A Fuzzy MCDM Approach to Determine Critical Evaluation Criteria in Washing Liquid Material Selection Procedure

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1 Proceedngs of he World Congress on Engneerng 2016 Vol I, June 2 - July 1, 2016, London, U.K. A Fuzzy MCDM Approach o Deermne Crcal Evaluaon Crera n Washng Lqud Maeral Selecon Procedure Mehap Dursun and Özlem Arslan Absrac Selecon of an approprae maeral has become a key ssue n he desgn and developmen of ne producs. Maeral selecon can be veed as a complcaed mulcrera decson makng (MCDM) problem hch requres he consderaon of mulple conflcng crera. The am of hs paper s o presen a fuzzy mul crera decson makng (MCDM) approach based on 2-uple fuzzy lngusc model, lngusc herarches and qualy funcon deploymen (QFD) o deermne he mporance of selecon crera n maeral selecon procedure. The proposed mehodology llusraed hrough a case sudy of ashng lqud maeral selecon procedure. Index Terms Lngusc herarches, maeral selecon, ne produc developmen, qualy funcon deploymen, 2- uple fuzzy lngusc represenaon N I. INTRODUCTION EW produc developmen process (NPD) s consdered as he key facor of compeon among dfferen markes [1]. I s based on converng an dea no vsble, ouchable eny. The purpose s meeng he desres of hgher qualy and performance a loer cos [2]. To make proper decsons n NPD s val because he falure rae doesn underesmae and cos of falure s very hgh. Maeral selecon s a challengng procedure n NPD. I s seen as a mul-crera decson makng (MCDM) problem n engneerng because of requrng o consder mulple crera from dfferen dmensons. Beng able o selec proper maerals and succeed o mach he requremens n he producon process s sgnfcan. Improper maeral selecon may affec he performance of producs negavely, hus producvy, success and presge of he frm are also effeced poorly []. The purpose of maeral selecon process s o consue effecve produc ha gves maxmum performance a mnmum cos. In he leraure, here are some arcles relaed o maeral selecon. Chaeree and Chakrabory [4] appled four preference rankng based MCDM mehods o solve a maeral selecon problem. Grubba and Vnodh [] ulzed Ths ork has been fnancally suppored by Galaasaray Unversy Research Fund. M. Dursun s an Asssan Professor of Indusral Engneerng, Galaasaray Unversy, Orakoy, Isanbul 47, Turkey (fax: ; e-mal: mdursun@gsu.edu.r). Ö. Arslan s an MS suden of Indusral Engneerng, Galaasaray Unversy, Orakoy, Isanbul 47, Turkey (e-mal: ozlemarslan@gmal.com) ISBN: ISSN: (Prn); ISSN: (Onlne) VIKOR mehod as MCDM ool o deermne he mos approprae maeral for nsrumen panel used n elecrc panel. Rahman e al. [6] proposed a knoledge based decson suppor sysem o make deal maerals selecons for roof desgn. The procedure ulzed TOPSIS mehod o faclae selecon process. Lu e al. [] proposed an approach ha employs MCDM mehod h nerval 2-uple lngusc nformaon o solve he maeral selecon problem n o dfferen cases, for an auomave company and for a flyheel respecvely. Anokumar e al. [7] nroduced 4 dfferen MCDM mehods, fuzzy analyc herarchy process (FAHP)-echnque for Order of Preference by Smlary o Ideal Soluon (TOPSIS), FAHP-VIKOR, FAHP-ELECTRE and FAHP-PROMTHEE o selec maeral for he ppes n sugar ndusry by akng no accoun dfferen alernaves and evaluaon crera. Lu e al. [8] negraed decson-makng ral and evaluaon laboraory (DEMATEL) based analyc neork process (ANP) and VIKOR o resolve he bush maeral selecon problem ha consss of many nerdependen crera. Lao [] presened nerval ype 2 fuzzy mul-arbue decson makng for maeral selecon. The mehod s llusraed n an engneerng applcaon of maeral selecon n a e fuel sysem. Govndan e al. [10] consruced a model o selec he mos approprae consrucon maeral by ulzng DEMATEL, ANP and TOPSIS. Ths paper focuses on deermnng he mporance of selecon crera, hch are consdered o evaluae ashng lqud ha mees he needs of boh cusomers and frms. A fuzzy mul-crera group decson makng approach based on qualy funcon deploymen (QFD), 2-uple fuzzy lngusc represenaon and lngusc herarches s presened. QFD s used o ncorporae cusomer requremens no he evaluaon process. 2-uple fuzzy lngusc represenaon and lngusc herarches are employed o unfy mulgranular lngusc nformaon provded by decson makers. The res of hs paper s organzed as follos. In Secon 2, QFD as nroduced brefly. In secon, and secon 4, 2-uple fuzzy lngusc represenaon and lngusc herarches are presened, respecvely. The proposed algorhm s explaned n secon and a case sudy s llusraed n secon 6. Fnally, concludng saemens are gven n he las secon.

