Vehicle selection for public transportation using an ... - Semantic Scholar

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Journal of Intelligent & Fuzzy Systems 26 (2014) 2467–2481 DOI:10.3233/IFS-130917 IOS Press

Vehicle selection for public transportation using an integrated multi criteria decision making approach: A case of Ankara Serhat Aydına,b,∗ and Cengiz Kahramana,b a Aeronautics b Industrial

and Space Technologies Institute, Turkish Air Force Academy Yesilyurt, Bakirkoy, Istanbul, Turkey Engineering Department, Istanbul Technical University Macka, Besiktas, Turkey

Abstract. In this paper, we consider the problem of bus selection for public transportation using a hybrid multicriteria decision making approach. The problem includes several conflicting factors which are economic, social, and technological factors. The integrated approach brings the flexibility of fuzzy AHP and simplicity of fuzzy VIKOR methodology together. To demonstrate the applicability of the methodology, a case study for Ankara, the capital city of Turkey, is given. A four levels hierarchy is established, and three experts are utilized for assessing the pairwise comparison matrices. The weights of the criteria are determined by fuzzy AHP and then the alternatives are ranked by fuzzy VIKOR. A sensitivity analysis is also made to see how sensitive our decision to the changes in parameters of methodology is. Buckley’s fuzzy approach is finally implemented to problem and the obtained results are compared. Keywords: Multicriteria, vehicle selection, AHP, VIKOR, fuzzy

1. Introduction In the last two decades of 20th century, there has been growing concern about pollution in many countries and in particular about the effects of transportation sources to this problem [1]. The possible decline of oil supplies in the future is forcing countries to consider alternative energy sources. Owing to quickly consumption of fossil fuels by human being, their increasing costs, and the impact of the CO2 emissions on the climate, the design of highly efficient energy supply systems and using alternative energy sources is essential for sustainable energy supply in the future [2]. There is unprecedented concern about fuel prices and oil depletion. There is also high level of concern about global warming and how to respond it. As a result of these concerns many ∗ Corresponding author. Serhat Aydın. Tel.: +90 533 4697187; E-mail: [email protected].

countries are attempting to find solutions for decreasing energy resources and its effects [3]. Recently, most modern automobiles run on petroleum based liquid fuels like gasoline and diesel which are in limited supply. These fuels cause high levels of air pollution and affect climate change and global warning significantly. These factors contribute to a shift towards alternative energy sources for automobiles [4]. Gasoline-electric hybrid vehicles, flex fuel/E85 vehicles, natural gas vehicles, clean diesel and biodiesel vehicles are some options of the Alternative Fuel Vehicles (AFVs). Multicriteria decision making (MCDM) refers to screening, prioritizing, ranking, or selecting a set of alternatives under usually independent, incommensurate, or conflicting criteria [5]. MCDM includes both multiattribute decision making (MADM) and multiobjective decision making (MODM) problems. MADM refers to making preference decision among the

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S. Aydın and C. Kahraman / Vehicle selection for public transportation using an integrated MCDM approach

available alternatives that are characterized by multiple and conflicting attributes [6]. Since selecting the best AFV needs both tangible and intangible criteria to be used at the same time, it is regarded as a MCDM problem. There are many methods to overcome MCDM problems; Analytic Network Process (ANP), Analytic Hierarchy Process (AHP),Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Vise Kriterijumska OptimizacijaI Kompromisno (VIKOR), Elemination and Choice Translating Reality English (ELECTRE), Preference Ranking Organisation Method for Enrichment Evaluations (PROMETHEE), Multiattribute Utility Analysis (MAUT), etc. In many MCDM problems, precise data are not available and difficult to be exposed. So, experts need natural language expression rather than crisp numerical values in the evaluation. To deal with the uncertainty, the fuzzy set theory was developed to overcome vagueness in human thoughts and perceptions. The fuzzy set theory was developed by Zadeh [7] and it is widely used in MCDM problems because of its ability to quantify the subjectivity in human judgments. AHP is an analytical method which can be applied to problems having multiple alternatives and multiple criteria. AHP doesn’t require complex mathematical operations. It is based on developing synthesized pairwise comparison matrix and identifying priority vector. AHP uses integers in computing importance scale; however, real-world problems involve substantial vagueness and uncertainty, which necessitates using fuzzy numbers. Therefore, AHP and the fuzzy set theory are combined and transformed into an integrated model called fuzzy AHP. There have been lots of fuzzy AHP methods used in the literature. The first study on fuzzy AHP was performed by Laarhoven and Pedrycz [8] and fuzzy scores were defined by triangular membership functions. Buckley [9] determined fuzzy scores by trapezoidal membership functions and Buckley criticized Laarhoven and Pedryzs’ method in many ways. Chang [10] brought forward the extent analysis method based on the utilization of triangular fuzzy numbers for pair-wise comparisons. Zeng et al. [11] developed a modified fuzzy AHP for the project risk assessment. We preferred Zeng et al.’s [11] method to other modified AHP methods due to its ability to handle experts knowledge, judgments, historical data about alternatives. Kahraman et al. [12] compared renewable energy alternatives by using Zeng et al.’s method. Aydın and Kahraman [13] used this method to determine the best supplier for a firm.

VIKOR methodology was developed to solve MCDM problems with conflicting and non-commensurable criteria. Opricovic and Tzeng [16] developed VIKOR, the Serbian name: Vlse Kriterijumska Optimizacija I Kompromisno Resenje, which means multi-criteria optimization and compromise solution. VIKOR has a simple computation procedure that allows simultaneous consideration of the closeness to ideal and the anti-ideal alternatives [14]. Opricovic and Tzeng [17] made a comparison of VIKOR with PROMETHEE, ELECTRE and TOPSIS approaches. Tzeng et al. [15] used VIKOR and TOPSIS to determine the best compromise solution among alternative fuel modes. Kaya and Kahraman [18] used fuzzy VIKOR and AHP approach to determine the best renewable energy alternative for Istanbul. The motivation behind our study is the need for the multicriteria selection of bus alternatives, which will be bought among many brands and models by Ankara municipality. The aim of the study is to determine the best fuel bus alternative for Ankara Municipality by using an integrated fuzzy AHP-VIKOR methodology and to provide a perspective for the advantages of using alternative fuel buses for Ankara. In the methodology, the weights of the criteria were determined by Zeng et al.’s [11] fuzzy AHP and the best alternative fuel bus was selected by fuzzy VIKOR. To the best of our knowledge, this integrated methodology is first time used for the solution of AFV selection problem. We used a fuzzy AHP methodology developed by Zeng et al.’s [11] methodology because of its ability to handle experts knowledge, judgments, and historical data. The methodology uses an evaluation scale including linguistic expressions, crisp numerical values, and fuzzy numbers and range numerical values. This scale provides a more flexible evaluation compared with the other fuzzy AHP methods. The consistency of the fuzzy pairwise comparison matrices is a problem which is not considered in most of the fuzzy AHP studies. In our study we first defuzzified the fuzzy pairwise comparison matrices and then calculated the crisp consistency ratios (CR). When an inconsistent matrix (CR < 0.10) was produced, it was reevaluated until a consistent matrix was obtained. In the second step fuzzy VIKOR was applied to the problem because the methodology has a simple computation procedure that allows simultaneous consideration of the closeness to ideal and anti-ideal solutions. VIKOR provides a maximum group utility of the majority, and a minimum of the individual regret of the opponent. The integrated fuzzy AHP & VIKOR methodology has been applied to many problems in the literature by

