A hybrid MCDM approach for evaluating an automobile purchase ...

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Int. J. Information and Decision Sciences, Vol. 5, No. 1, 2013

A hybrid MCDM approach for evaluating an automobile purchase model G. Sakthivel* and M. Ilangkumaran Department of Mechatronics Engineering, K.S. Rangasamy College of Technology, Tiruchengode-637 215, Namakkal, Tamil Nadu, India Fax: +914288-274860 E-mail: [email protected] E-mail: [email protected] *Corresponding author

G. Nagarajan I.C. Engineering Division, Department of Mechanical Engineering, Anna University, Chennai 600025, India E-mail: [email protected]

A. Raja, P.M. Ragunadhan and J. Prakash Department of Mechatronics Engineering, K.S. Rangasamy College of Technology, Tiruchengode-637 215, Namakkal, Tamil Nadu, India Fax: +914288-274860 E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] Abstract: This paper describes an application of hybrid multi criteria decision making (MCDM) technique for the selection of the best car. This study focuses on five alternatives and evaluation criteria such as safety, performance, economic aspect, exterior, convenience, dealer, warranty and emissions to select the best car. Two models are proposed to evaluate the best car. The first model, fuzzy analytical hierarchy process (FAHP) is integrated with Preference Ranking Organization METHod for Enrichment Evaluation (PROMETHEE) technique. The second model, FAHP is integrated with hierarchy grey relation analysis (GRA) technique. Here, the FAHP is used to analyse the structure of car selection problem and to determine the weights of the criteria. The hierarchical GRA and PROMETHEE techniques are used to obtain the final ranking of the cars. Keywords: car purchase model; multi criteria decision making; MCDM; hierarchy GRA; fuzzy analytical hierarchy process; FAHP; Preference Ranking Organization METHod for Enrichment Evaluation; PROMETHEE; fuzzy set theory.

Copyright © 2013 Inderscience Enterprises Ltd.

A hybrid MCDM approach for evaluating an automobile purchase model

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Reference to this paper should be made as follows: Sakthivel, G., Ilangkumaran, M., Nagarajan, G., Raja, A., Ragunadhan, P.M. and Prakash, J. (2013) ‘A hybrid MCDM approach for evaluating an automobile purchase model’, Int. J. Information and Decision Sciences, Vol. 5, No. 1, pp.50–85. Biographical notes: G. Sakthivel is an Associate Professor of Mechatronics Engineering at K.S. Rangasamy College of Technology, Tiruchengode, India. He completed his BE in Mechanical from K.S. Rangasamy College of Technology, Tiruchengode in the year 2001. He completed his MTech in Mechatronics from Vellore Institute of Technology, Vellore in the year 2003. He has published more than 15 papers in international and national conferences. He is a life member of ISTE. His research interest is alternative fuels, maintenance management and automotive electronics. M. Ilangkumaran is a Professor of Mechatronics Engineering at K.S. Rangasamy College of Technology, Tiruchengode, India. He completed his BE in Mechanical from K.S. Rangasamy College of Technology, Tiruchengode in the year 1999. He completed his ME in Industrial Engineering from Kumaraguru College of Technology, Coimbatore in the year 2001. He received his PhD in the area of maintenance management in the year 2010. He has published more than six papers in national conferences. He has published six papers in international journals. He is a life member of ISTE. His research interest is maintenance management and automotive electronics. G. Nagarajan is a Professor in I.C. Engineering Division, Mechanical Engineering, College of Engineering, Guindy at Anna University, Chennai. He completed his BE in Mechanical from Bangalore University, Bangalore in the year 1986. He completed his ME in Internal Combustion Engineering from Anna University, Chennai in the year 1988. He received his PhD in the area of Internal Combustion Engineering in the year 2000. He has published more than 70 papers in international journals and nine papers in national journals. He is a life member of ISTE and SAE. His research interest is automobile engineering and internal combustion engines. A. Raja is a student of ME in Industrial Safety Engineering at K.S. Rangasamy College of Technology, Tiruchengode, Tamil Nadu, India. P.M. Ragunadhan is a student of ME in Industrial Safety Engineering at K.S. Rangasamy College of Technology, Tiuchengode, Tamil Nadu, India. J. Prakash is a student of ME in Industrial Safety Engineering at K.S. Rangasamy College of Technology, Tiruchengode, Tamil Nadu, India.

