Chapter 2 An Intuitionistic Fuzzy MCDM Approach for Effective Hazardous Waste Management

Transcription

1 Chapter 2 An Intutonstc Fuzzy MCDM Approach for Effectve Hazardous Waste Management Gülçn Büyüközkan and Fethullah Gocer Abstract Improperly handled hazardous waste can pose sgnfcant threat to human health and the envronment. Safety of waste transportaton s an mportant aspect of hazardous waste management. Ths makes the evaluaton and selecton of the most sutable hazardous waste transportaton frm (HWTF) a crucal problem for hazardous waste generators. A number of factors affect the selecton of the proper HWTF, whch need to be addressed wth usually vague and mprecse data provded by a team of experts from dfferent backgrounds. Ths chapter proposes a systematc and ntegrated mult crtera decson makng (MCDM) approach to support the HWTF selecton process. Ths approach s based on the Technque for Order of Preference by Smlarty to Ideal Soluton (TOPSIS) method n an ntutonstc fuzzy (IF) envronment. A Group Decson Makng (GDM) approach s utlzed by the means of IF to mnmze the bas stemmng from experts fuzzy evaluatons and to better manage the assocated uncertantes and partalty. A real case applcaton from Turkey s presented to llustrate the use of the proposed methodology. 2.1 Introducton In modern socetes, almost all materals, devces and objects sooner or later turn nto waste (Gumus 2009). Waste can be classfed as hazardous or non-hazardous, dependng on whether they exhbt partcular characterstcs. Hazardous waste has been defned for the frst tme n the USA n early 1980s (Marnkovć et al. 2008)as unwanted flammable, oxdzng, posonous, radoactve, toxc or explosve materals whch pose a threat to humans or envronment when handled mproperly. Sources of hazardous waste are varous; t may be produced n hosptals, by metal fnshng or tmber treatment processes, petrol storage, pant manufacture etc. G. Büyüközkan (&) F. Gocer Industral Engneerng Department, Galatasaray Unversty, Ortakoy, Istanbul, Turkey e-mal: gulcn.buyukozkan@gmal.com F. Gocer e-mal: fgocer@gsu.edu.tr Sprnger Internatonal Publshng Swtzerland 2017 C. Kahraman and I.U. Sarı (eds.), Intellgence Systems n Envronmental Management: Theory and Applcatons, Intellgent Systems Reference Lbrary 113, DOI / _2 21

2 22 G. Büyüközkan and F. Gocer Economc growth and ndustral prosperty globally undergone n recent decades has accelerated the generaton of hazardous waste (Duan et al. 2008), puttng hazardous waste concerns nto agenda of many developed or developng countres, whch has led to the exploraton of alternatve ways for proper hazardous waste management and handlng. Consderng assocated dangers, t presents to humans and envronment, preventon of contamnaton by hazardous waste s vtal, underlnng the mportance of ts safe transportaton. However, hazardous waste generators beleve that safe transportaton regulatons are partcularly enforced by polcy makers because other partes handle those processes (Gumus 2009; Orford 2007). For these reasons, generators explore safe and cost-effectve solutons n hazardous waste management (HWM), presentng a problem wth several dfferent objectves. For a commercal frm, for nstance, the most feasble HWM soluton mght be the opton wth the mnmum cost, whereas a publc authorty mght look for the soluton wth lowest spllage or leakage rsk. Therefore, a hazardous waste transportaton frm (HWTF) must have a certan level of qualty, safety, servce and responsblty at the same tme, n an envronment where t s expected to comply wth legslaton and act correctly (Ho 2011). In ths chapter, a Group Decson Makng (GDM) approach s mplemented for the selecton of the most sutable HWTF. At frst, the lterature about HWM and Technque for Order Preference by Smlarty to Ideal Soluton (TOPSIS) methods under Intutonstc Fuzzy (IF) envronment wll be revewed. Followng that, the proposed methodology structure wll be explaned and a real case from Turkey wll be presented. Then, procedural IF TOPSIS steps and related calculatons wll be provded to ntroduce the technque. A numercal applcaton of the case study wll be llustrated at the fnal stage n order to dsplay how the proposed method functons. 2.2 Lterature Revew Hazardous Waste Management Hazardous waste wth explosve, gntable/flammable, oxdzng, posonous, corrosve, radoactve or toxc characterstcs can be generated durng petrol storage, metal fnshng, pant manufacturng, dry cleanng and hosptals, besde others. If handled poorly, hazardous waste wll cause sgnfcant damage to both humans and envronment, puttng specfc emphass on choosng the rght transportaton and dsposal frm for hazardous waste. Hsu et al. (2008) selected the most sutable medcal hazardous waste dsposal frm wth the help of AHP and a modfed Delph technque. They suggested that ther method reduced overhead costs and thus enhanced the management of hazardous waste. Ho (2011) suggested a fuzzy AHP method for ths knd of evaluaton wth whch medcal and health care