S. Aydın and C. Kahraman / Vehicle selection for public transportation using an integrated MCDM approach

now. Our study is different from the previous studies since Zeng et al.’s fuzzy AHP and VIKOR were not been integrated before and it has not been applied to the vehicle selection problem by now. We also handle the same problem integrating Buckley’s fuzzy AHP & fuzzy VIKOR. The rest of the paper is organized as follows. In Section 2, a literature review is given. In Section 3, the proposed model is explained. A numerical illustration is presented in Section 4. In section 5, a sensitivity analysis is given. In section 6, Buckley’s fuzzy AHP is implemented to problem. Finally, conclusions are presented in Section 6.

2. Literature review Recently many studies have focused on the market analysis of AFVs and its advantages of usage. Bunch et al. [19] investigated potential demand for alternative fuel vehicles in California. Kurani et al. [20] framed electric vehicles purchase decision in terms of a household’s entire stock of vehicles, car purchase behavior and travel behavior. Brownstone et al. [21] designed a micro-simulation demand forecasting system to produce annual forecast of new and used vehicles demand by vehicle type and geographic area. Jeremy and Richard [22] proposed a life cycle model for performing level-playing field comparisons of emissions, cost, and energy efficiency trade-offs of AFVs through the fuel production chain and over a vehicle lifetime. Nessbitt and Sperling [23] examined seven widely accepted hypotheses regarding the potential fleet market for AFVs. Dagsvik et al. [24] analyzed the potential demand for AFVs by using random utility model. Morita [25] researched development of AFVs and their power source in 21st century. Johnsson and Ahman [2, 6] compared environmental impact of AFVs. Winebrake and Creswick [27] evaluated the future of hydrogen fuelling vehicles for transportation. They utilized scenario analysis to build their evaluation model. Mourato et al. [28] studied drivers’ preferences for fuel cell taxis and showed that the willingness to participate in a pilot project seems to be driven mostly by drivers’ expectations by using regression method. O’Garra et al. [29] investigated the determinants of knowledge and acceptability of hydrogen vehicles among London resident. Janssen et al. [30] used balanced scorecard approach to identify difficulties and chances in the market penetration process of natural gas cars. Ahn et al. [31] enabled Bayesian approach to analyze impact of

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adding AFVs to the market. Heinz and Erdmann carried out a study of public attitudes through brief face to face interviews and an online survey to university students which revealed an overall support for hydrogen technologies vehicles. Heffner et al. [32] offered an approach for the adaption of fuel cell cars. They argued fuel cell cars’ functional, economic and environmental benefits that attract new buyers. Ma et al. [33] combined of AHP and logit regression model for market forecasting model for AFVs. Erdem et al. [34] used a web-based survey to determine the consumers’ willingness to pay a premium for hybrid automobiles in Turkey. Maria et al. [35] put forward public attitudes toward and demand for AFVs and their paper gave an overview of various conceptual frameworks. Mabit and Fosgerau [36] investigated the potential future of AFVs in Denmark. Behnam et al. [37] considered the problem of alternative-fuel buses selection using two novel fuzzy multiple criteria decision-making methods. Zhang et al. [38] analyzed consumer awareness towards electric vehicle and examined the factors that are the most likely to affect consumers’ choice for electric vehicle in China.

3. An integrated fuzzy AHP & VIKOR methodology There have been lots of fuzzy AHP methods used in the literature. In this paper, the modified fuzzy AHP method proposed by Zeng et al. [11] will be used. In the following, the steps of the method are given: Step 1. Compare the factors using pairwise comparisons: The members in the assessment group need to compare the criteria in the hierarchical structure using pairwise comparisons. Step 2. Convert the preferences into Symetrical Trapezoidal Fuzzy Numbers (STFNs): STFNs are employed to convert experts’ judgments into a universal format for the composition of group preferences. These expressions are described below [39]: • A crisp number “x” is converted to a STFN as ˜ = (x, x, x, x), (ie., a = b = c = d = x), A • A linguistic term, “about x”, is converted to a ˜ = (x − 1, x, x, x + 1), (ie. a = STFN as A x − 1, b = c = x, d = x + 1), • A range, the scale is likely between (x, y), is ˜ = (x, x, y, y), converted to a STFN as A (ie., a = b = x, c = d = y),

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• A triangular fuzzy number, T˜ = (x, y, z), ˜ = (x, y, y, z), is converted to a STFN as A (ie. a = x, b = c = y, d = z), • If a decision maker cannot compare any two ˜ = factors at all, then it is represented with A (0, 0, 0, 0), (ie. a = b = c = d = 0). Step 3. Aggregate individual STFNs into group STFNs: In Step 3, we have individual experts’ evaluations which are represented by STFNs. Then we must convert individual ones to group assessment. To calculate the aggregation of the comparisons of the attributes, Equation (1) is used. a˜ ij = a˜ ij1 ⊗ c1 ⊕ a˜ ij2 ⊗ c2 ⊕ .... ⊕ a˜ ijm ⊗ cm (1) where a˜ ij is the aggregated fuzzy score of attribute I when compared to attribute j for i, j = 1, 2, . . . , n; a˜ ij1 , a˜ ij2 , . . . , a˜ ijm are the corresponding STFN scores of attribute i comparing to attribute j measured by experts E1 , E2 , . . . , Em , respectively. Step 4. Defuzzify the aggregated STFN score: The aim of this step is to convert the aggregated STFN score to crisp values. To
perform this step  Equation (2) is used. a˜ ij = aija , aijb , aijc , aijd represents an aggregated STFN, where aij represents a crisp value. 
aija + 2 aijb + aijc + aijd aij = (2) 6 Step 5. Calculate the priority weights of factors: In order to calculate priority weights of the attributes, a pairwise comparison matrix which is composed of aij values is used. Assuming A1 , A2 , . . . , An represent a set of attributes in one group, pairwise comparisons between Ai and Aj yield an n×n matrix defined by Equation (3). A1 1  1 A = aij = A2 a12 A3 . . .  An 1 a1n A1

A2 . . . An a12 . . . a1n 1

. . . a2n

. . . . . . . . . i, j = 1, 2, . . . , n  1 a2n . . . 1 (3)  where aij = 1 and aji = 1 aij

Table 1 Fuzzy Evaluation Scores for the Alternatives Linguistic terms

Fuzzy score

Very poor (VP) Poor (P) Medium poor (MP) Fair (F) Medium good (MG) Good (G) Very good (VG)