1

Introduction

Cars have become an indispensable part of human life. They touch the lives of millions everywhere on this planet for their daily needs (Byun, 2001). The growth of the Indian middle class, coupled with their increasing purchasing power, along with the strong growth of economy over the past few years has attracted major auto manufacturers to the Indian market. It is obvious that the car market is gearing up for all kinds of car models.

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In olden days, there were only higher end cars available, which were affordable only for the rich people. In the modern era, the trend has started to change: the person from the average class tops the ranking in purchasing passenger cars. Purchase of the higher end cars were only 35% whereas the average class interest was 65% in buying a car as per the statistics given by the Society of Indian Automobile Manufacturers (SIAM, 2006). Due to high competition among mid segment cars in the market, the manufacturers are focusing to deliver additional features other than that of price and fuel economy. The customers are given a chance to evaluate the cars with a number of influencing criteria such as safety, comfort, economic aspect, exterior, convenience, dealer and warranty. So it is a multi criteria decision making (MCDM) problem. Byun (2001) proposed the analytical hierarchy process (AHP) model for car selection problem; his paper fails to consider emission criterion for the evaluation process. Calef and Goble (2007) have reported that pollution is a major problem in the automobile sector. The MCDM method for selecting the best car is useful to both the customers and the manufacturers. The major advantage of the hierarchical structure is that it allows for a detailed, structured and systematic decomposition of the overall problem into its fundamental components and interdependencies, with a large degree of flexibility. Tuzkaya (2009) implemented fuzzy analytical hierarchy process (FAHP) in evaluating the environmental effects of transportation modes in Turkey. Tang and Beynon (2005) used FAHP method to assist a car rental company for selecting the type of fleet car to be adopted. Lim et al. (2006) investigated the ranking of cars depending upon the effect of the operating conditions such as mileage of the cars, engine speed, fuel and lubricating oil compositions in the emissions using Preference Ranking Organization METHod for Enrichment Evaluation (PROMETHEE). Tzeng et al. (2005) utilised the AHP and other outranking methods for selecting the most suitable bus in Taiwan. Lim et al. (2007) used PROMETHEE to investigate the effect of fuel characteristics and engine operating conditions from heavy duty diesel buses. Cascales and Lamata (2009) selected AHP for the cleaning system of engine maintenance. Sapuan et al. (2010) proposed AHP for selecting the suitable composite material for automobile bumper beam. Nepal et al. (2010) used FAHP to prioritise the customer satisfaction attributes in target planning for automotive product development. Mayyas et al. (2011) assisted an AHP method for the material selection of automobile body panels. In this literature, only a few researchers have contributed to car selection problem using MCDM technique. Even though the AHP is widely used in many decision making problems, very few authors have listed the limitations of its usage. The ranking of AHP is not precise enough. The conventional AHP cannot reflect the human thinking style (Deng 1999; Cheng et al., 1999; Mikhailov, 2003; Chan, 2003). Numerical values are exact numbers that are useful only for crisp decision making applications. In order to deal with indistinctness of human thought, Zadeh (1965) introduced fuzzy set theory to express the linguistic terms in decision making process. To overcome the shortcoming of the existing research work in car purchase model, the fuzzy linguistic terms are used with AHP and proposed as FAHP. The FAHP is used for determining the weights of the criteria. The ranking of the car model is determined with the help of grey relation analysis (GRA) and PROMETHEE. The rest of this paper is organised as follows: In the second section, FAHP, PROMETHEE and GRA are summarised. In this section, literature review and


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methodology for each technique is also given. In the third section fuzzy set theory, fuzzy numbers and its algebraic operations are explained. The proposed model is explained in section four. An application of the proposed model is elaborated in Section 5. In the sixth section, the obtained results are discussed. Finally, in Section 7, the paper is concluded with suggestions for future research.

