Research on Supplier Evaluation about Delivery Ability Based on Hesitant Fuzzy Linguistic Term Set and Linear Assignment

Transcription

1 Interntionl Core Journl of Engineering Vol. No. 08 ISSN: -89 Reserh on Supplier Evlution bout Delivery Ability Bsed on Hesitnt Fuzzy Linguisti Term Set nd Liner Assignment Nin Zhng, Cilin Luo, Deqing Fu, Jixin Chen Shool of Eonomis nd Mngement, Chongqing University of Posts nd Teleommunitions, Chongqing 0006, Chin. Abstrt Conerning to the urrent "mismth" problem between the supplier bility to deliver nd the ompny bility to respond to onsumer needs, the im of this pper is to develop n pproh for supplier seletion bsed on hesitnt fuzzy lnguge evlution nd inomplete weight informtion. Firstly, originl lnguge evlution informtion is trnsformed into hesitnt fuzzy linguisti term set (HFLTS). By using the generlized normlized distne of hesitnt fuzzy linguisti term set to mesure the distne between two linguisti vribles, the reltive loseness oeffiient in regrd to the positive idel point nd the negtive idel point is obtined. Then, the priority order of lterntive suppliers is quired by estblishing liner ssignment deision mking model with inomplete weight. Finlly, numeril exmple is given to illustrte the rtionlity of the proposed method, nd the sensitivity nlysis shows tht deision results re stble. Keywords Hesitnt fuzzy linguisti term set (HFLTS); inomplete weight; liner ssignment; delivery bility; supplier seletion.. Introdution Delivery bility refers to the bility of supplier to provide ompny produts or servies s greed. The stronger supplier delivery bility, the fster the ompny n mke deisions to respond to onsumer demnd nd inrese onsumer stisftion, so supplier delivery bility impts diretly the ompny bility to respond to ustomer demnd[]. However, in reent yers, it hs been ommon to see tht ompnies re unble to provide onsumers produts or servies in time beuse of insuffiient supplier supply pity. For exmple, in 07, fter the sle of Xiomi 6, due to insuffiient supplier supply bout mobile phone essory proessors, the ompny ould not send Xiomi 6 to onsumers in time. Consumers expressed strong disstisftion with this sitution nd even bndoned phones, whih resulted in shrp drop in phone sle nd ompny profit. It n be seen tht supplier delivery bility plys deisive role in meeting onsumer needs. If the ompny nnot provide high qulity delivery servies, it will lose ustomer benefits. Therefore, it is espeilly importnt for ompnies to use resonble pproh to selet the supplier with best delivery bility to respond quly to onsumer demnd. In the proess of evluting supplier delivery bility, on the one hnd, deision mkers re more inlined to use fuzzy lnguge rther thn preise numbers to express their views, nd often hesitte between severl evlution vlues. On the other hnd, the importne of eh evlution riterion is different, whih is refleted in different vlues of ttribute weights. Usully, the obtined weight informtion is inomplete beuse of limited onditions, just only inluding weight reltionship nd vlue rnge. 9