(0, 0, 1) (0, 1, 3) (1, 3, 5) (3, 5, 7) (5, 7, 9) (7, 9, 10) (9, 10, 10)

After obtaining the pairwise comparisons matrix, the priority weights of factors can be calculated by using the arithmetic averaging method. 1 n aij n wi = i, j = 1, 2, . . . , n. (4) j=1 n k=1 akj where wi is the section weight of Ai . Assuming that Ai has t upper sections at different (i) level in the hierarchy, and wsection is the section weight of the ith upper section which contains Ai in the hierarchy, the final weight wi of Ai can be derived by wi = wi ×

t 

w(i) group

(5)

i=1

After obtaining the weight vector via Zeng et al.’s methodology, we continue implementing the steps of VIKOR. The methodology simply works on the principle that each alternative can be evaluated by each criterion function; the compromise ranking will be presented by comparing the degree of closeness to the ideal alternative. First of all, experts identify the objective of the decision making process and define the problem scope in VIKOR methodology. And then a finite set of relevant attributes are defined. All criteria, sub-criteria and alternatives are determined and a hierarchical form called “value tree” is structured. And then appropriate linguistic variables are identified [13]. Table 1 gives the linguistic scale for evaluation of alternatives. Triangular fuzzy numbers are preferred in our study because humans often prefer expressing their vague estimates as “around a value”. Assuming that a decision group has K people, the ratings of alternatives with respect to each criterion can be calculated as:  1  1 x˜ ij = (6) x˜ ij (+) x˜ ij2 (+) . . . (+) x˜ ijK K where x˜ ijK is the rating of the K th decision maker for ith alternative with respect to jth criterion

S. Aydın and C. Kahraman / Vehicle selection for public transportation using an integrated MCDM approach

After obtaining the weights of criteria and fuzzy ratings of alternatives with respect to each criterion, we can now express the fuzzy multi-criteria decision-making problem in matrix format as, ⎤ ⎡ x˜ 11 x˜ 12 · · · x˜ 1n ⎥ ⎢ · · · x˜ 2n ⎥ ⎢ x˜ 21 ⎥ ⎢ ˜ (7) D=⎢ . .. .. ⎥ ⎥ ⎢ .. . · · · . ⎦ ⎣ x˜ m1 x˜ m2 · · · x˜ mn W = [w1 , w2 , . . . , wn ] , j = 1, 2, . . . , n where x˜ ij is the rating of the alternative Ai with respect to criterion j (i.e. Cj ) and wj denotes the importance weight of Cj . Next step is to defuzzify the fuzzy decision matrix and convert the fuzzy weight of each criterion into crisp

˜ i = v(S˜ i − S˜ ∗ )/( S˜ − − S˜ ∗ ) + (1 − v) Q ˜ ∗ )/(R ˜i −R ˜− −R ˜ ∗) (R

c1 + 4c2 + c3 (8) 6 Next step is to determine the fuzzy best value (FBV, f˜ j∗ ) and fuzzy worst value (FWV, f˜ j− ) of all criterion functions. ∼

P(C) = C =

f˜ j∗ = max x˜ ij , j ∈ B; f˜ j− = min x˜ ij , j ∈ C i

i

(9)

where the ith function represents a benefit f˜ j∗ = min x˜ ij , j ∈ B; f˜ j− = max x˜ ij , j ∈ C i

i

(10)

where the ith function represents a cost ˜ j (f˜ j∗ − x˜ ij )/(f˜ j∗ − Then, the values w − ˜ i are computed in order to obtain: f˜ j ), S˜ i and R S˜ i =

n 

˜ j (f˜ j∗ − x˜ ij )/(f˜ j∗ − f˜ j− ) w

(14)

˜ i are related to a maximum The indices min S˜ i and min R i

i

majority rule, and a minimum individual regret of an opponent strategy, respectively. “v” is introduced as the weight of the strategy of the maximum group utility, usually “v” is assumed to be 0.5. Then rank the alternatives by sorting the values S, R, and Q in decreasing order. The results are three ranking lists. Propose as a compromise solution the alternative (a ), which is ranked the best by the measure Q (minimum) if the following two conditions are satisfied: C1. “Acceptable advantage” Q(a ) − Q(a ) ≥ DQ

∼

values. A fuzzy number C = (c1 , c2 , c3 ) can be transformed into a crisp number by employing the below equation [31].

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(15)



where a is the alternative with second position in the ranking list by Q; DQ = 1/(j−1); and “j” represents the number of alternatives. C2. “Acceptable stability in decision making” Alternative a must also be the best ranked by S or/and R. This compromise solution is stable within a decision making process, which could be: “voting by majority rule” (when v > 0.5 is needed), “by consensus” v = 0.5, or “with vote” (v < 0.5). Here, “v” is the weight of the decision making strategy “the majority of criteria” (or “the maximum group utility”) If one of the conditions is not satisfied, then a set of compromise solutions is proposed, which consist of: Alternative a and a if only condition C2 is not satisfied, or alternative a , a , . . . . . . , a(n) if condition C1 is not satisfied; and a(n) is determined by the relation Q(a(n) − Q(a )) < DQ for maximum n (the position of these alternatives are “in closeness”)

(11)

j=1

4. Case study ˜ i = max[w ˜ j (f˜ j∗ − x˜ ij )/(f˜ j∗ − f˜ j− )] R j

(12)

where S˜ i refers to the separation measure of Ai from ˜ i to the separation measure the fuzzy best value, and R of Ai from the fuzzy worst value. ˜ i values are ˜ ∗, R ˜ − and Q In the next step, S˜ ∗ , S˜ − , R calculated: S˜ ∗ = min S˜ i , S˜ − = max S˜ i i

˜∗

i

˜−

˜ i , R = max R ˜i R = min R i

i

(13)

Public transportation activity is one of the most powerful indicators of economic development and human prosperity. Bus transportation plays a major role in the provision of the public transport. Bus is a very efficient mode of transport, which is cheap, flexible and, in many cases, tailored to the needs of users both in terms of capacity and speed. From an economic, environmental and social point of view, bus still remains the most universal solution for a balanced and sustainable urban development [40].