2

Methods

2.1 The FAHP method AHP is a method proposed by Saaty (1980). In the AHP, the decision problem is structured hierarchically at different levels with each level consisting of a finite number of elements Khajeeh (2010). Laarhoven and Pedrycz (1983) have applied fuzzy logic principles in AHP and proposed it as FAHP. In the literature, FAHP has been widely applied in many complicated decision making problems. Chou and Liang (2001) combined fuzzy set theory with AHP for shipping company performance evaluation. Chang et al. (2003) have applied FAHP method to determine the weights of criteria for performance evaluation of airports. Hwang and Ko (2003) presented the AHP and FAHP to find the optimal decision of restaurant types and their locations. Hsieh et al. (2004) provided a fuzzy multi-criteria analysis approach to choose the plan and design of public office buildings. Lin et al. (2006) integrated FAHP approach to the international competition level for a comparative analysis of the suitable location mode for Singapore International Airport. Hwang and Hwang (2006) proposed FAHP method for food service strategy evaluation process. Ayag and Ozdemir (2006) evaluated machine tool alternatives by applying an intelligent approach based on FAHP. Huang Lin et al. (2008) presented a FAHP method for the selection of government sponsored technology development projects. Khoram et al. (2007) used FAHP to prioritise the methods related to reuse of treated wastewater in Iran. Khajeeh (2010) presented FAHP as a decision tool for finding the best course of actions to bring about water conservation. Khorasani and Bafruei (2011) developed FAHP for the selection of potential suppliers in the pharmaceutical industry. The procedural steps as involved in FAHP method are listed below: Step 1

A complex decision making problem is structured using a hierarchy. The FAHP initially breaks down a complex MCDM problem into a hierarchy of inter-related decision elements (criteria). With the FAHP, the criteria are arranged in a hierarchical structure similar to a family tree. A hierarchy has at least three levels: overall goal of the problem at the top, multi criteria that define criteria in the middle, and decision criteria at the bottom (Albayrak and Erensal, 2004).

Step 2

The crisp pair-wise comparison matrix A is fuzzified using the triangular fuzzy number (TFN) M = (l, m, u), the l and u represent lower and upper bound range respectively that might exist in the preferences expressed by the decision maker. The membership function of the TFNs M1, M3, M5, M7, and M9 are used to represent the assessment from equally preferred (M1), moderately preferred

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G. Sakthivel et al. (M3), strongly preferred (M5), very strongly preferred (M7), and extremely preferred (M9). This paper employs a TFN to express the membership functions of the aforementioned expression values on five scales which are used for FAHP listed in Table 1. Let C = {C j j = 1, 2,… , n} be a set of criteria. The result of the pair-wise comparison on ‘n’ criteria can be summarised in an (n × n) evaluation matrix A in which every element aij (i, j = 1, 2,… , n) is the quotient of weights of the criteria, as shown: ⎡ a11 ⎢a A = ⎢ 21 ⎢ ⎢ ⎣ an1

Step 3

a12 a22 an 2

a1n ⎤ a2 n ⎥⎥ , a = 1, a ji = 1/ aij , aij ≠ 0. ⎥ ii ⎥ ann ⎦

(1)

The mathematical process is commenced to normalise and find the relative weights of each matrix. The relative weights are given by the right Eigen vector (W) corresponding to the largest Eigen value (λ max), as Aw = λmax w

(2)

It should be noted that the quality of output of FAHP is strictly related to the consistence of the pair-wise comparison judgments. The consistency is defined by the relation between the entries of A : aij × a jk = aik . The consistency index (CI) is CI = ( λmax − n ) ( n − 1)

Step 4

(3)

The pair-wise comparison is normalised and priority vector is computed to weigh the elements of the matrix. The values in this vector sum to 1. The consistency of the subjective input in the pair-wise comparison matrix can be determined by calculating a consistency ratio (CR). In general, a CR having a value less than 0.1 is good (Saaty, 1980). The CR for each square matrix is obtained from dividing CI values by random consistency index (RCI) values. CR = CI / RCI

(4)

The RCI which is obtained from a large number of simulations runs and varies depending upon the order of matrix. Table 2 lists the value of the RCI for matrices of order 1 to 10 obtained by approximating random indices using a sample size of 500. The acceptable CR range varies according to the size of matrix that is 0.05 for a 3 by 3 matrix, 0.08 for a 4 by 4 matrix and 0.1 for all larger matrices having n ≥ 5. If the value of CR is equal to, or less than that value, it implies that the evaluation within the matrix is acceptable or indicates a good level of consistency in the comparative judgments represented in that matrix. In contrast, if CR is more than the acceptable value, inconsistency of judgments within that matrix has occurred and the evaluation process should therefore be reviewed, reconsidered and improved.

