Transformer Maintenance Policies Selection Based on an Improved Fuzzy Analytic Hierarchy Process

JOURNAL OF COMPUTERS, VOL. 8, NO. 5, MAY 203 343 Trsformer Mitece Policies Selectio Bsed o Improved Fuzzy Alytic Hierrchy Process Hogxi Xie School of Computer sciece d Techology Chi Uiversity of Miig & Techology, Xuzhou, Chi xiehx@cumt.edu.c Lipig Shi School of Iformtio d Electricl Egieerig Chi Uiversity of Miig d Techology, Xuzhou, Jigsu 226, Chi shilipig98@26.com Hui Xu School of Computer sciece d Techology Chi Uiversity of Miig & Techology, Xuzhou, Chi xuhui@cumt.edu.c Abstrct A systemtic study of the optiol mitece strtegies of the Trsformer is coducted d set of geerl fctors which should be cosidered i the mitece strtegies is estblished. A Fuzzy Alytic Hierrchy Process (FAHP bsed o the gol progrmmig is proposed i view of the defects of the trditiol Fuzzy Alytic Hierrchy Process (FAHP, d the specific pplictio process of this method i the trsformer mitece strtegies selectio is described. I dditio, compriso with the stdrd Alytic Hierrchy Process is mde to clrify the vlidity of the method proposed i this pper. Idex Terms Fuzzy Alytic Hierrchy Process, Mitece Strtegies,Gol Progrmmig I. INTRODUCTION Equipmet mitece cost is the mi cost of productio i curretly mufcturig firms. For these firms, mitece cost c rech 5 70% of productio costs, vryig ccordig to the type of idustry[]. O the other hd, the moey spet o mitece due to improper mitece d excess mitece is bout oe-third of totl mitece costs, which cuse eormously wist. So select the optiml mitece strtegy could reduce overll ruig costs sigifictly d icrese eterprise productivity Mitece strtegies c be divided ito fult mitece, scheduled mitece, coditio bsed mitece, d relibility bsed mitece, totl productive mitece, predictive mitece d other repirs. Fult mitece ws the erliest pplied mitece strtegies, which mes the mitece did t begi util the equipmet filure showed. This strtegy is ppretly uble to esure the relibility d security of the system. The remiig severl mitece strtegies c be summrized to prevetive mitece. This mes tht mitece strtegies c be divided ito fult mitece d prevetive mitece of two ctegories. Prevetive mitece is mde depedig o the mesured dt from set of sesors system which icludig vibrtio moitorig, lubrictig lysis, d ultrsoic testig etc. I order to esure miti the system or equipmet i good coditio, prevetive mitece should be the better choices. It is oe of importt decisio-mkigs i eterprise to choose the best mitece methods for differet devices. At preset there hve bee lot of the reserch chievemets i this field. Azdivr d Shu[2] hve proposed selectio of the best mitece methods for devices uder the eviromet of just-i-time system. I the thesis, 6 ttributes tht ifluece the selectio of mitece methods re tke ito ccout d the mitece methods for devices re selected ccordig to these ttributes. Luce [3], Okumur d Okio[4] hve put forwrd selectio of the best mitece methods ccordig to differet productio losses d differet costs of vrious mitece methods. Bevilcqu d Brgli[] hve dopted the lytic hierrchy process (AHP to solve the problem of choosig mitece methods i Itli refiery. I the pper, reltively comprehesive evlutio ttributes re preseted i detil. However, the APH cot etirely d ppropritely del with the fuzzy multi-ttribute decisio-mkig problems tht re hrd to qutify i the selectio of mitece methods. Thir Zulkifli et l.[5] propose ew mitece optimiztio model. The frequecy of filures d doi:0.4304/jcp.8.5.343-350