2 Interntionl Core Journl of Engineering Vol. No. 08 ISSN: -89 Evlution riteri on supplier seletion hve been fous t home nd brod. Some sholrs hve studied them from different spets. For exmple, bsed on the performne-elstiity perspetive, M et l. [] performed omprehensive nlysis of relevnt domesti nd foreign supplier evlution riteri, nd used severl riteri suh s delivery time, fter-sle servie, nd informtion shring to elborte supplier evlution riterion system. Zhou et l. [] onstruted n evlution riterion frmework from produt qulifition rte, on-time delivery rte nd servie level, nd evluted suppliers in vrious stges. Pn et l. [] seleted seven evlution riteri suh s qulity, prie, prodution delivery, servie nd more, then onduted more detiled evlution nlysis of supplier seletion. Dey et l. [] onsidered trditionl performne evlution riteri suh s qulity, delivery time ost nd other ftors suh s risk, business, soil, environment for supplier performne omprehensive ssessment. The bove indites tht supplier evlution riteri hve been grdully improved, but delivery bility is often inluded in other supplier evlution riteri system. Therefore, in order to evlute supplier delivery bility better, it is neessry to estblish evlution riteri bout it. Deision mkers tend to use fuzzy lnguge rther thn preise numbers to express evlution opinions, nd usully hesitte between severl evlution vlues [6]. The lnguge evlution is hesitnt nd fuzzy. Some sholrs hve onduted relevnt reserh on this sitution. Bsed on fuzzy set [7], Torr [8] defined hesitnt fuzzy set nd proposed tht element membership ould be omposed of severl possible vlues, then sholrs introdued the set into vrious evlution deision mking fields. For exmple, mking ll evlution experts stisfied with deision results, Wei et l. [9] proposed onsensus model bsed on hesitnt fuzzy linguisti deision mtrix to selet the best prodution ple. It showed tht this method ould mke full use of originl informtion to obtin expert onsensus by orreting informtion. Liu [0] used n intervl hesitnt fuzzy PROMETHEE multiple ttribute deision mking method to obtin the priority index of lterntives. The results showed tht hesitnt fuzzy lnguge improved informtion ggregtion effet. Zho et l. [] estblished hesitnt fuzzy multiple ttribute deision mking model for supplier seletion bsed on VIKOR. The model mintined originl informtion integrity by diretly proessing lnguge. It n be seen tht hesitnt fuzzy lnguge reserves originl linguisti informtion vlue so tht it improves the effetiveness of relisti deision- mking results bout supplier with best delivery bility. Another issue relted to supplier delivery bility evlution is bout ttribute weights of evlution riteri. At present, most reserhes re bsed on the known weights. However, due to some limited onditions, weight informtion obtined by deision mkers is inomplete. Some sholrs hve onduted relted reserh on weight solving. For exmple, bsed on weight onstrint set, Ye et l. [] designed single-objetive optimiztion model to determine ttribute weights by the weighted verge opertor of preferene degree nd TOPSIS. Zho et l. [] estblished n ttribute weight trget plnning model bsed on intervl intuitionisti fuzzy ross entropy to obtin set of objetive weight vlues. Sho et l. [] proposed nonliner progrmming ttribute weight solution model bsed on Jynes mximum entropy priniple nd fir lterntive ompetition. Although trditionl weight solution methods n obtin set of resonble weight vlues, these methods need to optimize results ontinully. In this proess, too muh informtion will be generted, whih my ffet the effetiveness of deision results. Therefore, it is very importnt to dopt weight solution method tht n fully utilize weight informtion nd simplify solving proess. The objetive weight n be obtined by riterion weight reltionship nd its vlue rnge through liner ssignment method. The method n not only solve inomplete weight informtion, but lso simplify lultion proess to obtin the rnking of the lterntives. In view of bove nlysis, s for the mismth problem between supplier delivery bility nd ompny response to onsumer demnd, the liner ssignment method n obtin the rnking of the lterntives to determine the optiml supplier [] with inomplete weight informtion. However, it nnot diretly del with hesitnt fuzzy lnguge. This pper proposes new liner ssignment deision mking method bsed on HFLTS. The reminder of this pper is orgnized s follows: In 0

3 Interntionl Core Journl of Engineering Vol. No. 08 ISSN: -89 Setion, we mke problem desription. In Setion, HFLTS is briefly reviewed, nd the generlized normlized distne of the set is defined. In Setion, we develop liner ssignment method with inomplete weight informtion bsed on HFLTS nd propose detiled solutions. In Setion, numeril exmple nd its sensitivity nlysis re given to illustrte the proposed method. The pper is onluded in Setion 6.. Problem Desription As onsumer demnds for ompny response inrese, supplier delivery bility beomes the fous. However, in reent yers, suppliers hve filed to provide onsumers produts or servies in time ording to their greement, whih mkes ompnies lose onsumers nd redue business profits. For this sitution, the pper foused on solving supplier delivery bility evlution nd seletion problem. Considering hesitnt fuzzy lnguge evlution nd inomplete weight informtion, new liner ssignment method bsed on HFLTS ws proposed to hoose the best supplier. Supposing tht ompny hd lterntive suppliers, reorded s A,,, m. Let C,,, n be delivery bility evlution riteri set. The evlution vlues of the lterntive i i,,..., m stisfying riterion j j,,..., n were expressed by hesitnt fuzzy linguisti vribles i i (HFLVs) S S j S j m H H s s H, s S. Sine evlution riteri weight informtion is usully T inomplete [6-7], let W,,, be the ttribute weight vetor, in whih wj 0 j,... n n j w j,nd w w w n ws set of weight informtion. For i j, wi wk ; wi wk i, i 0; wi w w wl, k k k k l; wi iwk, 0 i ; i wi i i, 0 i i i Where i,,, m, k,,, m, k,,, m, j,,, n., The ore of the seletion problem ws how to solve hesitnt fuzzy lnguge evlution nd inomplete weight informtion, nd then to obtin the rnking of the lterntive suppliers to determine the supplier with best delivery bility.. Preliminries Definition [8] Let S s,, 0 sg be set of linguisti evlution set on given domin, bsed on hesitnt fuzzy set [8], HFLTS is expressed s follows: 0 g H, HS S, S s,, s () Where HS is set of linguisti vribles in HFLTS, nd desribes possible linguisti vlue of vrible S. For onveniene, HS is nmed HFLV. Bsed on the generl ide Yger[9] first proposed nd used for deision mking, the generlized normlized distne mesure of HFLTS ws used to mesure the distne between two HFLVs. Definition Let H S nd H S be two HFLVs. The generlized normlized distne of HFLTS between two vribles is defined s:

4 Interntionl Core Journl of Engineering Vol. No. 08 ISSN: -89 D H, H S S HS HS Sl H S l H () Where S s,, 0 sg, And 0, if distne; if distne. l H S nd l H S, the distne D HS, HS, the distne D HS, HS re the number of the ftors in the H S nd H S, respetively. trnsforms into the hesitnt stndrdized Hmming trnsforms into the hesitnt stndrdized Euliden. Liner Assignment Deision Mking Model for Supplier Delivery Ability. Evlution Criteri of Supplier Delivery Ability Before seleting the supplier with best delivery bility, pproprite evlution riteri must be determined. However, most delivery bility evlution riteri re inluded in terms of servie, prodution, nd qulity. For exmple, Hn et l. [0] omprehensively evluted lterntive suppliers bsed on riteri suh s qulity, demnd response pity, delivery puntulity rte, nd prodution flexibility. Wng et l. [] seleted supplier by four spets from development, prourement, prodution nd qulity. The prodution dimension inluded two evlution riteri, delivery timeliness nd supply pity. Bsed on omprehensive priniple nd typil priniple, Wu et l. [] estblished supplier evlution riterion system bout 8 seondry riteri by five dimensions from ompny qulifition, servie level, stbility nd more. The first-level riterion servie level inluded seond-level riteri suh s order response speed nd on-time rrivl rte. In word, it is neessry to develop detiled supplier delivery bility evlution riteri. Bsed on relevnt litertures, suppliers were evluted through produt omplete delivery rte, doument informtion ury, prourement proessing effiieny, nd mrket djustment flexibility, s shown in Tble. Criteri produt omplete delivery rte doument informtion ury prourement proessing effiieny Tble. Supplier delivery bility evlution riteri Desription Completion bout tht the right produt ws delivered to the right person in the right wy, t the right time nd ple. The integrity of informtion relted to the produt, suh s outbound informtion nd delivery informtion. Completion bout opertionl tsk suh s order proessing nd rgo ping during this period from reeiving orders to shipping. mrket djustment flexibility Adptbility in terms of goods, personnel, funds nd more under hnging mrket.. Liner Assignment Deision Mking Model Liner ssignment method ws extended to deision mking proess with hesitnt fuzzy lnguge evlution informtion nd inomplete weight informtion for the optiml supplier seletion problem bout delivery bility. Firstly, Originl linguisti evlution informtion ws trnsformed into HFLV. Then, by the reltive loseness oeffiient of eh lterntive in regrd to the positive idel point nd the negtive idel point, the superiority s well s inferior reltionship of eh lterntive in eh evlution riterion nd the dding-weight rnk frequeny mtrix were obtined. Finlly, liner