A hybrid MCDM approach for evaluating an automobile purchase model Table 1

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Nine-point scale of relative importance

Degree of preference

Definition

Explanation

(1 1 1)

Equally preferred (M1)

(2 3 4)

Moderately (M3)

(4 5 6)

Strongly (M5)

Experience and judgement strongly or essentially favour one activity over another.

(6 7 8)

Very strongly (M7)

An activity is strongly favoured over another and its dominance demonstrated in practice.

(8 9 9)

Extremely (M9)

Table 2

Two activities contribute equally to the objective. Experience and judgement slightly favour one activity over another.

The evidence favouring one activity over another is of the highest possible order of affirmation.

Random consistency index (RCI)

No

1

2

3

4

5

6

7

8

9

10

RCI

0

0

0.52

0.89

1.11

1.25

1.35

1.40

1.45

1.49

2.2 The PROMETHEE method The PROMETHEE is a multi-criteria decision- making method developed by Brans et al. (Brans and Vincke, 1985; Brans et al., 1986). It is one of the best known and most widely applied outranking methods because it follows a transparent computational procedure and can be easily understood by decision makers. The PROMETHEE I method can provide the partial ordering of the decision alternatives, whereas, PROMETHEE II method can derive the full ranking of the alternatives. In this paper, the PROMETHEE II method is employed to obtain the full ranking of car alternative. There are a few applications of PROMETHEE in the literature. Taleb and Mareschal (1995) applied PROMETHEE to select feasible water resource for Jordan. Goumas and Lygerou (2000) used PROMETHEE as an approach for the evaluation and ranking of alternative energy exploitation schemes of a low temperature geothermal field. Albadvi et al. (2007) applied PROMETHEE for ranking the alternatives and determining the best position for TV market. Dagdeviren (2008) proposed an integrated approach which employs AHP and PROMETHEE for the equipment selection problem. Rousis et al. (2008) determined the final ranking of an alternative system for selecting a suitable waste management of electrical and electronic equipment waste for reuse, recycling and other forms of recovery using PROMETHEE. Beynon and Wells (2008) presented PROMETHEE-based preference ranking of a small set of motor vehicles and relates to minimal changes that would be necessary to a vehicle’s emissions. Wang et al. (2008) applied fuzzy PROMETHEE for evaluating IS outsourcing suppliers. Zhang et al. (2009) approached fuzzy AHP for ranking contaminated sites based on comparative risk methodology. It combines the concepts of fuzzy sets to represent uncertain site information with the PROMETHEE. Behzadian et al. (2010) proposed the PROMETHEE methods for selecting the best compromise alternatives. Lee and Chang (2010) used PROMETHEE II in the evaluation of quality of the portal website service which is an important way to known the quality of the portal website service. Athawale and Chakraborty (2010) solved a location selection problem and obtained valuable results in

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framing the location selection strategies by the PROMETHEE II method. In this paper, the PROMETHEE is integrated with FAHP and proposed as FAHP-PROMETHEE for car purchase problem. The procedural steps involved in PROMETHEE II method are listed below (Athawale and Chakraborty, 2010): Step 1

Normalising the decision matrix using the following equation:

( )

( )

( )

Rij = ⎡ X ij − min X ij ⎤ ⎡ max X ij − min X ij ⎤ i = 1, 2,… , n; j = 1, 2,… , m (5) ⎣ ⎦ ⎣ ⎦

where Xij is the performance measure of ith alternative with respect to jth criterion. For non-beneficial criteria, equation (6) can be rewritten as follows:

( )

( )

( )

Rij = ⎡ max X ij − X ij ⎤ ⎡ max X ij − min X ij ⎤ ⎣ ⎦ ⎣ ⎦

Step 2

(6)

Calculating the evaluative differences of ith alternative with respect to other alternatives. This step involves the calculation of differences in criteria values between different alternatives pair-wise.

