An Integrated Approach Based on Fuzzy Ahp and Grey Relational Analysis for Heating Source Selection

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1 An Integrated Approach Based on Fuzzy Ahp and Grey Relatonal Analyss for Heatng Source Selecton Assoc. Prof. Arzu Organ Res. Assst. Engn Yalçn Pamukkale Unversty, Busness Admnstraton, Turkey Abstract Decson makng has always been dffcult for enterprses n an extremely compettve envronment. It s one of the toughest decsons to select heatng source source. It s dffcult to take nto consderaton factors such as qualty of energy source, polluton degree of envronment, attanablty, sustanablty. Due to ths hardshp, Mult crtera decson makng method s benefcal for solvng such knd of problems. Grey relatonal analyss and fuzzy AHP are effcent methods of multple crtera decson makng. In ths paper, the best heatng source source selecton has been carred out by fuzzy AHP ntegrated grey relatonal analyss. In the phase of determnng crtera weghts s used by fuzzy AHP, whle determnng rankng of alternatves, grey relatonal analyss s used. The crtera used n ths study are ecofrendly level, cost, attanablty, calorfc value and process ablty. The alternatves used n ths study are coal, natural gas, desel and electrcty. Out comes show that Grey Relatıonal Analysıs can be used successfully n the process of solvng heatng source selecton problems Keywords: Fuzzy AHP, Grey Relatonal Analyss, Heatng Source Introducton Heatng source takes the lead both n domestc and nternatonal domans as a strategc agenda tem. Heatng source frms have reached the most valuable and turnover. It s one of the most mportant prortes to supply nonstop, relable and cheap heatng sources n globalzng world. It has become one of the most mportant decsons for frms operatng n foregn-dependent countres n terms of underground sources to select the most proper source n the producton process. Managers should take nto consderaton many crtera such as the cost of heatng source, avalablty, qualty and polluton degree of heatng source whle decdng whch alternatve s better than any other. 221

2 Decson makng has become of utmost mportance for frms n an extremely compettve envronment. The solutons of decson-makng problems have been seek for scentfc ways not for ntutve ways as a result of development n scence and technology. Decson-makng s very tough when demanded am s determned by many parameters and there are unque advantages for each alternatve. Wthn ths framework, there are many methods to overcome these hurdles (Kaya et al. 2008: 8). Decson-makng nvolves crtera and alternatves to choose. The crtera usually have dfferent mportance and the alternatves n turn dffer n our preference for them on each crteron. To make such tradeoffs and choces we need a way to measure. Measurng needs a good understandng of methods of measurement and dfferent scales of measurement (Saaty, 2004: 1). Decson analyss can be depcted as a way to propose mathematcal, statstcal and numercal methods to solve problems faced by the enterprses. Decson analyss technques can be appled to many felds n enterprses such as human source management, operaton management, fnancal management, materal purchase (Organ, 2013: 252). Multple crtera decson-makng s one of the most wdely-used branch of decson analyss. At the same tme, multple crtera decsonmakng contans methods to help evaluate many crtera, classfy and rankng of alternatves. Multple crtera decson-makng s dvded nto two as mult obectve and mult attrbute decson-makng. Wthn ths dvson, AHP, ELECTRE, PROMETHEE, TOPSIS, COPRAS and grey relatonal analyss can be set as example to mult attrbute decson-makng (Atıcı and Ulucan, 2009:164). The choce of heatng source s very crtcal for busness. There are lots of crtera and alternatves when decdng to use a heatng source for enterprses. That s why managers go through a rough perod whle decdng whch alternatve s more preferable. Ths study ams to solve ths dffcult decson by fuzzy AHP ntegrated grey relatonal analyss out of multple crtera decson-makng methods. Methodology AHP and Fuzzy AHP Analytc herarchy process (AHP) s a decson-makng model that ads n makng decsons n our complex world. It s a three part process whch ncludes dentfyng and organzng decson obectves, crtera, constrants and alternatves nto a herarchy; evaluatng parwse comparsons between the relevant elements at each level of the herarchy; and the synthess usng the soluton algorthm of the results of the parwse comparsons over all the levels. Further the algorthm result gves the relatve mportance of alternatve courses of acton (Saaty, 1988: 110). 222