5 Interntionl Core Journl of Engineering Vol. No. 08 ISSN: -89 ssignment model ws built to get set of weight vlues nd the rnking of lterntive suppliers. The speifi deision steps were s follows. Step. Obtin originl ssessments provided for this deision mking problem. Aording to four delivery bility evlution rules, originl evlution informtion ws obtined. Step. Convert originl evlution informtion into HFLVs. The lnguge evlution expression ws ompred with the linguisti evlution set, then originl evlution informtion ws onverted into HFLTS of n lterntive in the riterion. Step. Determine reltive loseness oeffiient. The distne between two HFLVs ws mesured by H S i j the generlized normlized distne of HFLTS. Then reltive loseness oeffiient in regrd to the positive idel point nd the negtive idel point under hesitnt fuzzy environment ws lulted by Eqution () [-]. j D HS, HS S, S S, S j j D H H D H H () j m j m Where HS mx i HS nd HS min i HS were the positive idel point nd the negtive idel point, respetively. Obviously, we knew tht 0 for every nd, nd if, then, if, then. As the reltive loseness oeffiient grows higher, the evlution vlue beomes better []. Step. Get the rnking of lterntives under eh evlution riterion. Aording to reltive loseness oeffiient vlue in different riteri, the lterntives were sorted in desending order of vlues. Step. Build the rnk frequeny mtrix. Aording to the bove rnking of the lterntives in eh evlution riterion, the rnk frequeny mtrix ws obtined. H S j H S 0 H S H S j H S st nd mth m m m m m mm i A j C Where the element i m; k,,, m) represented the frequeny tht ws listed s the th stndrd rnking by rnking m lterntives regrding to eh riterion j C in the light of desending order of vlues (If the lterntives hd something to do with riterion, then! blned rnkings were mde list seprtely). Step6. Construt the dding-weight rnk frequeny mtrix. Bsed on the bove rnk frequeny mtrix, the dding-weight rnk frequeny mtrix ws quired. k (,,, A st nd mth m A m A m m m mm Where wj w j w j. Eh entry of the dding-weight rnk frequeny mtrix mesured the onsisteny within ll riteri in rnking the i th lterntive k th. The greter the ssignment pointed by, the lrger onsisteny tht would root in ssigning i to the k th overll rnk. Step7. Estblish the liner ssignment deision mking model. i

6 Interntionl Core Journl of Engineering Vol. No. 08 ISSN: -89 Mx m m i k m p, i,,, m; k m p,,,, ; k m i Subjet to T W w, w,, w n ; n wj, p 0 or, for ll i nd k. j Where the permuttion mtrix P ws squre ( m m ) mtrix. Note tht the vlue ws the result of stndrd rnking, nd ws unknown nd ws undeided by the model. Step8. Solve the bove model, nd get the ttribute weight W s well s the optiml permuttion * mtrix P. Step9. Choose the supplier with best delivery bility. The optiml rnking of lterntives ws quired by, then the optiml supplier ws hosen. * AP p. A Numeril Exmple In order to gin ompetitive dvntge in n eonomilly globlized mrket, ompny intended to selet supplier with strong delivery bility for long-term oopertion. After preliminry seletion, there were five lterntive suppliers, lled s A,,,,. The five lterntives greed tht the ompny would selet the best one by four delivery bility evlution riteri, they were produt omplete delivery rte ( ), prourement proessing effiieny ( ), nd mrket djustment flexibility ( C,,,. Some informtion bout ttribute weight ws given s follows: ), doument informtion ury ( p ), lled s w w, w w, w w, w w 0., w w 0.0, w w w w, w w w w, 0. w 0., 0. w 0., n w 0.7w, w 0. w, wj, wj 0, j,,,,. j Let X x0 : extremely low, x : very low, x : low, x : medium, x : high, x : very high, x6 : perfet be the linguisti evlution set. Speifi steps were s follows: Step. Aording to evlution rules of four delivery bility riteri, lterntive suppliers were evluted. The originl evlution informtion ws shown in Tble. Tble. The originl evlution informtion High, Medium, Low High, Medium, Low Low, Very Low Very High, Low, Very Low Low, Very Low High, Very Low High, Medium, Low High, Low Very High, High, Medium High, Medium, Very Low High, Low Perfet, Low Perfet, Very High, High Very High, Low, Very Low Perfet, Low, Very Low High, Medium, Very Low Perfet, Medium, Low Very Low Medium, Very Low High, Medium, Very Low Step. The lnguge evlution expression ws ompred with the linguisti evlution set, nd ws onverted into HFLV, s shown in Tble.