Step 3

Calculating the preference function, Pj (i, i ′). The preference functions require the definition of some preferential parameters, such as the preference and indifference thresholds. However, in real time applications, it may be difficult for the decision maker to specify which specific form of preference function is suitable for each criterion and also to determine the parameters involved. To avoid this problem, the following simplified preference function is adopted here: Pj (i, i ′) = 0, if Rij ≤ Ri′j

(

(7)

)

Pj (i, i ′) = Rij − Ri′j , if Rij > Ri′j

Step 4

(8)

Calculating the aggregated preference function taking the criteria weights into account. Aggregated preference function, ⎣⎢ ∑

π (i, i ′) = ⎡

w × Pj (i, i ′) ⎤ j =1 j ⎦⎥

m

∑

m j =1

wj

(9)

where, ‘wj’ is the relative importance (weight) of jth criterion. Step 5

Determining the leaving and entering outranking flows as follows: Leaving (or positive) flow for ith alternative,

ϕ + (i ) =

1 n −1

∑

n i′

= 1 π (i, i ′) (i ≠ i ′)

Entering (or negative) flow for ith alternative,

(10)


ϕ − (i ) =

1 n −1

∑

n i′

= 1 π (i ′, i ) (i ≠ i ′)

57 (11)

where ‘n’ is the number of alternatives. Here, each alternative faces (n – 1) number of other alternatives. The leaving flow expresses how much an alternative dominates the other alternatives, while the entering flow denotes how much an alternative is dominated by the other alternatives. Based on these outranking flows, the PROMETHEE I method can provide a partial pre-order of the alternatives whereas the PROMETHEE II method can give the complete pre-order by using a net flow, though it loses much information of preference relations. Step 6

Calculating the net outranking flow for each alternative.

ϕ (i ) = ϕ + (i ) − ϕ − (i ) Step 7

(12)

Determining the ranking of all the considered alternatives depending on the values of φ(i). The higher the value of φ(i), the better is the alternative. Thus, the best alternative is the one having the highest φ(i) value.

2.3 The GRA method The grey relational analysis, proposed by Deng (1989), is a method that can measure the correlation between series and belongs to the category of the data analytic method or geometric method. The measured series can be either of time series or index series. Usually, researchers will set the target series based on the objective of the studied problem as the reference series. Hence, the purpose of grey relational analysis technique is to measure the relation between the reference scheme and comparison scheme. There are a few studies that applied GRA in the literature. Chang et al. (1999) determined the risk priority number in failure mode and effects analysis (FMEA) using grey theory by assigning relative weighting coefficient without any utility function. Chang et al. (2000) presented a fast and effective methodology for the optimisation of the injection moulding process parameters of short glass fibre reinforced polycarbonate composites. Fu et al. (2001) evaluated the effect of environmental factors on corrosion of oil tubes in gas wells and found out the main factors using GRA. Lin and Lin (2002) proposed GRA for the optimisation of the electrical discharge machining process with multiple performance characteristics. Chang et al. (2003) utilised the GRA to select the criteria for performance evaluation of airports. Chen and Tzeng (2004) solved the problem of choosing the best host country for an expatriate assignment using GRA. Lai et al. (2005) determined the best design combination of product form elements for matching a given product image represented by a word pair using GRA. Kung and Wen (2007) used GRA to find the significant financial ratio variables and other financial indicators affecting the financial performance of venture capital enterprises. Xu et al. (2007) introduced the idea of GRA, and proposed a new conflict reassignment approach of belief functions. Lo (2008) decided to choose a group of optimal stocks in the stock market using GRA. Lin (2008) proposed a method for electrocardiogram heartbeat discrimination using GRA to quantify the frequency components among the various ECG

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beats. Hsu and Wang (2009) proposed GRA for forecasts integrated circuit outputs. In this paper the FAHP-GRA is proposed as the evaluation model for car purchase problem. In grey relational analysis, when the range of the sequence is large or the standard value is enormous, the function of factors is neglected. However, if the factors, goals and directions are different, the grey relation might produce incorrect results. Therefore, one has to preprocess the data which are related to a group of sequences, which is called ‘grey relational generation’ (Chang and Lu, 2007). Data preprocessing is a process of transferring the original sequence to a comparable sequence. For this purpose, it is normalised in the range between zero and one. Two different linear normalisation expressions are applied to the indices data (Zhou and Zhang, 1995; Ye, 2003). For benefit indices, the normalised data can be obtained by, xij =

si ( j ) max i {si ( j )}

(13)

while for cost indices, the normalised data can be obtained by, xij =

min i {si ( j )}

(14)

{si ( j )}

Evidently, the larger the normalised datum is, the better the performance will be. The optimal normalised datum should be equal to one. Thus the ideal scheme (or the reference scheme) can be expressed as S0 = ( s01 , s02 ,… , s0 n ) = (1, 1,… ,1) .