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S. Aydın and C. Kahraman / Vehicle selection for public transportation using an integrated MCDM approach Table 2 The distribution of the brand and models of buses [41]

Brand BMC (Diesel) Man SL (Diesel)

Man (Diesel) Man with CNG Man with CNG Man with CNG and air-conditioned Man with CNG and air-conditioned Man with CNG and air-conditioned Man with bellow (Diesel) Mercedes (Diesel)

Mercedes with bellow (Diesel) Ikarus (Diesel) Ikarus with bellow (Diesel) Total

Model

Number of vehicle

1994 1987 1988 1995 2006 2007 2008 2009 2010 2011 1994 1987 1988 1999 1999 1992 1993 1991

2 3 4 5 70 400 90 350 210 40 50 11 15 197 70 162 75 36 1,790

In this study we research the most reasonable alternative fuel bus for public transportation in Ankara. Especially, with using Liquefied petroleum gas (LPG) in 1995, AFVs have been taken into consideration in Turkey. Today, about 3 million LPG vehicles are used and 8 million LPG filling stations services in Turkey. In parallel with developing technology, many different AFVs are used in the world. Ankara is the capital of Turkey, and it is the most populous second city in Turkey, and the most populous thirty-eighth city in the world. Elektrik Gaz Otob¨us (EGO) executes public transportation service in the name of the municipality. EGO has 1790 vehicles for public transportation. 1090 vehicles of 1790 are Compressed Natural Gas (CNG) buses, which are used first in 1990 in Ankara. The CNG buses are produced under the name of Lion’s Classic CNG in C¸ubuk in Man Factory. The buses have MAN E 2876 LUH02 welltype six-cylinder, Enhanced Environmentally Friendly Vehicle natural gas engines, 310 horsepower maximum power, with a cylinder capacity 12,186 cubic centimeters. The buses have four natural gas tanks with 1294 liter capacity. Exhaust emissions of CNG buses are 20 times less than Euro 3 diesel engine. Table 2 shows the distribution of the brand and models of vehicles’ park in the bus in EGO. And Table 3 shows statistical information about bus public transportation in Ankara in March. In this study, a four levels hierarchy composed of three main criteria, 17 sub-criteria, and nine alternatives was established. Figure 1 illustrates the hierarchy. The criteria were initially developed based on a litera-

Table 3 Statistical information about bus public transportation in Ankara in March [41] Statement Time per vehicle per day Passengers per vehicle per day Of fuel per vehicle per day (Lt) Of fuel per vehicle per day (m3 ) The monthly total diesel fuel (Lt) The monthly total gasoline fuel (Lt) The monthly total natural gas l (m3 ) Average daily number of passengers The monthly total number of passengers

Numerical value 7.0 447 115 187 1,363,346 1,957 5,392,674 587,483 18,211,964

ture review, and shown in Table 4. For the assessment of criteria three experts who are one from the faculty members, one from the bus manufacturing engineers and one from the bus operators were assigned. These experts were selected to become representatives of the different areas, having different points of view to the problem. Different weights were assigned to three decision makers according to their experiences and knowledge on alternative fuel vehicles. The weights were 0.4, 0.3, and 0.3, and these weights were used in fuzzy AHP methodology. We evaluated nine alternative fuel buses for public transportation. The definitions of the buses are as follows; Compressed Natural Gas Buses (CNG) (A1 ): Compressed Natural Gas Buses are fueled with compressed natural gas (CNG) or liquefied natural gas (LNG).Natural gas buses use internal combustion engines that have been modified to use methane rather than gasoline as fuel. Compared with buses fueled with conventional diesel and gasoline, CNG buses can produce significantly lower amounts of harmful emissions. In addition, some natural gas vehicle owners report service lives two to three years longer than gasoline or diesel vehicles and extended time between required maintenance. The driving range of CNG buses generally is less than that of comparable gasoline- and diesel-fueled vehicles because of the lower energy content of natural gas [42, 43]. Electric Buses(A2 ): Electric vehicles produce no tailpipe emission and the miniscule amounts of “evaporative emission” they produce come from the evaporation of their lubricants. The bus’s batteries must be recharged from the “electrical grid” which in practice means a power hook-up at home, office, etc. Many electric buses also use “regenerative braking”, a procedure that generates electricity when the car is slowing down. The key advantage of an electric motor is its

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Fig. 1. The hierarchy for selection among the alternative fuel buses Table 4 Definition of Criteria Main criteria

Sub criteria

Definition of criteria

Type of criteria

Economic

Initial cost (C1 ) Maintenance cost (C2 ) Vehicle life (C3 ) Range (C4 ) Fuel cost (C5 ) Energy efficient (C6 ) Fuel Availability (C7 ) Air Pollution (C8 )

This criterion refers to the purchase price. This criterion is the sum of maintenance cost and repair cost. Longer life cycle for reduced waste and materials used. How far the reference bus could operate on a full tank. Cost of one liter fuel. This criterion represents the efficiency of fuel energy. This criterion evaluates the national and international sources of fuel. This criterion refers to the extent a fuel mode contributes to air pollution, since vehicles with diverse modes of fuel impact on air differently. This criterion refers to the noise produced during the operation of the bus. Reduction of emission to air, water, and land lifecycle. Reduction of luxury item or unrecyclable material to minimize impact on the environment. This criterion is presented as the number of seconds the vehicle would use to accelerate from 0 to 100 km/h. Safety is the study and practice of design, construction, equipment and regulation to minimize the occurrence and consequences of bus accidents. This criterion refers to the particular issue regarding sense of comfort, and the fact that users tend to pay attention to the accessories of the bus. Maximum passengers by sitting and standing in bus. User acceptance with ergonomic design and new usage patterns of bus.

Cost Cost Benefit Benefit Benefit Cost Benefit Cost

Social

Noise Pollution (C9 ) Reduce emission (C10 ) Dematerialization (C11 ) Technology

Performance (C12 ) Safety (C13 ) Sense of Comfort (C14 ) Vehicle Capacity (C15 ) User Acceptance (C16 )

ability to provide power and torque at almost any engine speed. Electric motors provide nearly peak power even at very low revolutions per minute, and this gives electric vehicles strong acceleration performance from a stop [42]. Plug-in Hybrid Electric Buses (A3 ): Plug-in hybrid electric buses (PHEBs) are powered by conventional or alternative fuels and by electrical energy stored in a battery. Using electricity from the grid to run the vehicle some of the time costs less and reduces petroleum con-

Cost Benefit Benefit Benefit Benefit Benefit Benefit Benefit

sumption compared with conventional vehicles. PHEBs might also reduce emissions, depending on the electricity source [43]. Hybrid Electric Buses with Diesel Engine (A4 ): The electric-diesel bus has an electric motor and small-sized diesel engine as its major sources of power. When electric power fails, the diesel engine can take over and continue the trip, while the kinetic energy rendered during the drive will be turned into electric power to increase the buses’ cruising distance [37].