2 Proceedngs of he World Congress on Engneerng 2016 Vol I, June 2 - July 1, 2016, London, U.K. II. QUALITY FUNCTION DEPLOYMENT Qualy funcon deploymen (QFD) s acceped as an mporan produc developmen mehod hch ams o conver cusomer requremens no acves o develop produc and servces [11]. OFD needs o denfy cusomer requremens and desres for beng able o consue produc and servces accordng o hese necesses and requremens. In hs ay, QFD res o maxmze cusomer sasfacon level. On he oher hand, desgnang resources by consderng cusomer needs leads o reducon n cycle me and fallng n producon cos [12]. QFD has 4 dfferen marces. Each marx has s on ask for phases n produc developmen process. These marces can be lsed as produc plannng, par deploymen, process plannng and producon/operaon plannng marces, respecvely. Produc plannng marx provdes ranslang cusomer needs (CNs) no measurable echncal arbues (TAs). Par deploymen marx convers mporan TAs o produc/par characerscs. Process plannng marx ranslaes mporan produc/par characerscs no manufacurng operaons. And producon/operaon plannng marx provdes o conver mporan manufacurng operaons o day o day operaons and conrols [1]. The frs of he four marces, also called he house of qualy (HOQ), s he mos frequenly employed marx n QFD. HOQ consss of seven cells, hch has dfferen ask. Each cell clarfes a relaonshp beeen CNs and TAs and among he TAs. The srucure of HOQ marx s presened n Fgure 1. Inner dependences among TAs unceranes and mprecson, usng compuaonal mehods can no be suffcen alone n some cases. Thus, usng lngusc nformaon makes easer decson makng process. Moreover, qualave evaluaon s easer and comforable for humans n erms of ransmng her opnons. 2-uple lngusc model s he mos convenen ay n lngusc decson makng. I as presened by Herrera and Marnez [14]. The man advanage of hs model s he prevenon of loss of nformaon. The basc represenaon of 2-uple fuzzy lngusc model s s, here s represens he lngusc label of he predefned lngusc erm se S T, and α s a numercal value. Comparson of lngusc 2-uples can be represened as follos: Le (s x, α 1 ) and (s y, α 2 ) be o 2-uples. If x < y hen (s x, α 1 ) < (s y, α 2 ) If x = y hen o If α 1 = α 2 hen (s x, α 1 ) and (s y, α 2 ) represen same nformaon. o If α 1 < α 2 hen (s x, α 1 ) < (s y, α 2 ) o If α 1 > α 2 hen (s x, α 1 ) > (s y, α 2 ) Imporan defnons are gven as follos: Defnon 1 [1]. Le L = (γ 0, γ 1,..., γ g ) be a fuzzy se defned n S T. A ransformaon funcon χ ha ransforms L no numercal value n he nerval of granulary of S T, [0,g] s defned as : F S 0, g, FS s,, T T g 0 0,1,..., g g 0 (1) Cusomer Needs (CNs) Imporanc e of CNs Techncal Arbues (TAs) Relaonshps beeen CNs and TAs Compeve Assessmen Marx here F(S T ) s he fuzzy ses defned n S T. Defnon 2 [14]: Le S s s,..., erm se and 0, g be a lngusc 0, 1 a value supporng he resul of a symbolc aggregaon operaon, hen he 2-uple ha expresses he equvalen nformaon o s obaned h he follong funcon: : 0, g S 0.,0., s, round (2), 0.,0. s g Fg. 1. The house of qualy Overall Prores of TAs and Addonal Goals III. 2-TUPLE FUZZY LINGUISTIC REPRESENTATION MODEL Decson makng s an acvy ha s relaed makng choce among alernaves n order o reach nended ams. Snce decson makng problems n real orld ncludes ISBN: ISSN: (Prn); ISSN: (Onlne) here round s he usual round operaon, s has he closes ndex label o β, and α s he value of he symbolc ranslaon. Proposon 1 [14]: Le S s s,..., be a lngusc 0, 1 erm se and s, be a 2-uple. There s a s g 1 funcon