(15)

The procedural steps as involved in GRA method are listed below: Step 1

The relational coefficient ξ0i(j) between the reference scheme S0 and the compared scheme Si for the jth index can be calculated by the following equation, which represents the relative distance between the two indices:

ξ 0i ( j ) =

{

}

{

min i min j x0 j − xij + ρ max i max j x0 j − xij

{

x0 j − xij + ρ max i max j x0 j − xij

}

},

(16)

i = 1, 2,… , m; j = 1, 2,… , n.

Index values of the reference scheme are all equal to one; therefore

{

}

min i min j x0 j − xij = 0. Typically the distinguishing coefficient ρ = 0.5. then

the grey relational coefficient can be simplified to

ξ 0i ( j ) =

{

0.5 max i max j x0 j − xij

{

}

x0 j − xij + 0.5 max i max j x0 j − xij

}

,

i = 1, 2,… , m; j = 1, 2,… , n.

Thus, the primary grey relational coefficient matrix for all indices of the optional schemes can be denoted as

(17)

A hybrid MCDM approach for evaluating an automobile purchase model gCs G=

gCs … … gCs

=

ξ01 (1) ξ02 (1) … … ξ0 m (1) ξ01 (2) ξ02 (2) … … ξ0 m (2)

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(18)

… … … … … … … … ξ01 (n) ξ02 (n) … … ξ0 m (n)

where gCk (k = 1, 2,… , s ) represents the grey relational coefficient vector for the indices subject to the kth criterion Ck, and it can be expressed as,

gCk =

ξ01 ( p ) ξ02 ( p ) … … ξ0 m ( p) ξ01 ( p + 1) ξ02 ( p + 1) … … ξ0 m ( p + 1) … … ξ01 (q)

… … ξ02 (q)

… … … …

… … ξ0m (q)

.

(19)

As mentioned before, Ip, Ip+1,…,Iq (1 ≤ p ≤ q ≤ n) are the indices subject to the kth criterion Ck. Hence, elements in each column ξ0i(p), ξ0i(p + 1),…,ξ0i(q) represent the relational coefficient between reference scheme S0 and optional scheme Si. Step 2

Accordingly the weighed primary grey relational coefficient vector of the indices subject to criterion Ck can be obtained as

(

δ Ck = WCk gCk = w1 p , w1p +1 ,… , w1q ξ01 ( p )

ξ02 ( p )

… ξ ( p + 1) ξ02 ( p + 1) … × 01 … … … … … ξ01 (q) ξ02 (q ) …

(

)

… ξ0m ( p) … ξ0 m ( p + 1) … … … … ξ 0 m (q )

(20)

)

= δ Ck (1), δ Ck (2),… , δ Ck (m) .

Similarly, we can get the corresponding weighed primary grey relational coefficient vector for any other criteria on the criterion level, which can be expressed as,

δ C1 (1) δ C1 (2) … … δ C1 (m) Gweighted =

δ C2 (1) δ C2 (2) … … δ C2 (m) … … … … … … … … δ Cs (1) δ Cs (2) … … δ Cs (m)

.

(21)

In order to improve the data comparability, the data normalisation of Gweighted with equations (13) and (14) is also necessary. By scaling the resulting δ Ck (i ) (i = 1, 2,…,m; k = 1, 2,…,s) the normalised weighed primary grey relational coefficient matrix can then be obtained as follows,

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δ C′ 1 (1) δ C′ 1 (2) … … δ C′ 1 (m) ′ Gweighted =

δ C′ 2 (1) δ C′ 2 (2) … … δ C′ 2 (m) … … … … … … … … δ C′ s (1) δ C′ s (2) … … δ C′ s (m)

,

(22)

where δ C′ k (i ) (i = 1, 2,…,m; k = 1, 2,…,s) is the grey relational coefficient resulting from the normalisation of δ Ck (i ). Again, equation (16) is used to calculate the grey relational coefficients between the reference scheme and optional schemes for a certain criteria. Thus the secondary grey relational grade vector can be obtained as follows:

ξC1 (1) ξC1 (2) … … ξC1 (m) Gc =

Step 3

ξC2 (1) ξC2 (2) … … ξC2 (m) … … … … … … … … ξCs (1) ξCs (2) … … ξCs (m)

(23)

.