3 2 An Intutonstc Fuzzy MCDM Approach 23 nsttutons could objectvely and systematcally choose approprate nfectous medcal waste dsposal frms. Usng a MCDA approach, Feo and Gs (2014) developed a hazardous waste mnmzaton procedure wth geographcal nformaton. In ther study, AHP s used to defne the prortes of evaluaton crtera for ts ease and usefulness. A HWM case study n the USA s done usng DEA-TOPSIS technques by Al et al. (2015). In another study, Mohsn et al. (2015) made an assessment of HWM proposal usng AHP. Abess and Saeed (2014) presented an approach for stng hazardous waste landfll n large areas usng ste screenng method and AHP. Ald (1996) suggested a mult objectve optmzaton model for the proper management of hazardous waste. They combned AHP wth a goal programmng approach to prortze conflctng goals. To the extent of our knowledge, the most recent studes about HWTF are presented by Gumus, Kabr and Sum. Kabr (2015) extended VIKOR method under fuzzy envronment for the selecton of HWTF. Kabr and Sum (2015) also proposed a method for selectng HWTF by usng AHP and PROMETHEE. Gumus (2009) evaluated a two-step methodology for HWTF by usng fuzzy AHP and TOPSIS. In ths study, an IF TOPSIS method s used n order to decde on the most approprate HWTF. It must be underlned that ths technque s appled for the problem evaluaton and the results of IF TOPSIS show the rankng order of the HWTFs. To the best of our knowledge, ths knd of a study has not appeared n related lterature n earler publcatons, dfferentatng tself by ntegratng TOPSIS and IF wth a GDM approach for a real case HWTF selecton problem IF TOPSIS Lterature In ths secton, lterature related to the TOPSIS technque under IF set s revewed. Ths lterature survey n the HWT context revealed that key aspects have been, for the most part, overlooked by researchers, ndcatng a research gap for selectng sutable HWTF. Fuzzy TOPSISI s commonly used n HWM to obtan the effectve rankng of HWTF. GDM s often preferred to avod the bas and mnmze the partalty n ths knd of decson process. From lterature, however, t s observed that n some stuatons classcal fuzzy sets can be nadequate and even defectve n handlng the ambguty of the concepts that are assocated wth human bengs subjectve judgments. IF sets, on the other hand, are useful tools to nvestgate the fuzzness n decson makers (DMs ) judgments n the complexty of soco-economc envronment and the lack of knowledge or data about the problem. A fuson of GDM wth DMs assessments s consdered as one unform group decson by means of IF set. Table 2.1 dsplays a summary of the TOPSIS lterature under IF or Interval Valued IF (IVIF) envronment wth an emphass on the focus and the employed technque.

4 24 G. Büyüközkan and F. Gocer Table 2.1 IF TOPSIS lterature Author Am of the study Appled technque GDM Illustratve or case study Boran et al. (2009) Suppler selecton IF TOPSIS X Illustratve Boran (2011) Suppler selecton IF TOPSIS X Illustratve Park et al. (2011) Equpment selecton IVIF TOPSIS X Illustratve Wang et al. (2011) Suppler selecton IVIF TOPSIS Illustratve Boran et al. (2012) Technology evaluaton IF TOPSIS Illustratve İntepe et al. (2013) Forecastng method IVIF TOPSIS X Illustratve Yue and Ja (2013) Partner selecton IF TOPSIS X Illustratve Alon et al. (2014) Machne selecton IF TOPSIS X Case study Kucukvar et al. (2014) Sustanablty performance IF TOPSIS X Illustratve L et al. (2014) Module parttonng IVIF TOPSIS X Case study evaluaton Long and Geng (2015) Module selecton IVIF TOPSIS Case study Wu (2015) Suppler selecton IF TOPSIS X Illustratve Wan et al. (2015) Technology selecton IF TOPSIS X Case study Wang et al. (2015) E-tenderng IF TOPSIS Illustratve Yang et al. (2015) Method proposal for IF TOPSIS X Illustratve dervng weghts Zhang and Xu (2015) Soft computng technque IVIF TOPSIS X Illustratve Josh and Kumar Personnel selecton IVIF TOPSIS X Illustratve (2016) Wan et al. (2016) Logstcs outsourcng IF TOPSIS X Illustratve 2.3 IF TOPSIS Methodology Ths secton presents the IF TOPSIS mult crtera GDM method. Let us denote, D ={D 1, D 2,, D k ) be a set of DMs, assume that the mportance of DM D k s λ k, where P K k¼1 k k ¼ 1, and C ¼fC 1 ; C 2 ;...; C n g be a set of crtera, w ¼ fw 1 ; w 2 ;...; w n g the weght vector of crtera, where w j 0; j ¼ 1; 2;...; n, P n j¼1 w j ¼ 1. The set of alternatves: A ¼ fa 1 ; A 2 ;...; A m g n the form of TIFN Intutonstc Fuzzy Sets In ths secton, the basc concept of ntutonstc fuzzy sets wll be brefly ntroduced. The Intutonstc Fuzzy Set (IFS) s developed by Atanassov (1986) and