344 JOURNAL OF COMPUTERS, VOL. 8, NO. 5, MAY 203 dowtimes re computed s prmeters d decisio mkig grid with fuzzy logic is pplied to the optimiztio of mitece strtegies selectio. Jfri et l.[6] proposed ew pproch to determie the best mitece strtegy. I order to obti the best result, the pproch cosiders ll the vriety i mitece criteri d their importce weights d lso the ucertity level. Li et l.[7] bsed o the updted equipmet sttus clculted relibility-bsed dymic mitece threshold (DMT. I this pper lso demostrted the beefits of the DMT i umericl cse study o drillig process. Whe choosig mitece methods, we eed to cosider my ttributes. Some ttributes re qutittive, such s hrdwre d softwre cost, triig cost, time betwee filures, equipmet relibility, etc., while some oes, such s security, flexibility, workers cceptbility, etc. re qulittive dt d usully fuzzy d ucerti. Fuzzy theory is pplied to determie the vlue of qutittive ttributes, d the fuzzy multi-ttribute decisio-mkig method c be used. There hve bee my implemeted MCDM methods i mitece strtegy selectio. Shrm et l.[8] usig the fuzzy iferece theory d MCDM evlutio methodology i fuzzy eviromet ssessed the most populr mitece strtegies. Al-Njjr d Alsyouf [9] idetify the criteri usig pst dt d techicl lysis of processes mchies d compoets for MCDM problem. They ssessed the cpbility of ech mitece pproch usig fuzzy iferece system (FIS. Filly they selected the efficiet mitece pproch by utilizig simple dditive weightig (SAW method. Mhdi Bshiri et l.[0] proposed iterctive pproch to rk the mitece strtegies usig qulittive d qutittive dt. Bsed o the determied criteri helps mgers selectig the best mitece strtegy. I order to esure the result more resoble withi the iterctio process mitece experts lso c provide d modify their preferece iformtio grdully. Mechefske d Wg [] hve dopted fuzzy logic to choose the best mitece methods. Whe usig fuzzy logic, first, orgiztiol gols re defied; secod, the weight of ech gol d the stisfctio of ech mitece method for differet gols re determied by the mgeril employees who hve tke prt i the fce-to-fce iterview; filly, the best mitece methods re selected ccordig to the equtio uder the fuzzy eviromet. However, most methods used for scorig qulittive ttributes belog to subjective scorig, which mkes the results rrely objective. Therefore, Wg et l[2] hve idicted tht the judgmets mde by decisio mkers re subjective d somewht iccurte, d the fuzzy AHP is used to solve this problem i the selectio of mitece methods. For this reso, the pper presets kid of fuzzy AHP bsed o the gol progrmmig to solve the selectio of mitece methods for trsformers. II. ALTERNATIVE MAINTENANCE STRATEGIES AND DECISION CRITERIA This pper mily cosiders four ltertive mitece methods, tht is, post-filure mitece, scheduled mitece, coditio-bsed mitece d predictive mitece. Whe choosig suitble mitece methods for lrge trsformers, the trsformer serviceme d relted decisio mkers first must be sure the relevt criteri sets(tht is, decisio-mkig ttribute sets tht eed to be cosidered i the selectio of mitece methods. The decisio-mkig criteri tht usully eed to be tke ito ccout i the selectio of mitece methods for trsformers re show i Tble I[, 3, 4]. TABLE I MAINTENANCE STRATEGIES SELECTION DECISION CRITERIA Mi Criteri Security(S Cost(C Added Vlue(AV Productio