inf. Eng., 213, 1212, [4] DD Shfe; JU Wekun; SM Chunyng. J. Convergence. Inf. Tec., 21, 54, [5] YJ Long; HM Chen. J. Com., 213, 212, [6] SH Thompson. Intel. J. Dt Coll. Pro., 212,114, [7] VD Rn; JB Merwe. Inter. Res. J., 211, 262, [8] CD Yong; KM Jn; GW We. J. Syst. Eng., 212, 112, [9] YY Shh; JH Shun. Int. Res., 21,711, [1] SW Gndh; LB Towen. Indus. Mn. Dt Sys., 211, 1711,