5 2 An Intutonstc Fuzzy MCDM Approach 25 consttutes an extenson of Zadeh s fuzzy set. It assgns a degree of membershp to each element and defnes a (crsp) set E, wth A Ebeafxed set. An IFS A n E s an object of the followng form: A ¼ fx; l A ðxþ; m A ðxþjx 2 Eg; The functons μ A :E [0, 1] and ν A :E [0, 1] defne the degree of membershp and the degree of non-membershp of the element x 2 E to the set A, respectvely. For every x 2 E: If 0 l A ðxþþm A ðxþ1: fhx; l A ðxþ; 1 l A ðxþjx 2 Eg p A ðxþ ¼1 l A ðxþ m A ðxþ; then p A ðxþ s the degree of non-determnacy (uncertanty) of the membershp of element x 2 E to set A. In the case of ordnary fuzzy sets, p A ðxþ ¼ 0 for every x 2 E Proposed Computatonal Steps In ths secton, computatonal steps for IF TOPSIS method s presented. Ths ntegrated method s qute sutable for solvng MCDM problems. The alternatves are ranked usng IF TOPSIS method, as adapted from the studes of Boran et al. (2011) and Boran (2011). The evaluaton of the study, whch s based on our method, s gven n Fg. 2.1 as a schematc dagram. The steps of the method for IF TOPSIS MCDM are as follows. Step 1: Construct a herarchy for the evaluaton of the problem. Defne the goal, objectve, attrbutes and alternatves for resolvng the problem. Step 2: Determne the weghts of Experts. Importance of experts s consdered as lngustc varables. The defned TIFNs seven-pont lngustc varable scale s ntroduced to estmate the weght of each DM n the GDM process. In order to express DMs ndvdual assessments more precsely, the lngustc varable scale, whch s adapted from the fve-pont scale of Boran et al. (2009) s mproved wth a mnor addton to ntermedate values. The new seven-pont scale used n DMs assessment stages ranges from Very Unmportant to Very Important, as presented n Table 2.2.

6 26 G. Büyüközkan and F. Gocer Fg. 2.1 The proposed IF TOPSIS MCDM methodology to determne the best alternatve for a HWTF Let Dk ¼ðl k ; v k ; p k Þ be an IF number for ratng of the kth DM. The weghts of the kth DM are obtaned usng the followng Eq. (2.1) whch s adapted from the study of Boran et al. (2009). h h l l k þ p k k 1 p k k k ¼ P h h ; where XK K k¼1 l k þ p k l k 1 p k k¼1 k k ¼ 1 ð2:1þ

7 2 An Intutonstc Fuzzy MCDM Approach 27 Table 2.2 Lngustc varable for the mportance of each DM Lngustc varables TIFNs µ υ Π Very mportant Important Somewhat mportant Medum mportant Somewhat unmportant Unmportant Very unmportant Step 3: Based on pror knowledge and expertse on ther specfc topcs, experts are requred to provde ther judgments. In ths step, assume that each expert provdes hs/her judgments on each factor n lngustc terms. Step 4: Transform Data nto TIFNs. Construct the preference relaton matrx for attrbutes and alternatves. After formng the herarchy, the preference relaton matrx s structured. Durng the preference relaton, a TIFNs preference scale s used for the evaluaton. Snce the lngustc terms are not mathematcally operable, the next step s to make a standardzaton of experts evaluatons by convertng them to TIFNs, once all lngustc assessments of factors from each expert are obtaned. The scale used n TOPSIS stage for preparng the preference relaton matrx ranges from 1 (Extremely Unmportant) to 9 (Extremely Important), as presented n Table 2.3. The lngustc scale s adapted from Abdullah and Najb (2014). Step 5: Aggregate ndvdual TIFNs nto group TIFNs for the attrbutes. In ths step, each ndvdual experts opnon s aggregated nto IF envronment. It has been decded to use the ntutonstc fuzzy weghted averagng (IFWA) operator whch s used to aggregate the matrx assessment of DMs nto a group Table 2.3 Lngustc varable for the mportance of factors (Abdullah and Najb 2014) Lngustc varable µ υ π Extremely unmportant EU Very strong unmportance VSU Strongly unmportant SU Moderately unmportant MU Equally mportant EI Moderately mportant MI Strongly mportant SI Very strong mportance VSI Extremely mportant EMI