Loss(PL Fesibility(F Subcriteri Security of Persoel(SP Security of Device (SD Security of Eviromet(SE Cost of Hrdwre(CH Security of Softwre(CS Security of Persoel Triig (CPT Spre Prts Ivetory(SPI Fult Idetifictio(FI Me Time Betwee Filures(MTBF Me Time to Repir(MTR Acceptce by workers(aw Techique Fesibility(TF III. USING FUZZY ANALYTIC HIERARCHY PROCESS AND GOAL PROGRAMMING TO SELECT MAINTENANCE STRATEGIES, FHP-GP-SMS A. Alytic Hierrchy Process, AHP The mi steps for usig the AHP c be summrized s[5, 6]:. The modelig of problems The decisio-mkig problems of the AHP should be divided ito differet hierrchicl structures. Ech hierrchy is composed of severl decisio-mkig fctors. A overll gol is t the top, group of ltertive solutios is t the bottom, d oe or more decisio-mkig criteri d sub-criteri re i the middle tiers. 2. To obti the locl weight vlue of evlutio criteri. As for criteri i hierrchy, decisio mkers should perform series of pirwise comprisos for ll the sub-criteri d the pros d cos of ltertives uder the hierrchy to estblish the compriso d judgmet mtrix. The reltive importce of decisio-mkig fctors (criteri weight d the pros d cos of ltertives is obtied through the comprtive judgmet mtrix. 3. The globl scorig of ltertives This step icludes criteri weight d the pros d cos of ltertives, d prioritizes these ltertives. Supposig there re m hierrchies i totl d the weight mtrix obtied through the judgmet mtrix is W,

JOURNAL OF COMPUTERS, VOL. 8, NO. 5, MAY 203 345 W2,, Wm, the globl scorig of ltertives re : W = W W2... W m W m. ( B. Fuzzy Comprtive Whe determiig the reltive importce betwee y two ttributes, decisio mkers sometimes re hrd to give defiite qulittive descriptio, but they my give fuzzy d ucerti oe, for exmple, oe ttribute is bout twice more importt th the other, oe ttribute is bout twice to four times more importt th the other, etc. It s difficult to use stdrd weight decidig method i AHP uder the circumstces, so some reserchers hve proposed usig fuzzy umbers or fuzzy sets to represet the results of pired comprisos betwee criteri d to estblish the fuzzy compriso d judgmet mtrix. Whe the two elemets of E i d E j i the sme hierrchy re compred, the comprtive result i fuzzy judgmet c be represeted by usig the fuzzy umber[7] of ã. The represettio methods d the wys to obti weight vlue of the trigulr fuzzy umber, Gussi fuzzy umber d criteri fuzzy umber re studied i the literture [8, 9]. Ispired by these ides, the pper pplies the trpezoidl fuzzy umber to express the ucerti results of pired comprisos. Defiitio : supposig the trpezoidl fuzzy umber of A = {( x, μ x } A( x X c be expressed s A = (, b, c, d, where b d c re mid-vlue of μ =, is the lower boud of the trpezoidl ( A( b x c fuctio d d is upper boud. Defiitio 2: the membership fuctio of trpezoidl fuzzy umbers c be expressed s follows: x, x b b μ x =, b x c ( d x. (2 A, c x d d c 0, otherwise where d d re respectively the lower boud d upper boud of the trpezoidl fuzzy umber, d b d c re mid-vlue. The fuzzy reciprocl judgmet mtrix of à c be obtied through the pirwise comprisos betwee criteri (sub-criteri or ltertives i the sme hierrchy, d expressed s: d A = { } = M 2 2 22 M 2 L L O L 2 M. (3 where is the umber of elemets i the hierrchy, ji = = (,,, d c b C. Clculte the Weights by Gol Plig Cosiderig the problem of obtiig the weight vlue of elemets (ltertives d evlutio criteri, the fuzzy judgmet mtrix