3 Proceedngs of he World Congress on Engneerng 2016 Vol I, June 2 - July 1, 2016, London, U.K. such ha from a 2-uple reurns s equvalen numercal value 0, g. Ths funcon s defned as 1 1 : S 0.,0. 0, G, s g g, Defnon [16, 17]: Le x s,...,, 1, 1 s n n be a se of lngusc 2-uples and W 1,..., n, n, 1 be her lngusc 2-uple assocaed eghs. The 2-uple lngusc eghed average x l s calculaed h he follong funcon: xl s1, 1, 1, 1... sn, n, n, n () n. 1 (4) n 1 1 h s, 1 and,. IV. LINGUISTIC HIERARCHIES A lngusc herarchy comprses se of levels. Each level s a lngusc erm se ha has dfferen granulary. The levels n hs herarchy s symbolzed as l(,)), here denoes he level of herarchy and ) denoes granulary of he lngusc erm se of he level [18]. The lngusc herarchy, LH can be consdered as he unon of all levels as LH l, n. The lngusc erm se of level +1 s obaned as [1] n L 1, 2. n L, 1 () Lngusc herarches are ulzed for prevenng nformaon loss n he unfcaon phase. The ransformaon funcon s formulzed as TF TF : l, n l, n 1 ) ) ) ) s, n s, n 1 1 The ransformaon funcon s becve ha provde ransformaons by prevenng loss of nformaon [18]. V. PROPOSED DECISION MAKING ALGORITHM Ths secon represens he fuzzy group decson makng mehodology, hch s based on QFD. The proposed mehodology employed lngusc herarches and 2-uple fuzzy lngusc represenaon model o unfy and aggregae mulgranular lngusc nformaon provded by decsonmakers. Moreover, uses QFD o deermne he eghs of he evaluaon crera. The dealed sepse represenaon of he proposed fuzzy MCDM algorhm s gven belo. (6) Sep 1. Consruc a decson-makers commee of Z (z=1,2,,z) expers, and denfy he CNs (=1,2,,m) and requred selecon crera (=1,2,,n). Sep 2. Consruc he decson marces for each decsonmaker ha denoe he eghs of each CNs, ~ z, relaonshps among CNs and TAs, ~ xz, and nner dependences among TAs, ~ ykz Sep. Unfy he mulgranular lngusc nformaon gven by he decson-makers no a lngusc erm se employng Eq. (6). Sep 4. Aggregae he eghs of each CNs, relaonshps among CNs and TAs, and nner dependences among TAs employng arhmec mean operaor. Sep. Compue he values of he aggregaed rangs. Sep 6. Calculae he orgnal relaonshp measure beeen * he h TA and he h CN, ~ x, employng Eq. (4). Sep 7. Compue he 2-uple lngusc eghed average for each TA. Sep 8. Rank he TAs accordng o he prncples of comparson of lngusc 2-uples gven n Secon III. VI. CASE STUDY The applcaon of he proposed mehodology s llusraed hrough a case sudy conduced n a deergen manufacurer facory locaed n souh par n Turkey. The facory has a capacy of producng 100 ons deergen n a day and s ranked among frs deergen manufacurers n Turkey. Frs, an analyss s conduced h qualy conrol deparmen and he feaures of deergens, expecaons of cusomers, facors ha effecs on producon process are saed. Then a survey s consruced h he conrbuon of qualy