8 28 G. Büyüközkan and F. Gocer opnon due to Xu (2011) snce IFWA weghts only the IF arguments but not the ordered poston and practcal n use. Step 6: Construct the aggregated IF preference relaton matrx 2 3 ^b 11 ^b ^b 1n b 21 ^b ^b 2n : B ¼ : : 5 ^b m1 ^b m2... ^b mn where ~b j ¼ l j ; t j ð ¼ 1; 2;...; n; j ¼ 1; 2;...; nþ and satsfes the followng Eqs. (2.2) and (2.3). ( ( )) ðl j Þ ¼ max l j ; max p l p l pj l p l pj þð1 l p Þð1 l pj Þ ðt j Þ t p t pj ¼ max t j ; max p t p t pj þð1 t p Þð1 t pj Þ ð2:2þ ð2:3þ Step 7: Obtan the prorty vector of crtera: w ¼ ðw 1 ; w 2 ;...; w n Þ T Weghts of the crtera can be estmated wth the help of the equaton proposed by Genç et al. (2010). h w j ¼ w L j ; wu j 0 ¼ P n j¼1 1 ; ð Þ 1 ~l j ~l j P n j¼1 1 ð 1 ~v j ~v j 1 C Þ A ð2:4þ Step 8: Aggregate ndvdual TIFNs nto group TIFNs for the alternatves. In ths step, each ndvdual expert s opnon s aggregated nto IF envronment and the aggregated IF decson matrces for each expert s constructed: Assume that R s the group decson makng matrx where

9 2 An Intutonstc Fuzzy MCDM Approach R k 11 R k 1n R ¼ R k 6 j ¼ ; kk R k m1 R k mn where R k j ¼ lk j ; tk j ; p j : Use the followng Eq. (2.5) for ndvdual aggregaton of each expert s opnons. R j ¼ IFWA k R ðþ k j ¼ k k r ðþ k j ð2:5þ Step 9: Determne the postve deal soluton and the negatve deal soluton. A* s the postve deal soluton, and A s the negatve deal soluton, A ¼ ~r 1 ; ~r 2 ;...; ~r n ;~r j ¼ l j ; t j ; p j ; j ¼ 1; 2;...; n ð2:6þ A ¼ ~r 1 ; ~r 2 ;...;~r n ;~r j ¼ l j ; t j ; p j ; j ¼ 1; 2;...; n ð2:7þ where l j ¼ max l j jj 2 J1 ; mn l j jj 2 J2 t j ¼ mn t j jj 2 J1 ; max t j jj 2 J2 l j ¼ mn l j jj 2 J1 ; max l j jj 2 J2 t j ¼ max t j jj 2 J1 ; mn t j jj 2 J2 Step 10: Calculate the weghted separaton measures. The weghted Hammng dstance s utlzed to calculate the separaton measures (Xu 2011). S L¼ 1 2 X n w L j j¼1 h l j l j þ v j v j þ p j p j ð2:8þ S U¼ 1 2 X n w U j j¼1 h l j l j þ v j v j þ p j p j ð2:9þ

10 30 G. Büyüközkan and F. Gocer S L¼ 1 2 S U¼ 1 2 X n w L j j¼1 X n w U j j¼1 h l j l j þ v j v j þ p j p j h l j l j þ v j v j þ p j p j ð2:10þ ð2:11þ Step 11: Calculate the relatve closeness coeffcents. C L¼ S L! ðs Þ U þ ðs Þ U C U¼ S U! ðs Þ L þ ðs Þ L ð2:12þ ð2:13þ Step 12: Rank the alternatves n ascendng order of the relatve closeness coeffcents. The best alternatve s selected n ascendng order of the relatve closeness coeffcent. The possblty degree formula, whch s proposed by Xu and Da (2002), s used to rank the alternatves as shown n Eqs. (2.14) and (2.15). b U a L pa ð bþ ¼ maxf1 max b U b L þ a U a L ; 0 ; 0g ð2:14þ a U b L pb ð aþ ¼ maxf1 max b U b L þ a U a L ; 0 ; 0g ð2:15þ 2.4 Case Study Company Background The proposed method has been mplemented n a chemcal company regstered n Turkey. Due to prvacy concerns, the dentty of the frm s kept anonymous. In ths chapter, the company s referred as ABC Company from now on. The ABC Company s establshed n 1924 to deal wth chemcals tradng wth recognzed nternatonal supplers, manly polymer emulsons and specalty chemcals. The frst polymer emulsons and textle auxlares nvestment of ABC had a plant capacty of 6000 tons. As of 2007, over the last 28 years ths producton