is show s the (3. The trpezoidl fuzzy umber of ã c be expressed s (,b,c,d, where i,j=,2,,, d d re respectively the lower boud d upper boud of the trpezoidl fuzzy umber, d b d c re mid-vlue. Supposig the ccurte result of weight vector T is w = ( w, w2,..., w, the vlue of weight rtio w i / should be similr to the iitil fuzzy judgmet, tht is: wi w j d. (4 where mes fuzzy less th or equl, w i >0, >0,d i j. The membership fuctio expressig decisio mkers precise weight rtio of w i / is itroduced. As ech ccurte weight vector w stisfies the bi-directiol iequlity i some degree, the membership fuctio c be used for mesuremet. Therefore, the followig fuctio is defied to represet the ukow weight rtio of w i / : wi wi, b b wi wi μ ( =, b c. (5 wi d wi, c d c I order to void the divisor beig zero, <b <c <d is ssumed. The optimiztio method of membership mximiztio c be used to obti the ccurte vlue of weight vectors ccordig to the fuzzy judgmet mtrix. The detils re s follows: Ad, Mx J = i= j= w μ (6 i (

346 JOURNAL OF COMPUTERS, VOL. 8, NO. 5, MAY 203 wi wi, b b w i wi, b c μ = w. (7 j wi d wi, c d d c 0, otherwise trpezoidl fuzzy umbers is give Revised ltertives d evlutio criteri Set up expert group N Strt Resoble ltertives d Criteri? Preset mitece strtegies d evlutio criteri s.t. Y 2 γ J, γ [ /, ]. 2 0 < w i,i =, 2,...,. After the weight vector of w = (w,w,...,w obtied through the bove formul is ormlized, the ultimte ormliztio ccurte vlue of weight vectors is obtied. I the pper, the membership fitess (MF is used [9] for mesurig whether the ccurte weight vlue is cosistet with the fuzzy judgmet mtrix, d c be expressed s: MF = 2 i= j= w i μ. (8 w j where the membership fuctio of μ (w i / represets the degree of the weight rtio of w / w pproximtig to the fuzzy combitio. As the i j trpezoidl membership fuctio is dopted i the pper, it c be kow < MF <, where MF represets ( the ccurteess of weight vectors deduced from the fuzzy judgmet mtrix. Whe MF =, the weight obtied from the judgmet mtrix is perfectly mtched. D. Usig Fuzzy Alytic Hierrchy Process Ad Gol Progrmmig to Select Mitece Strtegies, FHP-GP-SMS From the bove, the trsformer mitece model of fuzzy AHP bsed o the gol progrmmig proposed i this pper c be described s follows:. Estblish expert group for mitece. The expert group tkes chrge of ssigig the importce for evlutio criteri (C j, j=,2,, uder m kids of mitece strtegies. 2. Decide o mitece methods d evlutio criteri, d estblish the hierrchicl structure of the selectio of mitece methods for trsformers. 3. Accordig to the pirwise comprisos of evlutio criterios d criteri i the selectio of mitece methods for trsformers i hierrchies, the correspodig compriso d judgmet mtrix bsed o m 2 Compriso of mi criteri o qulittive descriptio Compriso of sub criteri o qulittive descriptio Fuzzy judgmet mtrix of criteri Get locl criteri weights N Get globl criteri weights Compriso betwee mi criteri d ltertives qulittive descriptio Compriso betwee sub criteri d ltertives qulittive descriptio fuzzy compriso mtrix of ltertives Score of sub criteri for ltertives Score of cdidte mitece strtegies Score resoble? Y Ed Figure Dt flow digrm of trsformer mitece strtegies selectio 4. Accordig to the methods metioed i this pper, the ccurte weight of criteri, the ccurte locl weight of its sub-criteri d further the globl weight of sub-criteri re obtied. 5. Perform the pirwise comprisos betwee ltertive mitece methods d sub-criteri i upper tier, d ccordig to the decisio mkers qulittive descriptio, chge the pirwise comprisos ito the compriso d judgmet mtrix bsed o trpezoidl fuzzy umbers. 6. Accordig to the methods of obtiig weight N