3 Analytc herarchy process (AHP) has been wdely used as a useful multple crtera decson-makng (MCDM) tool or a weght estmaton technque n many areas such as selecton, evaluaton, plannng and development, decson-makng, forecastng, and so on. The tradtonal AHP requres crsp udgments. However, due to the complexty and uncertanty nvolved n real world decson problems, a decson maker (DM) may sometmes feel more confdent to provde fuzzy udgments than crsp comparsons (Wang et al., 2008: 735). There has been serous crtcsm about AHP method although t s a common method. Frstly AHP method doesn t pay attenton to avalable ambguty wth regard to decson and crtera. Ths nfluences the result substantally. There may be some changes n the rankng of alternatves when a worse alternatve s added up to problem n AHP method. Ths case reveals that the results obtaned by AHP method don t guarantee true result every tme. Trangular fuzzy numbers are used to fuzzfy pecewse comparson matrx n fuzzy AHP. Trangular fuzzy numbers are used to determne the udgments of decson makers. After obtanng fuzzy performance, the am s to get ultmate results (Organ and Kenger, 2012: 122). Fuzzy AHP method can be consdered as an advanced analytcal technque ntroduced by Saaty s AHP method to model unconstructed problems n varous felds. Tradtonal AHP methods evaluate the udgments of decson maker, fuzzness, ambguty despte ts consstency wth regard to handlng both qualtatve and quanttatve crtera. Although the am of AHP method s to reveal expert opnon tradtonal AHP methods stll don t reflect human thought style. Snce the bass of prortes n AHP s perceptonal udgments of decson maker, fuzzy AHP acqures better soluton. That s why many researchers are nterested n fuzzy extenson of AHP method, ntroduced by Saaty (Özdağoğlu, 2008: 17). In our study, we appled to fuzzy AHP whle determnng weghts. The steps of fuzzy AHP method are as follows (Hseh et al., 2004: ). Step 1. Construct parwse comparson matrces among all the crtera accordng to decson makers opnon. A = 1 a a 1 n 1 a a 1 n a 1... a 2n 1/ a a 2n = a a / a 1/ a... 1 n1 n2 1n 2n 223

4 1,3,5,7,9 crteron s relatvely more mportant compared wth crteron a = 1, = ,3,5,7, 9 crteron s less mportant compared wth crteron Decson maker used fve scaled fuzzy comparson table whle evaluatng crtera. As t can be seen n Table 1. Table 1: The Lngustc Assessment Varables and ts Correspondng Scale n Terms of Trangular Fuzzy Numbers Step 2. Fuzzy geometrc mean and fuzzy weghts of each crteron are calculated usng Equaton (1) and (2). r = ( a 1... a... a n) n (1) 1 w = r [ r... r... r ] (2) 1 n Step 3. In the last step, Center of Area (COA) method s used to calculate Best Nonfuzzy Performance value (BNP). BNP w = ( U ) ( ) w Lw Mw Lw L ; =1,2,,n (3) 3 L w, M w, U w values are trangular fuzzy numbers and respectvely represent the lower, mddle and upper values. Grey Relatonal Analyss Grey system theory was used by Deng (1982). The grey system s defned as a system of partal defnton. The grey system theory s appled to solve partal nformaton problems such as decson-makng, weather predcton and mltary affars (Lang et al, 2014: 9). The fundamental defnton of greyness s nformaton beng ncomplete or unknown, thus an element from an ncomplete message s 1 224

5 consdered to be of grey element. Grey relaton means the measurements of changng relatons between two systems or between two elements that occur n a system over tme. The analyss method, whch measures the relaton among elements based on the degree of smlarty or dfference of development trends among these elements, s called grey relaton analyss (Feng and Wang, 2000:136). In grey relatonal analyss, black means that we have no nformaton on the other hand whte means that we have nformaton. A grey system has a level of nformaton between black and whte (Sreenvasulu and Rao, 2012: 71). Some nformaton s known and some nformaton s unknown. GRA s used to convert mult-response optmzaton nto a sngle response grey relatonal analyss (Jegan et al, 2012: 4008). Grey relatonal analyss has become more and more mportant recently. There are lots of studes about ths method recently. Some of these studes are as follows: Peker and Bak (2011), appled ths method to performance measurement of nsurance sector. Özdemr and Deste (2009), appled t to automotve sector. Ecer (2013), evaluated performance of prvate banks n Turkey. Chan and Tong (2006) used ths method for materal selecton, Lu and Wevers (2007) used ths method to evaluate road traffc safety. Erden and Cevz (2015), utlzed ths method for growth ratos evaluaton. The phases of GRA are as follows (Mehregan et al, 2012: , Zha et all, 2009: , Ecer, 2013: ) : Step 1. Constructon of Decson Matrx As n all mult-crtera decson-makng problems, frstly decson matrx s constructed. Step 2. Normalzaton of Decson Matrx If the target value of orgnal sequence s expected to be maxmum, then the orgnal sequence s normalzed as follows: x( ) mn x( ) * x = (4) maxx ( ) mn x ( ) If the expectancy s that smaller values are better, the orgnal sequence should be normalzed as follows: maxx ( ) x( ) * x = (5) maxx ( ) mn x ( ) 225