11 2 An Intutonstc Fuzzy MCDM Approach 31 capacty grew more than 30-fold to 200,000 tons per year, thanks to 5 plant expansons wth an ambton to grow and passon for ts busness. Envronment s a key concern for ABC, not only n producton, but also n new product development, both at ndvdual and corporate levels. ABC s well aware that reducng the use of Polyethylene (PE) adds up to szable benefts for the envronment. ABC s goal s to mprove the producton performance by analyzng each step n the producton, logstcs and transport and determne the way for decreasng energy consumpton, raw materal use, equpment wear and tear and byproducts and ncreasng the customer satsfacton, hygene, envronmental safety and the wellbeng of ts workers and communty. For ths reason, ABC s wllng to fnd a sutable HWTF for all ts hazardous waste Implementaton of the Proposed Methodology ABC s man objectve s to select the most sutable HWTF that can satsfy ts needs. There are 5 HWTF alternatves wth whch ABC has worked n the past for hazardous waste materal transportaton. At ths stage, experts earler works done wth the company s exstng frms s taken as reference. These 5 frms, referred as A 1, A 2,A 3,A 4 and A 5 from now on, are assessed n the followng case study. The crtera determned for the purpose of evaluatng and rankng alternatve transportaton frms are taken from smlar studes n lterature (Gumus 2009; Kabr and Sum 2015; Kabr 2015) and experts opnons. Three experts are desgnated for evaluaton; the logstcs and dstrbuton manager, the sales coordnaton manager and the health-safety and envronment specalst. ABC s logstc drector has been employed snce 1990 to manage stock levels, delvery tmes and negotatons wth customers and supplers, etc. He s one of the most experenced and longest servng staff of the company. ABC s sales coordnaton manager s workng for the company snce He has worked n dfferent departments n the company n the past and currently works as a manager for coordnatng the sales team, assessng the progress of the department and developng sales strateges. Health-safety and envronmental specalst works for the company n order to ensure that envronmental regulatons and workplace safety standards are fully met to protect the wellbeng of the publc and the envronment. She s employed n ABC snce The detals of the HWTF selecton process for ABC Company s llustrated below. Step 1. The herarchcal structure s constructed. The goal of fndng the best sutable HWTF and 5 transportaton frm alternatves for resolvng the problem s defned. The evaluaton crtera that are grouped under 10 categores for evaluatng transportaton frms are gven as follows: C 1 Economc Capablty (EC) Cost of Servce (CS) C 2

12 32 G. Büyüközkan and F. Gocer C 3 C 4 C 5 C 6 C 7 C 8 C 9 C 10 Fnancal Stablty (FS) Servce Capablty (SC) Servce Tme (ST) Experence and Qualfcaton (E&Q) Techncal Capablty (TC) Envronmental and Safety (ES) Hygene and Safety (HS) Takng Care of Human Health (TCH) Step 2. Weghts of the DMs are determned. Importance weghts of the experts are calculated, as seen n Table 2.4. Step 3. Experts judgments are collected for each HWTF. Table 2.5 shows the judgment matrx of the frst DM as an example. Table 2.6 shows the judgment matrx for all alternatves for each DM. Step 4. Lngustc data are transformed nto TIFNs. The sample of the transformed TIFNs s shown n Table 2.7 for the frst alternatve. Step 5. Indvdual data are aggregated nto group TIFNs. Table 2.8 dsplays B matrx, the group TIFNs for attrbutes. Table 2.4 Importance weghts of the experts DM-1 DM-2 DM-3 Lngustc terms Very mportant Important Medum mportant Weght Table 2.5 Judgment matrx of crtera for DM1 EC CS FS SC ST E&Q TC ES HS TCH EC EU EI SU SI EI EI SU SU VSU SU CS EI EU EI MU SI MI MU MU SU VSU FS MI EI EU EI SU EI SU VSU MU VSU SC VSU MI EI EU MU VSU MU SU SU SU ST EI SI MI SI EU MU EI VSU VSU VSU E&Q EI MU EI VSI SI EU MU SU MU SU TC MI SI MI SI EI SI EU VSU SU VSU ES MI SI VSI MI VSI MI VSI EU VSU SU HS VSI MI SI MI VSI SI MI VSI EU VSU TCH MI VSI VSI MI VSI VSI VSI MI VSI EU