JOURNAL OF COMPUTERS, VOL. 8, NO. 5, MAY 203 347 metioed i this pper, the weight of ll the criteri to ltertive mitece methods is obtied. 7. Prioritize these ltertives. To sum up, the trsformer mitece strtegies selectio c be showed by Fig. IV. CASE STUDY We dopt the fuzzy AHP bsed o the gol progrmmig metioed i the pper to choose the best mitece methods for the mi trsformer i Jigzhug col mie, Zozhug Miig Group. First of ll, hierrchicl chrt of mitece methods for trsformers is estblished d show i Fig 2. The professiols of trsformer mitece re sked to give qulittive descriptio of the reltive importce betwee decisio-mkig ttributes. Accordig to the evlutio criterios, experts suggestios i ccordce with TbleⅡ re coverted ito pirwise compriso mtrices tht re described by usig qulittive lguges. Ucerti judgmet Trpezoid Fuzzy Score Score About times less (/(+, /(+0.5, /(-0.5, / importt /(- Betwee c d d (/(d+0.5, 2/(c+d+, /c times less importt 2/(c+d-, /(c-0.5 Note: =2,3,4,,9. c,d=,2,,9,c<d. The qulittive descriptio of the pirwise comprisos for mi criteri is provided by experts, the it is coverted ito trpezoidl fuzzy umbers ccordig to the fuzzy qulittive scorig of Tble Ⅱ,, d the fuzzy pirwise compriso mtrices re obtied, s show i Tble III. TABLE Ⅲ FUZZY JUDGMENT MATRIX OF FIRST LAYER CRITERIA Trget S C AV PL F S (,,, (,.5,2.5,3 (3,3.5,4. (0.67,0.67,. (2,2.5,3.5, 5,5 33,2 4 C (/3,/2.5,,.5 (,,, (,.5,2. (/3,/2.5,/ (0.5,,2,2., 5,3.5, 5 AV (/5,/4.5,/3.5 (/3,/2.5,/ (,,, (/5,/4.5,/3 (/2.5,/2,,/3.5,.5,/3,2 PL (/2,/.33,/0. (,.5,2.5,3 (3,3.5,4. (,,, (2,2.5,3.5, 67,/0.67 5,5 4 F (/4,/3.5,/2.5 (/2.5,/2,, (0.5,,2, (/4,/3.5,/2 (,,,,/2 2 2.5.5,/2 Accordig to the method of obtiig weights metioed i this pper, the weights i Tble Ⅲ re obtied by usig the softwre of Ligo. Supposig γ=0.6, the objective fuctio vlue i the (6 is J [0,25]. The weights re obtied, s show i Tble IV. TABLE Ⅳ THE FIRST LAYER CRITERIA WEIGHTS Criteri S w C w 2 AV w 3 PL w 4 F w 5 Weights 0.3603 0.766 0.0800 0.2802 0.029 The qulittive descriptio of the reltive importce is give through the pirwise comprisos betwee sub-criteri i the secod lyer d mi criteri i the first lyer. After the coversio, the fuzzy judgmet mtrix is obtied, s show i Tble Ⅴ. The locl weights d globl weights of the sub-criteri re obtied, s show i Tble V. Figure 2 Hierrchy structure of trsformer mitece policy selectio TABLE II THE SCORE OF FUZZY QUALITATIVE DESCRIPTION Ucerti judgmet Trpezoid Fuzzy Score Score Almost equl (0.67,0.67,.33,2 bout times more (-,-0.5,+0.5,+ importt Betwee c d d (c-0.5,(c+d-/2,(c+d+/2,d d times more +0.5 importt TABLE V FUZZY JUDGMENT MATRIX OF SUB-CRITERIA IN SECURITY S SP SD SE SP (,,, (2,2.5,3.5,4 (5,5,5,6,5,7 SD (/4,/3.5,/2.5,/2 (,,, (,.5,2.5,3 SE (/7,/6.5,/5.5,/5 (/3,/2.5,/.5, (,,, C CH CS CPT CH (,,, (/3,/2.5,/.5, (,.5,2.5,3 CS (,.5,2.5,3 (,,, (3,3.5,4.5,5 CPT (/3,/2.5,/.5, (/5,/4.5,/3.5,/3 (,,, AV SPI FI SPI (,,, (/4.5,/4,/3,/2.5 FI (2.5,3,4,4.5 (,,, PL MTBF MTR MTBF (,,, (2,2.5,3.5,4 MTR (/4,/3.5,/2.5,/2 (,,, F AW TF AW (,,, (6,6.5,7.5,8 TF (/8,/7.5,/6.5,/6 (,,,