7 Interntionl Core Journl of Engineering Vol. No. 08 ISSN: -89 Tble. Convert originl evlution informtion into HFLVs s Step. The reltive loseness oeffiient in regrd to the positive idel point nd the negtive idel point ws lulted by Equtions 错误! 未找到引用源 nd 错误! 未找到引用源, s indited in Tble. For instne, let for n exmple:, tke D HS, HS S, S S, S D H H D H H s s s s s s s D HS, H S D, s s s s s s D HS, H S D, s s Tble. The reltive loseness oeffiient Step. The lterntive suppliers were sorted in desending order of vlue under the sme riterion. The results were shown in Tble. Tble. Ordering of the lterntives in eh riterion Criterion Ordering

8 Interntionl Core Journl of Engineering Vol. No. 08 ISSN: -89 Step. Estblishing the rnk frequeny mtrix ws indited in Tble 6. For instne, note tht hd first rnk twie (on nd ), seond rnk one (on ), fourth rnk one (on ) nd fifth rnk one (on ). Thus,,, 0,, nd. Tble 6. The rnk frequeny mtrix st nd rd th th Step6. Bsed on the bove rnk frequeny mtrix, omputing rnk frequeny mtrix were indited in Tble 7. For instne, wg nd estblishing the dding-weight. wg Tble 7. The dding-weight rnk frequeny mtrix st nd rd th th wg 0 wg wg wg 0 wg wg wg wg wg wg wg wg 0 0 wg wg wg wg wg wg wg wg wg Step7. Construt the liner ssignment deision mking model with p, s follows: Mx Z P k i i p, k,,,,; p, i,,,,; Subjet to k n w, w ; j j p or 0, for i=,,,,; k,,,,. Step8. Solve the bove model, nd quire the ttribute weight vetor W 0.6, 0.8, 0.8, 0.8 T s well * s the optiml permuttion mtrix P. 6

9 Interntionl Core Journl of Engineering Vol. No. 08 ISSN: -89 * P st nd rd th th Step9. The optiml supplier ws determined by the rnking of lterntives quired by ,,,, ,,,, * A P Finlly, the optimum rnking sequene ws. Thus, the best hoie ws. To demonstrte the impt of deision mker preferenes in this se, different vlues were utilized to rnk the lterntives. In Tble 8, the rnking sequenes were presented. The result ws different beuse the sequene of the lterntives were different ording to different vlues. Therefore, ompnies ould hoose desirble lterntive in ordne with its interest nd tul need. However, it ws noted tht the best lterntive ws ll the time in this exmple, whih illustrted the deision result stbility of the proposed method. * AP. Tble 8. The rnkings of lterntives by the different distne mesure Rnking Conlusion For supplier delivery bility evlution problem, evlution riteri were estblished from four spets inluding produt omplete delivery rte, doument informtion ury, prourement proessing effiieny, nd mrket djustment flexibility. Considering hesitnt fuzzy lnguge evlution nd inomplete weight informtion, new liner ssignment deision mking model bsed on HFLTS ws developed. Firstly, the originl lnguge ssessment informtion ws trnsformed into HFLVs. The generlized normlized distne of HFLTS ws utilized to mesure the distne between two HFLVs, nd the reltive loseness oeffiient in regrd to the positive idel point nd the negtive idel point ws quired. Then, bsed on the rnk frequeny mtrix nd inomplete weight onstrint onditions, liner ssignment model ws estblished. Finlly, set of ttribute weight vlues nd the rnking of the lterntives were obtined by solving the model, so tht the supplier with best delivery bility ws determined. The reserh shows tht the proposed method dels with hesitnt fuzzy lnguge well to preserve originl informtion vlue. In the simple proess, redundnt informtion is not generted, nd the error used by evlution informtion subjetivity is effetively redued, whih mkes deision result more 7