13 2 An Intutonstc Fuzzy MCDM Approach 33 Table 2.6 Judgment matrx of alternatves Crtera A 1 A 2 A 3 A 4 A 5 DM1 DM2 DM3 DM1 DM2 DM3 DM1 DM2 DM3 DM1 DM2 DM3 DM1 DM2 DM3 EC SI VSI MI MI EI VSI MI EI MU MI EI VSI MI MI MI CS MI SI SI MI MU SI EI SI EI EI MI EU EI SI EI FS MI EI VSI SI EI VSI MU MI MU SI EI VSI EI EI EI SC MU EI MU MU MI MU EI EI EI MU MI MU MU SU MU ST EI MI MI MI MU MU SI MU EI MI MU MU SI MU EI E&Q MU SI MI SU VSU EI MI EI MU MI MU SI EI MI EI TC MI MU EI SI VSU EI MU VSU SU EI SI MI SI EI EI ES VSI VSI VSI MI EI EI EI MI SI MI EI EI EI MI SI HS SI MI SI EI SI MI SI MI EI VSU EI MU MU MI MU TCH SI SI VSI MI MI MI MI MI MI MI MI MI MI EI MU

14 34 G. Büyüközkan and F. Gocer Table 2.7 TIFNs for the frst alternatve DM1 DM2 DM3 µ υ π µ υ π µ υ π A1 EC CS FS SC ST E&Q TC ES HS TCH Table 2.8 Aggregated TIFNs for attrbutes (B) EC CS FS SC ST l t t l l t l t l t EC CS FS SC ST E&Q TC ES HS TCH E&Q TC ES HS TCH l t l t l t l t l t EC CS FS SC ST E&Q TC ES HS TCH

15 2 An Intutonstc Fuzzy MCDM Approach 35 Step 6. Aggregated IF preference relaton matrx s constructed. After takng the judgments of experts about all crtera, the aggregated preference relaton matrx s formed and then usng the Eqs. (2.2) and (2.3), the consstent IF preference relaton matrx s constructed, as shown n Table 2.9. Step 7. Obtan the prorty vector. The prorty vector of crtera s estmated usng Eq. (2.4). Table 2.10 dsplays the calculated data. Step 8. Alternatves are aggregated nto group TIFNs. Table 2.11 dsplays the aggregated IF decson matrx for each alternatve. Step 9. Postve and negatve deal solutons are calculated. The postve and negatve deal solutons are calculated by consderng rankng values and Eqs. (2.6) and (2.7) (Table 2.12). Economc capablty, cost of servce and fnancal stablty crtera are consdered as cost crtera and the rest are consdered as beneft crtera. Table 2.9 IF preference relaton matrx for attrbutes (consstent B*) EC CS FS SC ST l t l t l t l t l t EC CS FS SC ST E&Q TC ES HS TCH E&Q TC ES HS TCH l t l t l t l t l t EC CS FS SC ST E&Q TC ES HS TCH

16 36 G. Büyüközkan and F. Gocer Table 2.10 Prorty weght vector Lower Upper EC CS FS SC ST E&Q TC ES HS TCH Table 2.11 IF decson matrx EC CS FS SC ST l t l t l t l t l t A A A A A E&Q TC ES HS TCH E&Q l t l t l t l t l t A A A A A Table 2.12 The negatve and postve deal solutons A* A EC CS FS SC ST E&Q TC ES HS TCH

17 2 An Intutonstc Fuzzy MCDM Approach 37 Step 10. Weghted separaton measures are calculated. Negatve and postve separaton measures, based on the weghted lower and upper hammng dstance for each alternatve, have been calculated usng the Eqs. (2.8), (2.9), (2.10), and (2.11) (Table 2.13). Step 11. Relatve closeness coeffcent s calculated. The dstances of each alternatve to the deal solutons and the closeness coeffcent are calculated as gven n Table Step 12. Alternatves are ranked. Fve canddate HWTF have been ranked n descendng order of the relatve closeness coeffcents. The canddates are ranked by usng the possblty degree formula, thus the matrx n Table 2.15 s created. The rankng of the alternatves s A 2 >A 1 >A 3 >A 4 >A 5. Fnally, A 2 s selected as the best alternatve for ABC Company. Table 2.13 Separaton measures S * S Upper Lower Upper Lower A A A A A Table 2.14 Closeness coeffcent Lower Upper Table 2.15 Possblty degree matrx A A A A A