348 JOURNAL OF COMPUTERS, VOL. 8, NO. 5, MAY 203 TABLE Ⅵ WEIGHT TABLE OF SECOND LAYER SUB-CRITERIA Sub Criteri Locl Weights Globl Weights SP w 0.6478 0.2334 SD w 2 0.2525 0.090 SE w 3 0.0997 0.0359 MF= CH w 2 0.2744 0.0485 CS w 22 0.5677 0.003 CPT w 23 0.579 0.0279 MF= SPI w 3 0.2496 0.0200 FI w 32 0.7504 0.0600 MF= MTBF w 4 0.748 0.2003 MTRw 42 0.2852 0.0799 MF= AW w 5 0.8667 0.0892 TF w 52 0.333 0.037 MF= It c be see tht ll the MF re. This shows tht the results obtied from the five fuzzy judgmet mtrices i the secod lyer re the sme i both three dimesios d two dimesios. The pirwise comprisos betwee ltertive mitece methods t the bottom lyer d sub-criteri t the upper lyer re performed, for exmple, the reltive importce of the pirwise comprisos betwee the sub-criteri of me time to repir d the ltertive mitece methods of post-filure mitece d coditio bsed mitece is obtied. Further the correspodig judgmet mtrix c be obtied, s show i Tble VII. TABLE Ⅶ SUB-CRITERIA IN SECURITY FUZZY COMPARISON MATRIX OF ALTERNATIVES SC CM SM CBM PM SP CM (,,, (/4,/3.5,/2.5, (/9,/8.5,/7.5, (/7,/6.5,/ /2 /7 5.5,/5 SM (2,2.5,3.5,4 (,,, (/4,/3.5,/2.5, (/3,/2.5,/ /2.5, CBM (7,7.5,8.5,9 (2,2.5,3.5,4 (,,, (,.5,2.5,3 PM (5,5.5,6.5,7 (,.5,2.5,3 (/3,/2.5,/.5, (,,, SD CM (,,, (/4,/3.5,/2.5, (/9,/8.5,/7.5, (/7,/6.5,/ /2 /7 5.5,/5 SM (2,2.5,3.5,4 (,,, (/5,/4.5,/3.5, (/3,/2.5,/ /3.5, CBM (7,7.5,8.5,9 (3,3.5,4.5,5 (,,, (,.5,2.5,3 PM (5,5.5,6.5,7 (,.5,2.5,3 (/3,/2.5,/.5, (,,, SE CM (,,, (/3,/2.5,/.5, (/9,/8.5,/7.5, (/5,/4.5,/ /7 3.5,/3 SM (,.5,2.5,3 (,,, (/5,/4.5,/3.5, (/3,/2.5,/ /3.5, CBM (7,7.5,8.5,9 (3,3.5,4.5,5 (,,, (,.5,2.5,3 PM (3,3.5,4.5,5 (,.5,2.5,3 (/3,/2.5,/.5, (,,, CH CM (,,, (0.67,0.67,.33,2(7,7.5,8.5,9 (5,5.5,6.5,7 SM (/2,/.33,/0.6(,,, (6,6.5,7.5,8 (4,4.5,5.5,6 7,/0.67 CBM (/9,/8.5,/7.5, (/8,/7.5,/6.5, (,,, (/3,/2.5,/ /7 /6.5, SC CM SM CBM PM PM (/7,/6.5,/5.5, (/6,/5.5,/4.5, (,.5,2.5,3 (,,, /5 /4 CS CM (,,, (,.5,2.5,3 (7,7.5,8.5,9 (4,4.5,5.5,6 SM (/3,/2.5,/.5, (,,, (5,5.5,6.5,7 (3,3.5,4.5,5 CBM(/9,/8.5,/7.5, (/7,/6.5,/5.5, (,,, (/3,/2.5,/ /7 /5.5, PM (/6,/5.5,/4.5, (/5,/4.5,/3.5, (,.5,2.5,3 (,,, /4 /3 CPT CM (,,, (,.5,2.5,3 (7,7.5,8.5,9 (4,4.5,5.5,6 SM (/3,/2.5,/.5, (,,, (4,4.5,5.5,6 (2,2.5,3.5,4 CBM(/9,/8.5,/7.5, (/6,/5.5,/4.5, (,,, (/3,/2.5,/ /7 /4.5, PM (/6,/5.5,/4.5, (/4,/3.5,/2.5, (,.5,2.5,3 (,,, /4 /2 SPI CM (,,, (/4,/3.5,/2.5, (/9,/8.5,/7.5, (/7,/6.5,/ /2 /7 5.5,/5 SM (2,2.5,3.5,4 (,,, (/4,/3.5,/2.5, (/3,/2.5,/ /2.5, CBM(7,7.5,8.5,9 (2,2.5,3.5,4 (,,, (,.5,2.5,3 PM (5,5.5,6.5,7 (,.5,2.5,3 (/3,/2.5,/.5, (,,, FI CM (,,, (0.67,0.67,.33,2(/9,/8.5,/7.5, (/7,/6.5,/ /7 5.5,/5 SM (/2,/.33,/0.6(,,, (/9,/8.5,/7.5, (/7,/6.5,/ 7,/0.67 /7 5.5,/5 CBM(7,7.5,8.5,9 (7,7.5,8.5,9 (,,, (,.5,2.5,3 PM (5,5.5,6.5,7 (5,5.5,6.5,7 (/3,/2.5,/.5, (,,, MTBF CM (,,, (/6,/5.5,/4.5, (/9,/8.5,/7.5, (/8,/7.5,/ /4 /7 6.5,/6 SM (4,4.5,5.5,6 (,,, (/7,/6.5,/5.5, (/4,/3.5,/ /5 2.5,/2 CBM(7,7.5,8.5,9 (5,5.5,6.5,7 (,,, (,.5,2.5,3 PM (6,6.5,7.5,8 (2,2.5,3.5,4 (/3,/2.5,/.5, (,,, MTR CM (,,, (/5,/4.5,/3.5, (/9,/8.5,/7.5, (/7,/6.5,/ /3 /7 5.5,/5 SM (3,3.5,4.5,5 (,,, (/7,/6.5,/5.5, (/6,/5.5,/ /5 4.5,/4 CBM(7,7.5,8.5,9 (5,5.5,6.5,7 (,,, (,.5,2.5,3 PM (5,5.5,6.5,7 (4,4.5,5.5,6 (/3,/2.5,/.5, (,,, AW CM (,,, (,.5,2.5,3 (2,2.5,3.5,4 (4,4.5,5.5,6 SM (/3,/2.5,/.5, (,,, (,.5,2.5,3 (3,3.5,4.5,5 CBM(/4,/3.5,/2.5, (/3,/2.5,/.5, (,,, (,.5,2.5,3 /2 PM (/6,/5.5,/4.5, (/5,/4.5,/3.5, (/3,/2.5,/.5, (,,, /4 /3 TF CM (,,, (,.5,2.5,3 (4,4.5,5.5,6 (7,7.5,8.5,9 SM (/3,/2.5,/.5, (,,, (2,2.5,3.5,4 (6,6.5,7.5,8 CBM(/6,/5.5,/4.5, (/4,/3.5,/2.5, (,,, (2,2.5,3.5,4 /4 /2 PM (/9,/8.5,/7.5, (/8,/7.5,/6.5, (/4,/3.5,/2.5, (,,, /7 /6 /2 Note : CM, SM, CBM d PM i the tble respectively refer to corrective mitece, scheduled mitece, coditio-bsed mitece d predictive mitece. The precise vlue of weights c be obtied by usig