6 Step 3. Constructon of Absolute Value Table The absolute value between x * 0 and x * s calculated as follows: 0 = x * ( ) * ( ) 0 x = 1,2,..,m (6) =1,2,..,m Step 4. Calculaton of Grey Relatonal Coeffcent Grey relatonal coeffcent s calculated to express the relatonshp between the deal and actual normalzed results and can be calculated as follows: mn + ξ max ɣ0()= (7) 0 ( ) + ξ max max = (8) maxmax ( ) mn = mnmn ( ) 0 (9) ξ s dstngushng or dentfcaton coeffcent.ξ s generally used as Step 5. Calculaton of Grey Relatonal Grade After gettng grey relatonal coeffcent, we take the average of grey relatonal coeffcent as the grey relatonal grade f all the crtera have equal mportance. The grey relatonal grade s calculated s as follows: n 1 Γ 0 = γ 0 ( ) =1,2,..,m (10) n = 1 However n real world, there can be dfferent weghts for the crtera. In ths case, the grey relatonal grade s calculated s as follows: where n Γ 0= γ 0 = 1 [ w( ). ( )] (11) w represents the normalzed value of attrbute. Therefore, f a comparablty sequence for an alternatve gets the hghest grey relatonal grade wth the reference sequence, t means that a partcular comparablty sequence s more mportant than the other comparablty sequences to the reference sequence t s the best alternatve to be chosen (Mehregan et al, 2012: ). 226

7 Applcaton An Integrated Approach Based On Fuzzy AHP And Grey Relatonal Analyss For Heatng Source Selecton The am of ths study s to determne the most sutable heatng source for a textle frm. As a heatng source, ths textle company has 4 dfferent alternatves. These nclude Coal, Natural Gas, Desel, and electrcty. The crtera to be taken nto account when choosng these alternatves are Cost, Attanablty, Ecofrendly, Calorfc Value and Processablty. In ths study, the best heatng source selecton for an enterprse s carred out wth AHP ntegrated Grey Relatonal Analyss. The lngustc varables used to evaluate alternatves are gven n Table 2. Table 2. The Lngustc Varables Used to Evaluate Alternatves Lngustc Varables Recprocal Scale Very Weak 1 Weak 3 Far 5 Good 7 Very Good 9 Interval Values 2,4,6,8 Data set prepared accordng to expert opnon s gven n Table 3. Table 3. Data Set Prepared Accordng to Expert Opnon MAX MİN MAX MAX MAX Eco frendly level Cost Attanablty Calorfc Value Processablty Coal Natural gas Desel Electrcty Normalzaton s carred out by Equatons (4) and (5). Normalzed decson matrx s gven n Table 4. Table 4. Normalzed Decson Matrx Eco frendly level Cost Attanablty Calorfc Value Processablty Coal ,5 Natural gas 0,75 0, ,6667 0,5 1 Desel 0, ,75 0,75 Electrcty 1 0,3333 0, After normalzaton, absolute value table s constructed by Equaton (6). Absolute value table s gven n Table

8 Ecofrendly level Table 5. Absolute Value Table Cost Attanablty Calorfc Value Processablty Coal ,5 Natural gas 0,25 0,8333 0,3333 0,5 0 Desel 0, ,25 0,25 Electrcty 0 0,6667 0, Then max and mn are obtaned as 1 and 0 respectvely. ζ s regarded as 0.5 as generally used. Grey relatonal coeffcent s calculated by Equaton (7). Grey relatonal coeffcent for each alternatve s gven n Table 6. Table 6. Grey Relatonal Coeffcent Eco Cost Attanablty Calorfc Processablty frendly level Value Coal 0,3333 0, ,5 Natural gas 0,6667 0,375 0,6 0,5 1 Desel 0,4 1 0, ,6667 0, Electrcty 1 0,4285 0,4285 0, ,33333 In the next step grey relatonal grade s calculated by usng weghts obtaned by fuzzy AHP.(The weghts used at ths stage have also been used n (Organ and Yalçın 2016:51-61) 1. Therefore weghtng steps of fuzzy AHP are gven as follows: The fuzzy parwse comparson matrx we get after expert evaluaton s gven n Table 7. Ecofrendly Cost Attanablty Calorfc level Value Ecofrendly 1,00 1,00 0,11 0,11 0,125 0,142 0,16 0,20 level 1,00 0,125 0,166 0,25 Cost 8,00 9,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 9,00 1,00 1,00 Attanablty 6,00 7,00 1,00 1,00 1,00 1,00 1,00 4,00 5,00 8,00 1,00 6,00 Calorfc 4,00 5,00 1,00 1,00 0,16 0,20 0,25 1,00 1,00 Value 6,00 1,00 1,00 Processablty 6,00 7,00 8,00 9,00 1,00 1,00 1,00 2,00 3,00 8,00 9,00 4,00 Table 7. The Fuzzy Parwse Comparson Processablty 0,125 0,142 0,166 0,11 0,11 0,12 1,00 1, ,25 0,33 0,50 1,00 1,00 1,00 1 Organ A. and Yalçın E. (2016). The Energy Source Selecton By Fuzzy Moora And Fuzzy AHP Method In A Textle Frm. In Arslan H. and Içbay M. (Ed.), Contemporary Approaches In Humantes, (pp.51-61), Frankfurt, Peter Lang Edton. 228