18 38 G. Büyüközkan and F. Gocer 2.5 Concluson MCDM methods are used for comparng, rankng and selectng multple alternatves wth multple crtera. When there are several alternatves avalable, MCDM can be used, snce a decson needs to be taken that s favorable over others. The HWTF selecton problem s often nfluenced by vagueness and uncertanty n practce snce DMs judgments cannot be explaned precsely n numercal values. Therefore, DMs preferences and evaluatons are very often expressed n lngustc terms. Some of researchers extend the typcal MCDM methods to the fuzzy envronment. A fuzzy MCDM s used n case of uncertanty and vagueness n DMs perceptons. A varety of dfferent MCDM/fuzzy MCDM approaches have been proposed by researchers (such as AHP, ANP, TOPSIS, ELECTRE, etc.). From lterature, t s observed that n some stuatons Fuzzy Sets can be nsuffcent for dealng wth subjectvty and ambguty whch s an unavodable aspect of human statements. IF sets, however, are useful tools to nvestgate the fuzzness n DMs judgments n the lack of knowledge or data about the problem. Ths study proposes ntegrated IF TOPSIS as a MCDM technque wth a group decson makng approach for a real case HWTF selecton problem n order to decde on the most approprate HWTF. Our approach s used to obtan the effectve rankng of HWTF alternatves. IF TOPSIS approach s a flexble and robust way for DMs to better understand a decson problem n case of uncertanty and vagueness n DMs perceptons. There are several future research drectons to follow ths study. Only ten crtera are used for ths analyss. More HWTF evaluaton crtera can be used to mprove the effectveness of the decson makng process. Also, the present approach only consders IF sets. Another promsng future work would be to consder the regular fuzzy logc and to compare the results by a senstvty analyss. Another area to be studed could be the use of other MCDM methods n ntegraton wth fuzzy or IF, AHP, TOPSIS or VIKOR, etc. n order to resolve these problems effectvely and satsfactorly. Acknowledgments The authors gratefully acknowledge the experts valuable contrbuton, whch has been vtal for the preparaton of ths study. The authors also acknowledge the fnancal support of the Galatasaray Unversty Research Fund (Project Number: ). References Abdullah, L., & Najb, L. (2014, December). Sustanable energy plannng decson usng the ntutonstc fuzzy analytc herarchy process: Choosng energy technology n Malaysa. Internatonal Journal of Sustanable Energy, Abess, O., & Saeed, M. (2014). Hazardous waste landfll stng usng GIS technque and analytcal herarchy process. Envronment Asa, 7(2),

19 2 An Intutonstc Fuzzy MCDM Approach 39 Al, M., Yadav, A., & Ans, M. (2015a). Assessment of hazardous waste management proposal: Usng the analytc herarchy process. Internatonal Journal of Economcs, Commerce and Management, III(7), Al, M., Yadav, A., Ans, M., & Sharma, P. (2015b). Multple crtera decson analyss usng Dea-TOPSIS method for hazardous waste management: A case study of the USA. Internatonal Journal of Managng Informaton Technology, 7(3), Ald, A. S. (1996). A multobjectve optmzaton model for the waste management of the petrochemcal ndustry. Appled Mathematcal Modellng, 20(12), Alon, D., Dulmn, R., & Mnnno, V. (2014). A peer IF-TOPSIS based decson support system for packagng machne selecton. Expert Systems wth Applcatons, 41(5), Atanassov, K. T. (1986). Intutonstc fuzzy sets. Fuzzy Sets and Systems, 20(1), Boran, F. E. (2011). An ntegrated ntutonstc fuzzy mult crtera decson makng method for faclty locaton selecton. Mathematcal and Computatonal Applcatons, 16(2), Boran, F. E., Boran, K., & Menlk, T. (2012). The evaluaton of renewable energy technologes for electrcty generaton n Turkey usng ntutonstc fuzzy TOPSIS. Energy Sources, Part B: Economcs, Plannng and Polcy, 7(1), Boran, F. E., Genc, S., & Akay, D. (2011). Personnel selecton based on ntutonstc fuzzy sets. Human Factors and Ergonomcs n Manufacturng, 21(5), Boran, F. E., Genç, S., Kurt, M., & Akay, D. (2009). A mult-crtera ntutonstc fuzzy group decson makng for suppler selecton wth TOPSIS method. Expert Systems wth Applcatons, 36(8), De Feo, G., & De Gs, S. (2014). Usng MCDA and GIS for hazardous waste landfll stng consderng land scarcty for waste dsposal. Waste Management, 34(11), Duan, H., Huang, Q., Wang, Q., Zhou, B., & L, J. (2008). Hazardous waste generaton and management n Chna: A revew. Journal of Hazardous Materals, 158, Genç, S., Boran, F. E., Akay, D., & Xu, Z. (2010). Interval multplcatve transtvty for consstency, mssng values and prorty weghts of nterval fuzzy preference relatons. Informaton Scences, 180(24), Gumus, A. T. (2009). Evaluaton of hazardous waste transportaton frms by usng a two step fuzzy-ahp and TOPSIS methodology. Expert Systems wth Applcatons, 36(2 PART 2), Ho, C. C. (2011). Optmal evaluaton of nfectous medcal waste dsposal companes usng the fuzzy analytc herarchy process. Waste management (New York, N.Y.), 31(7), Hsu, P.-F., Wu, C.-R., & L, Y.-T. (2008). Selecton of nfectous medcal waste dsposal frms by usng the analytc herarchy process and senstvty analyss. Waste management (New York, N.Y.), 28(8), İntepe, G., Bozdag, E., & Koc, T. (2013). The selecton of technology forecastng method usng a mult-crtera nterval-valued ntutonstc fuzzy group decson makng approach. Computers & Industral Engneerng, 65(2), Josh, D., & Kumar, S. (2016). Interval-valued ntutonstc hestant fuzzy choquet ntegral based TOPSIS method for mult-crtera group decson makng. European Journal of Operatonal Research, 248(1), Kabr, G. (2015). Selecton of hazardous ndustral waste transportaton frm usng extended VIKOR method under fuzzy envronment Golam Kabr. Internatonal Journal of Data Analyss Technques and Strateges, 7(1), Kabr, G., & Sum, R. S. (2015). Hazardous waste transportaton frm selecton usng fuzzy analytc herarchy and PROMETHEE methods. Internatonal Journal of Shppng and Transport Logstcs, 7(2), Kucukvar, M., Gumus, S., Eglmez, G., & Tatar, O. (2014). Rankng the sustanablty performance of pavements: An ntutonstc fuzzy decson makng method. Automaton n Constructon, 40, L, Y., Chu, X., Chu, D., Geng, X., & Wu, X. (2014). An ntegrated approach to evaluate module partton schemes of complex products and systems based on nterval-valued ntutonstc fuzzy sets. Internatonal Journal of Computer Integrated Manufacturng, 27(7),