JOURNAL OF COMPUTERS, VOL. 8, NO. 5, MAY 203 349 the improved fuzzy AHP method proposed i the pper, d the clculted results re show i Tble Ⅷ. The globl scorig of ltertives c be obtied ccordig to the globl weight of sub-criteri i Tble Ⅵ d the Tble Ⅷ, d the results re show i the lst lie of Tble Ⅷ. Therefore, the best mitece method for trsformers is coditio-bsed mitece. It is more suitble for trsformers th post-filure mitece d scheduled mitece becuse it c improve the sfety of trsformers, brig more dditiol beefits d reduce productio losses, d it is fr better th predictive mitece i the spects of fesibility, costs, etc., so it is resoble to regrd coditio-bsed mitece s mitece method of trsformers. TABLE VIII RESULTS OF FUZZY ANALYTIC HIERARCHY PROCESS BASED ON GOAL PROGRAMMING Mi Criteri S C AV PL F Sub Criteri CM SM CBM PM MF SP 0.055 0.450 0.4770 0.3265 0.9688 SD 0.0569 0.380 0.4833 0.327 0.9837 SE 0.0687 0.33 0.5353 0.2647 CH 0.4869 0.3823 0.0563 0.0845 0.9894 CS 0.5008 0.3437 0.062 0.0943 CPT 0.5086 0.3233 0.0599 0.082 SPI 0.0552 0.775 0.4604 0.3069 FI 0.0534 0.0637 0.5359 0.3475 0.9528 MTBF 0.0404 0.0925 0.5697 0.2974 0.7500 MTR 0.0548 0.50 0.5 0.3302 0.8750 AW 0.4378 0.3252 0.538 0.0832 TF 0.5446 0.2383 0.033 0.0738 0.9250 Score 0.705 0.802 0.3950 0.2530 I order to verify the rtiolity d correctess of the methods metioed i this pper, we lso use the AHP to choose the mitece methods for trsformers. The judgmet mtrix of AHP c be estblished by Tble Ⅱ d the qulittive descriptio mtrix of fuzzy judgmet, d the correspodig eigevectors for the mximum chrcteristic roots i judgmet mtrix is used to clculte the weight of criteri. The weights obtied from the AHP re show i Tble IX, d the evlutio results from AHP re show i Tble X. TABLE IX CRITERIA WEIGHTS OF ANALYTIC HIERARCHY PROCESS Mi Criteri Weights Sub Criteri Locl Weights Globl Weights S 0.322 SP 0.6667 0.24 C 0.76 AV 0.0748 PL 0.322 SD 0.2222 0.074 SE 0. 0.0357 CH 0.2857 0.0490 CS 0.574 0.098 CPT 0.429 0.0245 SPI 0.2 0.050 FI 0.8 0.0598 Mi Criteri F 0.3 Mi Criteri S C AV PL F Weights Sub Criteri Locl Weights Globl Weights MTBF 0.75 0.2409 MTR 0.25 0.0803 AW 0.8750 0.0974 TF 0.250 0.039 TABLE X THE RESULTS OF THE ANALYTIC HIERARCHY PROCESS Sub Criteri CM SM CBM PM Eige vlue CR SP 0.054 0.572 0.4948 0.2939 4.064 0.006 SD 0.0530 0.428 0.586 0.2856 4.0246 0.0092 SE 0.0667 0.333 0.5333 0.2667 4 0 CH 0.4477 0.43 0.0524 0.0867 4.025 0.008 CS 0.529 0.3248 0.0555 0.0978 4.0325 0.022 CPT 0.5357 0.2963 0.0599 0.082 4.004 0.0039 SPI 0.054 0.572 0.4948 0.2939 4.064 0.006 FI 0.062 0.062 0.5445 0.333 4.0206 0.0077 MTBF 0.0424 0.263 0.5338 0.2974 4.695 0.0635 MTR 0.0477 0.278 0.5238 0.3008 4.096 0.0360 AW 0.4773 0.2880 0.539 0.0809 4.02 0.0079 TF 0.5230 0.320 0.63 0.0487 4.0506 0.090 Score 0.763 0.87 0.3987 0.2380 From the lst lie i Tble X, it c be kow tht the best mitece method for trsformers obtied through the AHP is coditio-bsed mitece. The result is cosistet with the clculted result by usig the methods metioed i the pper, d the differeces of the globl scorig vlue of ltertive mitece methods re lso little, but the selectio of mitece methods for FHP-GP-SMS