conrol deparmen. Fve CNs hrough expecaons of cusomers are decded. These can be lsed as "easy resoluon n aer (CN 1 )", "eco frendly (CN 2 )", "an allergen (CN ), "cos effecve (CN 4 ), "hygenc (CN )". Fve TAs ha are consdered as evaluaon crera can be lsed as "ph (TA 1 )", "vscosy (TA 2 )", "anonc acve maeral (TA )", "nononc acve maeral (TA 4 )", "oal acve maeral (TA )". Four decson-makers (DM 1, DM 2, DM, DM 4 ) saed her opnons on he prepared survey. The lngusc herarchy, LH l1,, shon n Fgure 2 [20], s consdered as mulgranular lngusc conex, snce he granulary of s lngusc erm ses are very common n decson-makng problems. DM 1 used l(1,), DM 2 and DM used l(2,), and DM 4 preferred o use l(,), and DM preferred o use l(,) for rang he prepared survey. Frs, he decson-makers provded her opnons on he effecs of each TA on each CN. Then, hey saed he mporance of each CNs and fnally he dependences among TAs are gven. The lngusc erm se l(2,) s chosen as lngusc erms se o unfy he mulgranular lngusc nformaon provded by he decson-makers. The unfed assessmens of decsonmakers are aggregaed employng arhmec mean operaor and he resuls are gven n Fgure.. ISBN: ISSN: (Prn); ISSN: (Onlne)

4 Proceedngs of he World Congress on Engneerng 2016 Vol I, June 2 - July 1, 2016, London, U.K. assessmen s s 4 s s 4 s Fg. 2. The lngusc herarchy LH l1, [20] s 6 s 7 s 8 The orgnal relaonshp measure beeen CNs and TAs s calculaed as n Table I. TABLE I ORIGINAL RELATIONSHIP BETWEEN CNS AND TAS TA 1 TA 2 TA TA 4 TA CN 1 (, -0.21) (, 0.40) (s, -0.4) (s, -0.22) (s, -0.47) CN 2 (, 0.2) (s, -0.7) (s, -0.2) (s, -0.24) (s, -0.) CN (, -0.04) (, 0.47) (s, -0.1) (s, -0.4) (s, -0.44) CN 4 (, 0.27) (s, -0.08) (s, 0.21) (s, 0.26) (s, 0.07) CN (s, -0.1) (s, -0.22) (s, -0.1) (s, -0.21) (s, -0.24) 2-uple lngusc eghed average for each TA s compued and he TAs are ranked accordng o he prncples of comparson of lngusc 2-uples. The resuls are gven n Table II. TABLE II IMPORTANCE OF TAS TA 1 TA 2 TA TA 4 TA Imporance (, 0.27) (s, -0.6) (s, -0.2) (, 0.24) (s, -0.0) Rank IV III I V II Accordng o he resuls of he analyss, "anonc acve maeral (TA )" s deermned as he mos mporan evaluaon crera for ashng lqud maeral selecon procedure, hch s folloed by "oal acve maeral (TA )" and "vscosy (TA 2 )", "ph (TA 1 )", and "nononc acve maeral (TA 4 )", respecvely. Fg.. Unfed assessmens of decson-makers ISBN: ISSN: (Prn); ISSN: (Onlne)

5 Proceedngs of he World Congress on Engneerng 2016 Vol I, June 2 - July 1, 2016, London, U.K. VII. CONCLUSION Maeral selecon problem can be grouped as an mporan decson makng problems because of he consderaon of conflcng crera and alernaves ha have o be consdered smulaneously. In hs paper, a fuzzy mul-crera decson makng algorhm, hch combne 2-uple fuzzy lngusc modelng, lngusc herarches and qualy funcon deploymen s proposed o deermne he mporance of selecon crera n maeral selecon procedure. Fuure research mgh focus on he mprovemen of he proposed algorhm o consae he mos approprae maeral alernave for ashng lqud. [18] O. Cordon, F. Herrera, and I. Zr, Lngusc modelng by herarchcal sysems of lngusc rules, IEEE T. Fuzzy. Sys., vol. 10, no. 1, pp. 