20 40 G. Büyüközkan and F. Gocer Long, S., & Geng, S. (2015). Decson framework of photovoltac module selecton under nterval-valued ntutonstc fuzzy envronment. Energy Converson and Management, 106, Marnkovć, N., Vtale, K., Holcer, N. J., Dzakula, A., & Pavć, T. (2008). Management of hazardous medcal waste n Croata. Waste Management, 28(6), Orford, P. (2007). Hazardous waste A UK complance overvew. Renforced Plastcs, 51(3), Park, J. H., Park, I. Y., Kwun, Y. C., & Tan, X. (2011). Extenson of the TOPSIS method for decson makng problems under nterval-valued ntutonstc fuzzy envronment. Appled Mathematcal Modellng, 35(5), Wan, S.-P., Wang, F., & Dong, J.-Y. (2016). A novel group decson makng method wth ntutonstc fuzzy preference relatons for RFID technology selecton. Appled Soft Computng, 38(168), Wan, S.-P., Wang, F., Ln, L.-L., & Dong, J.-Y. (2015). Knowledge-based systems an ntutonstc fuzzy lnear programmng method for logstcs outsourcng provder selecton. Knowledge-Based Systems, 82, Wang, Z., L, K. W., & Xu, J. (2011). A mathematcal programmng approach to mult-attrbute decson makng wth nterval-valued ntutonstc fuzzy assessment nformaton. Expert Systems wth Applcatons, 38(10), Wang, Y., X, C., Zhang, S., Zhang, W., & Yu, D. (2015). Combned approach for government E-tenderng usng GA and TOPSIS wth ntutonstc fuzzy nformaton. PLoS ONE, 10(7), e Wu, J. (2015). A SD-IITFOWA operator and TOPSIS based approach for MAGDM problems wth ntutonstc trapezodal fuzzy numbers. Technologcal & Economc Development of Economy, 21(1), Xu, Z. (2011). Intutonstc preference modelng and nteractve decson makng. Berln: Sprnger. Xu, Z. S., & Da, Q. L. (2002). The uncertan OWA operator. Internatonal Journal of Intellgent Systems, 17(6), Yang, W., Chen, Z., & Zhang, F. (2015). New group decson makng method n ntutonstc fuzzy settng based on TOPSIS. Technologcal and Economc Development of Economy, 4913 (November), Yue, Z., & Ja, Y. (2013). An applcaton of soft computng technque n group decson makng under nterval-valued ntutonstc fuzzy envronment. Appled Soft Computng, 13(5), Zhang, X., & Xu, Z. (2015). Soft computng based on maxmzng consensus and fuzzy TOPSIS approach to nterval-valued ntutonstc fuzzy group decson makng. Appled Soft Computng, 26,

21