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Propane Buses (A5 ): Liquefied petroleum gas (LPG), commonly called propane, is a mixture of at least 90 percent propane, 2.5 percent butane and higher hydrocarbons, and ethane and propylene make up the remaining balance. It is a byproduct of natural gas processing and/or petroleum refining. A propane-powered bus cannot run as far on a tank of gas as a comparable gasoline-powered bus, but propane generates lower vehicle emission. Propane emits 64 percent less reactive organic compounds, 20 percent less nitrogen oxide, and 20 percent less carbon monoxide than similar gasoline buses [44]. Biodiesel Buses (A6 ): Biodiesel buses work with diesel fuels. Any bus with a diesel engine can run on biodiesel. Biodiesel refers to diesel fuels that are derived from biological sources such as plants and animals instead of petroleum. Biodiesel physical properties are similar to conventional diesel, but it is a cleaner-burning alternative. Using biodiesel in place of petroleum diesel reduces emission [42, 43]. Flexible Fuel Buses (A7 ): Flexible fuel buses (FFBs) have an internal combustion engine and are capable of operating on gasoline, E85 (a gasoline-ethanol blend containing 51% to 83% ethanol, depending on geography and season), or a mixture of the two. FFBs are different from conventional gasoline buses because they have to accommodate the unique fuel properties of ethanol. Converting a conventional gasoline bus to a flex fuel vehicle requires extensive modifications throughout the fuel system and electronic engine-control system. FFBs qualify for AFV tax credits and can provide emissions benefits [43]. Fuel Cell Buses (A8 ):The so-called fuel cell battery transform hydrogen and oxygen into power for buses. Hydrogen is not suitable for onboard storage. The research on a fuel cell-hydrogen bus has already been concluded with success, and test results with the experimental bus operating on hydrogen fuel indicate that this bus has a board surface in the burning chamber, low burning temperature, and the fuel is easily inflammable. Daimler-Benz company has already developed a prototype vehicle with a fuel cell. To date, the only vehicles offered for sale with fuel cell technology is the Zevco London taxi which was launched in London in July 1998. Due to the fact that the energy to operate this vehicle comes from the chemical reaction between hydrogen and oxygen, no detrimental substance is produced and only pure water, in the form of air, is emitted. A fully loaded fuel tank can last as far as 250 kilometers [1].

Fig. 2. Membership functions for linguistic evaluation. VL: Very Large, VP: Very Poor, L: Large, P: Poor, M: Medium, F: Fair, H: High, G: Good, VH: Very High, VG: Very Good.

Conventional Diesel Buses (A9 ): The diesel technology can reduce fuel consumption by 30 to 60 percent in some automobile models. The key benefit of the diesel process is its high efficiency. By using a much higher compression ratio than a conventional gasoline engine, the diesel engine is able to extract more power from the same amount of fuel. In addition, diesel fuel is typically more power-laden than gasoline [42]. After determining the evaluation criteria, the alternatives, the decision makers’ weight, the hybrid approach was implemented. Experts evaluated each criterion of the hierarchy. A score system is shown in Fig. 2. The first step was nor implemented, because this step was executed in VIKOR section. Subsequently, the pairwise comparisons were calculated. The pairwise comparisons of the main criteria are shown in Table 5. For example, the STFN of the pairwise comparison between “Economic” and “Social” was obtained as follows; a˜ 12 = (7, 7, 9, 9) ⊗ 0.40 ⊕ (5, 5, 5, 5) ⊗ 0.30 ⊕ (6, 6, 6, 6) ⊗ 0.30 a˜ 12 = (6.10, 6.10, 6.90, 6.90) Later, STFNs were converted to crisp values by using Equation (2). The STFN of the pairwise comparison between “Economic” and “Social” was defuzzified as follows. 6.10 + 2 (6.10 + 6.90) + 6.90 6 = 6.50

a12 = a12

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Table 5 Fuzzy weight of main criterion Economic Experts Economic

Social

Technology

Scale

E1 E2 E3 Aggregation E1 E2 E3 Aggregation E1 E2 E3 Aggregation

STFN

Social Scale 7.00 5.00

1.00

9.00 5.00 6.00

Technology

STFN

Scale

(7, 7, 9, 9) (5, 5, 5, 5) (6, 6, 6, 6) (6.1, 6.1, 6.9, 6.9)

3.00 A

3.00 5.00 3.00

1/3 1/5 1/5

1/3 1/3 1/3

1.00

STFN (3, 3, 3, 3) (4, 5, 5, 6) (3, 3, 3, 3) (3.3, 3.6, 3.6, 3.9) (1/3, 1/3, 1/3, 1/3) (1/5, 1/5, 1/3, 1/3) (1/5, 1/5, 1/3, 1/3) (0.22, 0.22, 0.33, 0.33)

1.00

After obtaining crisp values of attributes, pair-wise matrices were established by using Equation (3). For example the pairwise comparison matrix of main criteria is given below. ⎡

⎤ 1 6.50 3.6 ⎢ ⎥ Amain criteria = ⎣ 0.15 1 0.27 ⎦ 0.27 3.59 1 After establishing the pairwise comparison matrix, arithmetic averaging method was used to calculate the priority weights of the criteria. For example the priority weights of main criteria were calculated by using Equation (4) as follows: WEconomic = 0.67 WSocial = 0.08 WTechno log y = 0.24 The other weights of criteria were calculated by Zeng et al.’s modified fuzzy AHP model. Next step is the determination of the best AFV with fuzzy VIKOR. First, three experts evaluated the alternatives with respect to each criterion by using Table 1. Evaluation results are given in Table 6. The linguistic evaluations shown in Table 6 were converted into fuzzy numbers. Then aggregated fuzzy rating of alternatives was calculated to construct the fuzzy decision matrix and determine the fuzzy weight of each criterion. Then, using Equation (8), the crisp values for decision matrix were computed, and weight of each criterion was computed by Fuzzy AHP as shown in Table 7. By using Equation (9) and Equation (10) the best and the worst values of all criterion rating were determined as follows:

f1∗ = 0.11 f2∗ = 0.35 f3∗ = 0.75 f4∗ = 0.89 f5∗ = 0.93 ∗ f6∗ = 0.40 f7∗ = 0.89 f8∗ = 0.16 f9∗ = 0.20 f10 = 0.93

f1− = 0.75 f2∗ = 0.80 f3∗ = 0.40 f4∗ = 0.16 f5∗ = 0.35 ∗ f6∗ = 0.93 f7∗ = 0.45 f8∗ = 0.93 f9∗ = 0.84 f10 = 0.30 ∗ ∗ ∗ ∗ f11 = 0.75 f12 = 0.75 f13 = 0.75 f14 = 0.89 ∗ ∗ f15 = 0.84 f16 = 0.89 ∗ ∗ ∗ ∗ f11 = 0.30 f12 = 0.16 f13 = 0.50 f14 = 0.50 ∗ ∗ f15 = 0.16 f16 = 0.20

The values of S, R and Q were calculated for all alternatives as in Table 8. In the next step, using Equation (13) ˜ i values were calculated ˜ ∗, R ˜ − and Q S˜ ∗ , S˜ − , R as follows: ˜ ∗ = 0.10; R ˜ − = 0.27; S˜ ∗ = 0.28; S˜ − = 0.76; R ˜ Then using Equation (14) Qi values were calculated. In the calculations, weights of the strategy of the maximum group utility (v) were assumed to be 0.5, 0.3, and 0.8. Table 9 gives the values of Qi for different v s. As we can see in Table 9, A7 is the best alternative ranked with respect to Q. The conditions C1 and C2 are also satisfied. Consequently, based on the indices of different values of v, the ranking of the alternatives from the worst to the best is A1 , A5 , A2 , A4 , A8 , A9 , A6 , A3 , A7 . Compressed Natural Gas Buses was determined as the best alternative for EGO. 5. Sensitivity analysis In this section sensitivity analysis was performed in order to show how our model is sensitive to the chances