9 Fuzzy weghts are obtaned for each crtera usng Equaton (1). r 1 = (0,1940, 0,2135, 0,2437) r 2 = (0,974, 0,997, 1,015) r 3 = (1,888, 2,036, 2,168) r 4 = (0,693, 0,801, 0,944) r 5 = (2,491, 2,852, 3,103) Crtera weghts are calculated by usng Equaton (2). W 1 = (0,0259, 0,0309, 0,0390) W 2 = (0,1303, 0,1446, 0,1627) W = (0,2525, 0,2950, 0,3475) 3 W = (0.0927, 0,1160, 0,1512) 4 W 5 = (0,3326, 0,4133, 0,4972) Best non-fuzzy performance values are obtaned from defuzzfyng fuzzy crtera weghts wth Center of Area (COA) method by usng Equaton (3). BNP w1 = 0,0320 BNP w2 = 0,1459 BNP w3 = 0,2984 BNP w4 = 0,1200 BNP w5 = 0,4146 In the next step grey relatonal grade s calculated by usng weghts obtaned by fuzzy AHP. Grey relatonal grade s obtaned by Equaton (10) and grey relatonal grade and rankng of alternatves are gven n Table 8. Table 8. Grey Relatonal Grade and Rankng of Alternatves Eco Cost Attanablty Calorfc Processablty Γ Rankng frendly Value level Coal Natural gas Desel Electrcty Accordng to rankng of alternatves, t s obtaned that natural gas s frst alternatve, coal s the second, desel s the thrd alternatve, electrcty s the last alternatve. 229

10 Concluson Grey relatonal analyss has become more and more popular recently. Grey relatonal analyss reveals better results compared wth other statstcal methods. It also seems more proper compared wth other multple crtera decson-makng methods as t s easy to use. Accordng to results of the study, natural gas s the best alternatve for enterprse to use. Its eco-frendly level, affordablty, attanablty and processablty enable t to take the lead. After natural gas, coal seems to be second sutable heatng source for ths enterprse. When we glmpse at the features of coal, t can be preferable due to beng very affordable and attanable despte ts low eco-frendly level. Desel s the thrd alternatve the enterprse can select. Desel doesn t seem wse for enterprse as t s costly and low eco-frendly. Electrcty takes the last rank among alternatves. Despte ts hgh eco-frendly level, t doesn t seem logcal to use due to ts low calorfc value and processablty. References: Atc, K.B., and Ulucan, A. (2009). Mult Crtera Decson Analyss Approaches In Energy Proects Evaluaton Process and Turkey Applcatons Hacettepe Unversty, Journal Of Economcs And Admnstratve Scences, Vol:27, pp Chan J., and Tong T. (2006) Mult-crtera Materal Selectons and End-of- Lfe Product Strategy: Grey Relatonal Analyss Approach, Materals & Desgn, Vol: 28, No: 5, pp Feng, Cheng-Mn, and Wang, Rong-Tsu (2000). Performance Evaluaton For Arlnes Includng The Consderaton Of Fnancal Ratos, Journal Of Ar Transport Management 6, pp Ecer, F.(2013). Türkye dek Özel Bankaların Fnansal Performanslarının Karşılaştırılması: Dönem AİBÜ Sosyal Blmler Ensttüsü Dergs, Vol: 13, Issue: 2, pp Erden, C., and Cevz E. (2015). Gr Sstem Teors Kullanılarak Türkye nn Büyüme Oranı Faktörlernn Analz, SAÜ Fen Bl. Dergs, Vol: 19, Issue: 3, pp Hseh, T. Y., Lu, S. T., and Tzeng, G. H. (2004). Fuzzy MCDM Approach for Plannng and Desgn Tenders Selecton n Publc Offce Buldngs. Internatonal Journal of Proect Management, Vol: 22 (7), pp Jegan, T. C., Anand, M. D., and Ravndran, D. (2012). Determnaton of Electro Dscharge Machnng Parameters n AISI202 Stanless Steel Usng Grey Relatonal Analyss. Proceda Engneerng, Vol: 38, pp

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