10 Interntionl Core Journl of Engineering Vol. No. 08 ISSN: -89 stble. The method lso provides referene vlue for vrious linguisti mngement deision mking problems. Referenes [] Wng Y S. Fresh supplier seletion nd evlution [J]. Logistis Engineering nd Mngement, 06, 8(7): [] M S G, Guo J D, Zhng X L. Mnufturing supplier evlution from performne-resiliene prospetive [J]. Chinese Journl of Mngement, 07, (9): 0-. [] Zhou Q H, Wng Q. Reserh on low rbon supplier seletion bsed on intuitionisti fuzzy sets nd VIKOR [J]. Siene nd Tehnology Mngement Reserh, 07, 7(0): -7. [] Pn Y H, Zhn Y, M X. Reserh on influening ftors of supplier seletion of [] prefbrited housing omponents bsed on DEMATEL-BP Method [J]. Mthemtis in Prtie nd Theory, 07, 7(9): -. [6] DEY P K, BHATTACHARYA A, HO W. Strtegi Supplier Performne Evlution: A Cse-Bsed Ation Reserh of UK Mnufturing Orgnistion [J]. Interntionl Journl of Prodution Eonomis, 0, 66(): 9-. [7] Yng S H, Ju Y B. Multi-ttribute deision-mking method bsed on dul hesitnt fuzzy linguisti vribles [J]. Opertions Reserh nd Mngement Siene, 0, (): [8] Zdeh L A. Fuzzy sets [J]. Informtion nd Control, 96, 8(): 8-6. [9] Torr V. Hesitnt fuzzy Sets [J]. Interntionl Journl of Intelligent System, 00, (6): 9-9. [0] Wei C P, M J. Consensus model for hesitnt fuzzy linguisti group deision mking [J]. Control nd Deision, 08, (): 7-8. [] Liu N Y. Intervl hesitnt fuzzy PROMETHEE multi-ttribute deision mking method bsed on ssoition [J]. Mthemtis in Prtie nd Theory, 08, 8(): 7-. [] Zho J, Chen H Y. Fuzzy multiple riteri deision mking model for supplier seletion bsed on VIKOR method [J]. Fuzzy Systems nd Mthemtis, 06, 0(): 6-0. [] Ye F, Ye Y. An pproh for hybrid multiple ttribute deision mking with inomplete weight informtion [J]. Modern Eletronis Tehnique, 08, (6): 8-6. [] Zho M, Qin S S, Xie J H, et l. Intervl-vlued intuitionisti fuzzy multi-ttribute group deision mking onsidering risk preferene of deision mker [J]. Opertions Reserh nd Mngement Siene, 08, 7():7-6. [] Sho L S, Zho L L, Wen T X, et l. Bidiretionl projetion method with intervl-vlued intuitionisti fuzzy number [J]. Computer Engineering nd Applitions, 07, ():8-86. [6] Yng W, Wng C J, Liu Y. New multi-vlued intervl neutrosophi multiple ttribute deision mking method bsed on liner ssignment nd Choquet integrl [J]. Control nd Deision, 07, (7):8-. [7] Prk K S. Mthemtil progrmming models for hrterizing dominne nd potentil optimlity when multiriteri lterntive vlues nd weights re simultneously inomplete [J]. IEEE Trnstions on Systems, Mn, nd Cybernetis - Prt A: Systems nd Humns, 00, ():60-6. [8] Xu Z S, Chen J. An intertive method for fuzzy multiple ttribute group deision mking [J]. Informtion Sienes, 007, 77():8-6. [9] Yng S, Ju Y. Dul hesitnt fuzzy linguisti ggregtion opertors nd their pplitions to multi-ttribute deision mking [J]. Journl of Intelligent & Fuzzy Systems, 0, 7 () :9-97. [0] Yger R R. Generlized OWA Aggregtion Opertors [J]. Fuzzy Optimiztion & Deision Mking, 00, ():9-07. [] Hn E D, Xu G D. Supplier seletion deision mking method bsed on intuitionisti fuzzy ross entropy nd grey reltionl [J]. Siene Tehnology nd Engineering, 07, 7(7): -9. 8

11 Interntionl Core Journl of Engineering Vol. No. 08 ISSN: -89 [] Wng H J, Feng J Z, Zou H. A reserh on the evlution of strtegi module suppliers nd mngement mehnism from the perspetive of ollbortive innovtion [J]. Siene Reserh Mngement, 06, 7(): -. [] WU X H, Yo X, Li S H. Reserh on the seletion of low rbon logistis servie providers bsed on GST-ANP model [J]. Siene nd Tehnology Mngement Reserh, 0, (0): -8. [] Hwng C L, Yoon K. Multiple Attribute Deision Mking [M]. Springer Berlin Heidelberg, 98, 7 () :-. [] Szmidt E, Kprzyk J. A Similrity Mesure for Intuitionisti Fuzzy Sets nd Its Applition in Supporting Medil Dignosti Resoning [J]. 00, 070 (): [6] Xu Z, Zhng X. Hesitnt fuzzy multi-ttribute deision mking bsed on TOPSIS with inomplete weight informtion [J]. Knowledge-Bsed Systems, 0, (6): -6. 9