2476

S. Aydın and C. Kahraman / Vehicle selection for public transportation using an integrated MCDM approach Table 6 Evaluation scores of the AFVs

A1

A2

A3

A4

A5

A6

A7

A8

A9

E1 E2 E3 E1 E2 E3 E1 E2 E3 E1 E2 E3 E1 E2 E3 E1 E2 E3 E1 E2 E3 E1 E2 E3 E1 E2 E3

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

MP MP MP P F F G VG G MP MP F VP P VP P P P G G MG F F F P MP MP

MP F MP F F F F F MP MP F MP MP MP MP F F MP G G G F F MP F MP F

G G MG F MG MG MG F F MG F MG F MG MG MG MG F F F MG MG F F MG MG F

G G VG G MG G MP MP MP G G G F F F VP P P F F F VG G VG MP MP MP

F F F F MG F MG MG G MP MP MP VG VG VG G G VG MG F MG MG MG F F G G

MG F MG MG MG G G VG G F MP MP MP F F VG VG VG G G G G VG VG G G MG

G VG G MG F F MG G MG F MP F F F MP G G G G VG VG G G VG G MG G

P P VP MP MP MP G G MG F F F MP MP MP VG VG VG G G G VG G VG MP MP MP

P P P MP MP MP MG G MG MG F MG MP F F VG G G G G MG G G G MG MG MG

MP MP P F F MP VG P G G G MG MG F MG VG VG VG MG MG MG VG VG VG F F MG

F F MP F F F MP MP MP MG G G G G MG F F MG MP P MP MG MG F F F MG

P P VP MP P MP MP MP F F F F MP MP F G MG MG P P VP MG G G MG MG F

MG MG F MG F F MG MG MG F F F MG F MG G G MG MG F MG MG G F F F F

MG MG G G G MG MG G F F F F MG G P G VG VG MG MG MG VG G VG MG G F

VG G G G G MG P MP MP F F F MG MG G MG MG MG P VP P G G G MG G G

VG G VG F F F G G G F MG MG F F F MP P P G G VG MP MP MP P P P

Table 7 Crisp values for decision matrix and weight of each criterion Weight A1 A2 A3 A4 A5 A6 A7 A8 A9

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

0.27 0.35 0.40 0.70 0.40 0.11 0.20 0.75 0.50 0.30

0.10 0.40 0.50 0.45 0.40 0.35 0.45 0.80 0.45 0.45

0.05 0.75 0.60 0.55 0.60 0.60 0.60 0.45 0.45 0.40

0.20 0.84 0.75 0.35 0.80 0.50 0.16 0.50 0.89 0.35

0.03 0.50 0.55 0.70 0.35 0.93 0.84 0.60 0.60 0.70

0.01 0.60 0.70 0.84 0.40 0.45 0.93 0.80 0.89 0.75

0.01 0.84 0.55 0.70 0.45 0.45 0.80 0.89 0.84 0.75

0.03 0.16 0.35 0.75 0.50 0.35 0.93 0.80 0.89 0.35

0.02 0.20 0.35 0.70 0.60 0.45 0.84 0.75 0.80 0.65

0.01 0.30 0.45 0.64 0.75 0.60 0.93 0.65 0.93 0.55

0.00 0.45 0.50 0.35 0.75 0.75 0.55 0.30 0.60 0.55

0.04 0.16 0.30 0.40 0.50 0.40 0.70 0.16 0.75 0.60

0.10 0.60 0.55 0.65 0.50 0.60 0.75 0.60 0.65 0.50

0.02 0.70 0.75 0.65 0.50 0.55 0.89 0.65 0.89 0.65

0.10 0.84 0.75 0.30 0.50 0.70 0.65 0.16 0.80 0.75

0.01 0.89 0.50 0.80 0.60 0.50 0.25 0.84 0.35 0.20

in elements of decision matrices. Primarily, we changed experts’ weights in Zeng’s methodology. But we determined that changes in experts’ weights do not influence the final scores. We investigate the cause of this circumstance, and we obtained that experts have made almost the same assessment in questionnaire. So the changes in experts’ weights do not influence the final scores. After, we made some changes in the criteria weights in order to observe how it influence the final scores. So, in the present case; the criteria weight are (0.27, 0.10, 0.05, 0.20, 0.03, 0.01, 0.01, 0.03, 0.02, 0.01, 0.00, 0.04, 0.10, 0.02, 0.10, 0.01) respectively. In this way,

the ranking of the alternatives in descending order are A1 , A5 , A2 , A4 , A8 , A9 , A6 , A3 , A7 . In the second case; We changed the first criteria weight 0.27 to 0.00 and eleventh criteria weight 0.00 to 0.27, and thus the ranking of the alternatives in descending order are A8 , A5 , A4 , A2 , A1 , A9 , A6 , A3 , A7 respectively. In the third case; We changed the fourth criteria weight 0.2 to 0.00 and the tenth criteria weight 0.01 to 0.23, and consequently the ranking of the alternatives are A5 , A6 , A4 , A9 , A2 , A1 , A8 , A3 , A7 . We demonstrate that changes in criteria weights influence the final scores of alternatives so the ranking of alternatives.

S. Aydın and C. Kahraman / Vehicle selection for public transportation using an integrated MCDM approach Table 8 The values S, R and Q for all alternatives S R Q

Table 11 Interpretation of entities in a pair-wise comparison matrix

A1

A2

A3

A4

A5

A6

A7

A8

A9

x

0.28 0.10 1.00

0.41 0.12 0.79

0.64 0.25 0.18

0.43 0.12 0.78

0.29 0.12 0.93

0.37 0.22 0.54

0.76 0.27 0.00

0.34 0.17 0.75

0.51 0.16 0.56

≤ a/ d ≥  (di /a)  bi /c, ci /b

0.5 0.3 0.8



µwi (x)



0 0 1

  ai /d, bi /c

α ∈ [0, 1] α ∈ [0, 1]

ci /b, di /a

Table 9 The values of Qi different values of v

⎡

˜i Q

v

2477

A1

A2

A3

A4

A5

A6

A7

A8

A9

∼

0.00 0.00 0.00

0.20 0.12 0.32

0.81 0.49 1.31

0.22 0.13 0.35

0.06 0.04 0.10

0.47 0.28 0.76

1.00 0.60 1.60

0.26 0.16 0.43

0.42 0.25 0.63

i

z=⎣

n 

wi =

Trapezoidal fuzzy scale

Trapezoidal fuzzy reciprocal scale

Equal IntermediateValues Weakly important IntermediateValues Important Intermediate values Strongly important Intermediate Values Very strongly important