Finally, the integrated grey relational grade vector between reference scheme and the optional schemes for the overall objective is derived from the following

(

ξ = WC × GC = wC1 , wC2 ,… , wCk ,… , wCs

)

ξC1 (1) ξC1 (2) … … ξC1 (1) ×

ξC2 (1) ξC2 (2) … … ξC2 (1) … … … … … … … … ξCs (1) ξCs (2) … … ξCs (1)

(24)

= (1, 2,… , m).

Basically, the larger the integrated grey relational grade, the closer the relationship between the reference scheme and the given optional scheme. Thus, the largest grey relational grade is desired which corresponds to the selection of the best car.

3

Fuzzy set theory

A fuzzy set is a class of objects with grades of membership. It is characterised by a membership function which assigns a grade of membership ranging between zero and one to each object of the class (Zadeh, 1965). The classical set theory is built on the fundamental concept of whether a set is a member or not a member (Ertugrul and Tus, 2007). However, many real world applications cannot be handled by the classical set theory (Chen and Pham, 2001). Fuzzy sets theory has the capability of solving real world problems by providing a wider frame than that of the classic sets theory (Ertugrul and Tus, 2007). Zadeh (1965) proposed the fuzzy set theory for the scientific environment and later it has been made available to other fields as well. Expressions such as ‘not very


61

clear’, ‘probably so’ and ‘very likely’ represent some degree of uncertainty of human thought and are often used in daily life (Ertugrul and Tus, 2007). In our daily life there are different decision making problems of diverse intensity and if the fuzziness of human decision making is not taken into account, the results can be misleading (Tsaur et al., 2002). Fuzzy decision making turned out to be a rational approach towards handling of decision making that takes into account human subjectivity (Lai and Hwang, 1994). Bellman and Zadeh (1970) described the decision making methods in fuzzy environments. The use of fuzzy set theory allows the decision-makers to incorporate uncertain information into decision models (Kulak et al., 2005). Consequently, the fuzzy theory has become a useful tool for modelling human activities with uncertain information. Tsaur et al. (2002) used fuzzy decision making theory for the airline service quality evaluation. Therefore, this research incorporates the fuzzy theory into performance measurement by the evaluators’ subjective judgments. The fuzzy set theory resembles human reasoning with the use of approximate information and certainty to generate decisions and it is a better approach to convert linguistic variables to fuzzy numbers under ambiguous assessments. The fuzzy set theory which is incorporated with AHP allows a more accurate description of decision making process.

3.1 Fuzzy numbers The uncertain comparison ratios are expressed as fuzzy sets or fuzzy numbers. It is possible to use different fuzzy numbers according to the situation. In general, triangular and trapezoidal fuzzy numbers are used. Buckley (1985) initiated the use of trapezoidal fuzzy numbers to express the decision maker’s evaluation of alternatives while Laarhoven and Pedrycz (1983) used TFNs. Chang used TFNs for pair-wise comparison scale of FAHP. In common practice, the triangular form of the membership function is used most often (Ding and Liang, 2005; Kahraman et al., 2004; Karsak and Tolga, 2001; Xu and Chen, 2007). The reason for using a TFN is that it is intuitively easy for the decision-makers to use and calculate. In addition, modelling using TFNs has proven to be an effective way for formulating decision problems where the information available is subjective and imprecise (Kahraman et al., 2004; Chang and Yeh, 2002; Chang et al., 2007; Zimmerman, 1996). The evaluation criterion in the judgment matrix and weight vector is represented by TFNs. A fuzzy number is a special fuzzy set F = {(x, µF (x), x € R} where x takes its value on the real line R1: –∞ < x < + ∞ and µF(x) is a continuous mapping from R1 to the close interval [0, 1]. A TFN can be denoted as M = (l, m, u). The TFN can be represented as follows: x, l , ⎧ 0, ⎪ x −1 ⎪ , l ≤ x ≤ m, ⎪ μ A ( x) = ⎨ m − 1 ⎪ u − x , m ≤ x ≤ u, ⎪u − m ⎪ 0, x>u ⎩

According to the nature of TFN, it can be defined as a triplet (l, m, u). The TFN can be represented as Ã = (L, M, U), where L and U represent the fuzzy probability between the lower and upper boundaries of evaluation. The TFN is shown in Figure 2. The two fuzzy numbers Ã1 = (L1, M1, U1) and Ã2 = (L2, M2, U2) are assumed.