trsformers metioed i the pper c del with iccurte qulittive descriptio d fuzzy judgmet. For exmple, i the experts fuzzy evlutio, the fesibility is oe time to two times more importt th dditiol beefits, d i the fuzzy AHP, the ucerti fuzzy judgmet c be expressed s (0.5,,2,2.5, but the AHP cot solve this kid of problems. The rdom cosistecy (CR criteri i the judgmet mtrix c be used to tell whether the weight obtied through the AHP is resoble. The CR vlue of ll the sub-criteri is give i the rightmost colum of Tble 0. It c be see from Tble 0 tht the cosistecy of evirometl sfety, workers cceptbility, spre prts ivetory d persoel triig cost is best, while the cosistecy of me time betwee filures, me time betwee repirs d techicl fesibility i the judgmet mtrix is worst. This coclusio is cosistet with the MF i Tble 8. V. SUMMARY Firstly, the pper reviews the reserch sttus of the curret selectio of mitece methods d proposes usig the fuzzy AHP bsed o the gol progrmmig to solve the problems. Secodly, i order to overcome the disdvtges i trditiol fuzzy AHP, ew method for determiig the ccurte weight bsed o trpezoidl

350 JOURNAL OF COMPUTERS, VOL. 8, NO. 5, MAY 203 fuzzy umbers is proposed i the pper, d the ccurte weight i fuzzy compriso d judgmet mtrix c be give by usig this method, so s to void the problems cused by sequecig the fuzzy weight i the covetiol pproch. Filly, tkig the selectio of mitece methods for the mi trsformer i Jigzhug col mie, Zozhug Miig Group s exmple, the pper expouds the pplictio process of the metioed method, compres it with the stdrd AHP, d explis tht the results of the selectio of mitece methods obtied through the fuzzy AHP bsed o the gol progrmmig re resoble d fesible. ACKNOWLEDGMENT This work ws supported by the Reserch Fud for the Doctorl Progrm of Higher Eductio of Chi uder grt 200095004 d by the Key (Key grt Project of Chiese Miistry of Eductio uder grt 302. The uthors would like to express sicere pprecitio to the oymous referees for their detiled d helpful commets to improve the qulity of the pper. REFERENCES [] Azdivr F, Shu V. 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Hogxi Xie is curret Ph.D.cdidte t Chi Uiversity of Miig d Techology (CUMT, Chi. She received her MS degree i Computer Applictio Techology from CUMT i 2005, d her BS degree i Computer Sciece from CUMT i 2002. She is curretly lecture t school of Computer Sciece d Techology, CUMT. Her reserch iterests re i mitece, fult digosis, distributed prllel processig, dt miig, d eurl etwork. Lipig Shi is bor i 964, Ph.D. She is professor t School of Iformtio d Electricl Egieerig i CUMT. Her reserch iterests re col mie mechicl d electricl equipmet d utomtio, pplictio of power electroics i power systems, d equipmet d power grid opertio d fult digosis. She hs published more th 30 reserch ppers i jourls d itertiol cofereces d she hs wo more th 0 the provicil scietific reserch wrd.now she preside reserch fud for the Doctorl Progrm of Higher Eductio of Chi uder grt 200095004 d by the Key (Key grt Project of Chiese Miistry of Eductio uder grt 302. Hui Xu is curret Ph.D.cdidte t Chi Uiversity of Miig d Techology(CUMT, Chi. She received her MS degree i Computer Applictio Techology from CUMT i 2005, d her BS degree i Computer Sciece from CUMT i 2002. She is curretly lecture t school of Computer Sciece d Techology, CUMT. Her reserch iterest is computtio itelligece d colbed methe et l.