2-20, [1] F. Herrera and L. Marínez, A model based on lngusc 2-uples for dealng h mulgranular herarchcal lngusc conexs n mulexper decson-makng, IEEE T. Sys. Man Cy. B., vol. 1, no. 2, pp , [20] V.N. Huynh, C.H. Nguyen, and Y. Nakamor, MEDM n general mul-granular herarchcal lngusc conexs based on he 2-uples lngusc model, Granular Compung, 200 IEEE Inernaonal Conference on, vol. 2, pp , 200. REFERENCES [1] S. L. Bron and K. M. Esenhard, Produc developmen: Pas research, presen fndngs and fuure drecons, Academy of Managemen Reve, vol. 20, pp. 4-78, 1. [2] D. Maffn and P. Braden, Manufacurng and suppler roles n produc developmen, Inernaonal Journal of Producon Economcs, vol. 6, pp , [] H. C. Lu, L. Lu, J. Wu, Maeral selecon usng an nerval 2-uple lngusc VIKOR mehod consderng subecve and obecve eghs, Maerals and Desgn, vol. 2, pp , 201. [4] P. Chaeree and S. Chakrabory, Maeral selecon usng preferenal rankng mehods, Maerals and Desgn, vol., pp. 84-, [] R. J. Grubha and S. Vnodh, Applcaon of fuzzy VIKOR and envronmenal mpac analyss for maeral selecon of an auomove componen, Maerals and Desgn, vol. 7, pp , [6] S. Rahman, H. Odeynka, S. Perera, and Y. B, Produc-cos modellng approach for he developmen of a decson suppor sysem for opmal roofng maeral selecon, Exper Sysems h Applcaons, vol., pp , [7] L. Anakumar, M. Ilangkumaran, and V. Sasrekha, Comparave analyss of MCDM mehods for ppe maeral selecon n sugar ndusry, Exper Sysems h Applcaons, vol. 41, pp , [8] H. C. Lu, J. X. You, L. Zhen, and X. J. Fan, A novel hybrd mulple crera decson makng model for maeral selecon h argebased crera, Maerals and Desgn, vol. 60, pp. 80-0, [] T. W. Lao, To nerval ype 2 fuzzy TOPSIS maeral selecon mehods, Maerals and Desgn, vol. 88, pp , 201. [10] K. Govndan, K. M. Shankar, and D. Kannan, Susanable maeral selecon for consrucon ndusry A hybrd mulcrera decson makng approach", Reneable and Susanable Energy Reves, vol., , [11] J. A. Carnevall, and P. C. Mguel, Reve, analyss and classfcaon of he leraure on QFD-Types of research, dffcules and benefs, Inernaonal Journal of Producon Economcs, vol.114, pp , [12] E. E. Karsak, S. Sozer, and S. E. Alpekn, Produc plannng n qualy funcon deploymen usng a combned analyhc neork process and goal programmng approach, Compuers & Indusral Engneerng, vol. 44, no. 1, pp , 200. [1] M. L. Shllo, Advanced QFD - Lnkng echnology o marke and company needs, Ne York: Wley, 14. [14] F. Herrera and L. Marínez, An approach for combnng lngusc and numercal nformaon based on 2-uple fuzzy represenaon model n decson-makng, Inernaonal Journal of Uncerany, Fuzzness and Knoledge-Based Sysems, Vol. 8, no., pp. -62, [1] F. Herrera and L. Marínez, A 2-uple fuzzy lngusc represenaon model for compung h ords, IEEE Transacons on Fuzzy Sysems, Vol. 8, no. 6, pp , [16] E. Herrera-Vedma, F. Herrera, L. Marínez, J. C. Herrera, and A. G. López, Incorporang flerng echnques n a fuzzy lngusc mulagen model for nformaon gaherng on he eb, Fuzzy Ses and Sysems, vol. 148, no. 1, pp. 61-8, [17] W. P. Wang, A fuzzy lngusc compung approach o suppler evaluaon, Appled Mahemacal Modellng, vol. 4, pp , ISBN: ISSN: (Prn); ISSN: (Onlne)