(1, 1, 1, 1) (1, 2, 2, 3) (2, 3, 3, 4) (3, 4, 4, 5) (4, 5, 5, 6) (5, 6, 6, 7) (6, 7, 7, 8) (7, 8, 8, 9) (8, 9, 9, 10)

(1, 1, 1, 1) (1/3, 1/2, 1/2, 1) (1/4, 1/3, 1/3, 1/2) (1/5, 1/4, 1/4, 1/3) (1/6, 1/5, 1/5, 1/4) (1/7, 1/6, 1/6, 1/5) (1/8, 1/7, 1/7, 1/6) (1/9, 1/8, 1/8, 1/7) (1/10, 1/9, 1/9, 1/8)

for all i

(16)

j=1

The fuzzy weight wi is given as

Table 10 Interpretation of entities in a pair-wise comparison matrix Linguistic scale

⎤1/n ∼ tij ⎦ ,

⎤−1 ⎡ n  ∼ ∼ zi ⊕ ⎣ zj ⎦ j=1

(17)

In the following discussion, we will detail the derivation ∼ of fuzzy weight wi . Let the left leg and right leg of t ij

be, respectively, defined as ⎡ fi (α) = ⎣

n 

⎤1/n ((bij − aij )α + aij ⎦

, α ∈ [0, 1]

j=1

(18) ⎡ 6. Comparison with Buckley’s fuzzy AHP

gi (α) = ⎣

In this section, the obtained results by the integrated methodology are compared with the results of Buckley’s fuzzy AHP. Buckley extended Saaty’s AHP method to incorporate fuzzy comparison ratios aij . He pointed out that Van Laarhoven and Pedrycz’s (1983) method was subject to two problems. First, the linear equations of obtained equations do not always have a unique solutions. Second, they insist on obtaining triangular fuzzy numbers for their weights. Buckley’s (1985) approach is shown in the following steps. Step 1. Consult the decision makers, and obtain the ∼ comparison matrix a whose elements are t = ij

(aij , bij , cij , dij ), where all i and j are trapezoidal fuzzy numbers. Table 10 shows the linguistic scale for evaluation of alternatives Step 2. The fuzzy weights wi can be calculated as follows. The geometric mean for each row is determined.

n 

⎤1/n ((cij − d)α + bij ⎦

, α ∈ [0, 1] (19)

j=1

Furthermore, let ⎡ aij = ⎣

n 

⎤1/n (aij )⎦

(20)

j=1

a=

m 

ai

(21)

i=1

Similarly, we can define bi and b, ci and c, and di and d. The fuzzy weight wi is determined as   ai b i c i d i wi = , , , , ∀i (22) d c b a Where the membership function µwi (x) is defined as follows: Let x be a real number on the horizontal axis. The µwi (x) can be summarized as in Table 11.

A1 A2 A3 A4 A5 A6 A7 A8 A9

C1

A1

(1, 1, 1, 1) (1/6, 1/5, 1/5, 1/4) (1/9, 1/8, 1/8, 1/7) (1/6, 1/5, 1/5, 1/4) (1/4, 1/3, 1/3, 1/2) (1/8, 1/7, 1/7, 1/6) (1/10, 1/9, 1/9, 1/8) (1/7, 1/6, 1/6, 1/5) (1/8, 1/7, 1/7, 1/6)

A2 (4, 5, 5, 6) (1, 1, 1, 1) (1/8, 1/7, 1/7, 1/6) (1/4, 1/3, 1/3, 1/2) (2, 3, 3, 4) (1/8, 1/7, 1/7, 1/6) (1/10, 1/9, 1/9, 1/8) (1/5, 1/4, 1/4, 1/3) (1/6, 1/5, 1/5, 1/4)

A3 (7, 8, 8, 9) (6, 7, 7, 8) (1, 1, 1, 1) (6, 7, 7, 8) (7, 8, 8, 9) (2, 3, 3, 4) (1/4, 1/3, 1/3, 1/2) (4, 5, 5, 6) (2, 3, 3, 4)

(4, 5, 5, 6) (2, 3, 3, 4) (1/8, 1/7, 1/7, 1/6) (1, 1, 1, 1) (3, 4, 4, 5) (1/6, 1/5, 1/5, 1/4) (1/9, 1/8, 1/8, 1/7) (1/4, 1/3, 1/3, 1/2) (1/5, 1/4, 1/4, 1/3)

A4 (2, 3, 3, 4) (1/4, 1/3, 1/3, 1/4) (1/9, 1/8, 1/8, 1/7) (1/5, 1/4, 1/4, 1/3) (1, 1, 1, 1) (1/8, 1/7, 1/7, 1/6) (1/9, 1/8, 1/8, 1/7) (1/6, 1/5, 1/5, 1/4) (1/7, 1/6, 1/6, 1/5)

A5 (6, 7, 7, 8) (6, 7, 7, 8) (1/4, 1/3, 1/3, 1/2) (4, 5, 5, 6) (6, 7, 7, 8) (1, 1, 1, 1) (1/5, 1/4, 1/4, 1/3) (4, 5, 5, 6) (1, 2, 2, 3)

A6

Table 12 Pair-wise comparison of applicants for initial cost A7 (8, 9, 9, 10) (8, 9, 9, 10) (2, 3, 3, 4) (7, 8, 8, 9) (7, 8, 8, 9) (3, 4, 4, 5) (1, 1, 1, 1) (4, 5, 5, 6) (2, 3, 3, 4)

A8 (5, 6, 6, 7) (3, 4, 4, 5) (1/6, 1/5, 1/5, 1/4) (2, 3, 3, 4) (4, 5, 5, 6) (1/6, 1/5, 1/5, 1/4) (1/6, 1/5, 1/5, 1/4) (1, 1, 1, 1) (1/4, 1/3, 1/3, 1/2)

A9 (6, 7, 7, 8) (4, 5, 5, 6) (1/4, 1/3, 1/3, 1/2) (3, 4, 4, 5) (5, 6, 6, 7) (1/3, 1/2, 1/2, 1) (1/4, 1/3, 1/3, 1/2) (2, 3, 3, 4) (1, 1, 1, 1)

2478 S. Aydın and C. Kahraman / Vehicle selection for public transportation using an integrated MCDM approach

S. Aydın and C. Kahraman / Vehicle selection for public transportation using an integrated MCDM approach

    When x ∈ adi , bci or x ∈ cbi , dai , the x is calculated as    fi (a)/g(a), if x ∈ ai /d, bi /c x= (23)   gi (a)/f (a), if x ∈ ci /b, di /a Where f (α) =

m 

fi (α) ve g(α) =

i=1

m 

gi (α),

i=1

Step 2 is repeated for all the fuzzy performance scores. Step 3. The fuzzy weights and fuzzy performance scores are aggregated. The fuzzy utilities Ui , ∀i, are obtained based on Ui =

n 

wj rıj , ∀i

(24)

j=1

Application of Buckley’s Fuzzy AHP: Step 1. Decision makers evaluated alternatives as per each criteria. In this step only calculation of initial cost is given for illustration. In this method, agreed decision of decision makers are used. Step 2. For the pair wise comparison matrix for initial cost, the geometric mean is:  a1=

1/9

9 

= (a11 ∗ a12 ∗ a13 ∗ a14 ∗ a15

a1j

∗a16 ∗ a17 ∗ a18 ∗ a19 ) = (1 ∗ 4 ∗ 7 ∗ 4 ∗ 2 ∗ 6 ∗ 8 ∗ 5 ∗ 6)1/9

a9 =

9 

= 4.09 1/9 a9j

= (a91 ∗ a92 ∗ a93 ∗ a94 ∗ a95

J=1

ai bi ci di

1

2

3

4

5

6

7

8

9

4.09 4.89 4.89 5.64

1.88 2.29 2.29 2.56

0.25 0.30 0.30 0.37

1.27 1.56 1.56 1.92

2.74 3.35 3.35 3.92

0.36 0.45 0.45 0.56

0.19 0.22 0.22 0.27

0.78 0.96 0.96 1.18

0.44 0.58 0.58 0.74

Similarly we can get bi and b, ci and c, and di and d. They are summarized as in Table 13. Thus, (a, b, c, d) = (12.00, 14.61, 14.61, 17.17) Then performance scores rj1, j = 1, 2, 3, 4, 5, 6, 7, 8 and 9 can be obtained as:   a1 b1 c1 d1 r11 = , , , = (0.24, 0.33, 0.33, 0.47) d c b a  r21 =

a2 b2 c2 d2 , , , d c b a

 = (0.11, 0.16, 0.16, 0.21)

We repeat step 2 on the other reciprocal matrices one by one. The results are the fuzzy numbers ri2 , ri3 , ri4 , ri5 , ri6 , ri7 , ri8 , ri9 , and wj , ∀i, j. All the fuzzy performance scores of the factors and fuzzy weights in the hierarchy are calculated. Step 3. The fuzzy weights and fuzzy performance scores are aggregated. So the fuzzy utilities Ui , ∀i, are obtained. U1 = (0.172, 0.501, 0.578, 1.480)

U4 = (0.160, 0.435, 0.570 , 1.435) U5 = (0.170, 0.495, 0.535 , 1.465) U6 = (0.075, 0.103, 0.118 , 1.205) U7 = (0.070, 0.095, 0.110 , 1.113) U8 = (0.160, 0.395, 0.620 , 1.395)

= (1/8 ∗ 1/6 ∗ 2 ∗ 1/5 ∗ 1/7

U9 = (0.150, 0.400, 0.579 , 1.377)

= 0.44 Similarly, we get other aij values. Hence, 9 

U3 = (0.068, 0.095, 0.112 , 1.170)

∗a96 ∗ a97 ∗ a98 ∗ a99 ) ∗1 ∗ 2 ∗ 1/4 ∗ 1)1/9

a=

Table 13 Geometric mean

U2 = (0.161, 0.468, 0.512 , 1.440)

J=1



2479

ai = 4.09 + 1.88 + 0.25 + 1.27 + 2.74

j01

+ 0.36 + 0.19 + 0.78 + 0.44 = 12

To determine the rank of final fuzzy utilities, the area-based ranking method which was developed by Kahraman and Tolga [45] is used. The ranking results are shown in Table 14. Consequently, based on Buckley’s approach the ranking of the alternatives in descending order are, A1 , A5 , A2 , A4 , A8 , A9 , A6 , A3 , A7 . Compressed Natural Gas Buses was determined as the best alternative for EGO.

2480

S. Aydın and C. Kahraman / Vehicle selection for public transportation using an integrated MCDM approach Table 14 The ranking of alternatives

Alternatives I(ω) Comparison Alternatives I(ω) Comparison A 1 − A2 A 1 − A3 A 1 − A4 A 1 − A5 A 1 − A6 A 1 − A7 A 1 − A8 A 1 − A9 A 2 − A3 A 2 − A4 A 2 − A5 A 2 − A6 A 2 − A7 A 2 − A8 A 2 − A9 A 3 − A4 A 3 − A5 A 3 − A6 A 3 − A7 A 3 − A8

0.52 0.75 0.51 0.54 0.74 0.77 0.52 0.54 0.50 0.47 0.48 0.51 1.00 0.51 0.52 0.73 0.74 0.51 0.51 0.72

A1 A1 A1 A1 A1 A1 A1 A1 A2 A2 A5 A2 A2 A2 A2 A4 A5 A6 A3 A8

> A2 > A3 > A4 > A5 > A6 > A7 > A8 > A9 > A3 > A4 > A2 > A6 > A7 > A8 > A9 > A3 > A3 > A3 > A7 > A3

A 3 − A9 A 4 − A5 A 4 − A6 A 4 − A7 A 4 − A8 A 4 − A9 A 5 − A6 A 5 − A7 A 5 − A8 A 5 − A9 A 6 − A7 A 6 − A8 A 6 − A9 A 7 − A8 A 7 − A9 A 8 − A9

0.71 0.51 0.71 0.66 0.51 0.51 0.73 0.68 0.51 0.53 0.56 0.76 0.69 0.73 0.72 0.51

A9 A5 A4 A4 A4 A4 A5 A5 A5 A5 A6 A8 A9 A8 A9 A8

> A3 > A4 > A6 > A7 > A8 > A9 > A6 > A7 > A8 > A9 > A7 > A6 > A6 > A7 > A7 > A9

The obtained results were compared with the actualized case in Ankara Municipality and it was seen that most of the vehicles were compatible but some were not. We proposed the developed methodology to Ankara Municipality in purchasing decisions for vehicles.

cities in Turkey can use CNG buses for public transportation. It will provide benefits to national income and environment. For further research, the findings of our study can be compared with the results of other multicriteria techniques like fuzzy TOPSIS, fuzzy ANP, fuzzy PROMETHEE. And this methodology can be implemented to assess alternative fuel personnel vehicles. References [1]

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7. Conclusion Recently the world has stood an increasing demand for energy and public transportation services in a developing economy. Sustainability energy and public transportation systems have the precedence of the political agenda in many countries. Because of the excessive population, public transportation gets more difficult and governments produce policies for less exhaust gas. In this paper, the public transportation of Ankara was investigated. Hence an integrated Fuzzy AHP- Fuzzy VIKOR methodology was implemented to select the best alternative fuel bus. First of all, a four levels hierarchy composed of three main criteria, 17 sub-criteria, and nine alternatives was established. The weights of the criterion and sub-criteria were determined by fuzzy AHP. And then by using VIKOR, the nine alternatives were ranked. Compressed Natural Gas Buses was determined as the best alternative according to the determined criteria for Ankara. In Ankara, 1090 over 1790 buses are Compressed Natural Gas buses. According to this research the other 700 buses can be converted to CNG buses. And the other

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