62

G. Sakthivel et al. Ã1 ⊕ Ã2 = ( L1 , M1 , U1 ) ⊕ ( L2 , M 2 , U 2 ) = ( L1 + L2 , M1 + M 2 , U1 + U 2 ) Ã1 ⊗ Ã2 = ( L1 , M1 , U1 ) ⊗ ( L2 , M 2 , U 2 ) = ( L1 L2 , M 1M 2 , U1U 2 ) Ã1 − Ã2 = ( L1 , M1 , U1 ) − ( L2 , M 2 , U 2 ) = ( L1 − L2 , M 1 − M 2 , U1 − U 2 ) Ã1 ÷ Ã2 = ( L1 , M 1 , U1 ) ÷ ( L2 , M 2 , U 2 ) = ( L1 U 2 , M1 M 2 , U1 L2 ) Ã1−1 = ( L1 , M 1 , U1 )

Figure 1

−1

= (1 U1 ,1 M 1 ,1 L1 )

Proposed methodology

A hybrid MCDM approach for evaluating an automobile purchase model Figure 2

63

Triangular fuzzy numbers

μ A ( x)

1

0

4

L

M

U

The proposed methodology

The proposed methodology consists of FAHP integrated with GRA and FAHP integrated with PROMETHEE method for the purchase of the best car among the alternatives. It contains three basic stages: 1

identification of the criteria

2

FAHP computations

3

ranking the alternatives using GRA and PROMETHEE.

The schematic diagram of the proposed methodology for the selection of the best car is shown in Figure 1. In the first stage, the methodology of the alternatives and their evaluation criteria are identified and a decision hierarchy is framed out. The FAHP is structured such that the objective is given the first priority; main criteria and sub-criteria are at the second and third levels respectively and then alternatives, at the fourth level. The decision hierarchy is approved by the decision making team at the end of the first stage. After the approval of decision hierarchy, the criteria used in the technology selection are assigned with weights using FAHP in the second stage. In this phase, pair-wise comparison matrices are framed using Saaty’s scale. After the pair-wise comparison, the relative weights of each criterion are computed using eigen vector method. In the last stage of the proposed methodology, the best car is selected according to the ranking obtained though PROMETHEE and GRA.

5

Numerical application of proposed methodology

The planned methodology is applied for customer satisfaction to select a suitable car that convinces their needs. The automotive industry manufactures different models of cars in different brand names approximately 1,045,881 cars per annum as per the statistics given by Society of Indian Automobile Manufacturers (2006). The end product must be achieved through the various processes of selecting a car with the best features and the required criteria. As per the directions from automotive industries managers and

64

G. Sakthivel et al.

engineers, it is mandatory to select a suitable car for the newly buying customer in view of achieving better efficiency.

5.1 Data gathering The criteria and sub-criteria have to be most customary and imperative in the best car selection process. Choosing the possible criteria and sub-criteria for the selection of a best car that satisfies the purchaser’s desires involves a decision making process which includes experts concerned from the organisation. In this work, criteria and sub-criteria have been considered and adopted from the literature survey and the existing customers. Based on the survey and the connoisseur’s view, eight main criteria and forty sub-criteria have been finalised for the selection of the best model car. The decision hierarchy is created for the selection of the best car with the main criteria, sub-criteria and the alternatives as shown in Figure 3. The identified potential of each alternative with respect to qualitative criteria can be classified into four grades with linguistic terms such as excellent (0.9), good (0.7), moderate (0.5), poor (0.3) and very poor (0.1) and are tabulated in Table 3. The explanation of the criteria is given below: 1

Safety: The state of being safe. Every single customer seeks for this criterion during the purchase of a car. It is analysed through the six sub criteria, namely seatbelt, body, alarm, impact, ABS (anti-lock braking system) and airbags.

2

Performance: One of the most significant aspects which satisfies the customer before buying a car. It is analysed through six sub criteria, namely: speed, braking, torque, noise, comfort and cornering.

3

Economic aspect: The customers always look into the budget before the purchase of a car model. The consumers should be satisfied with the budget in getting a car of their choice. It is analysed through the following categories: resale, insurance, price, fuel and equipment.

4

Exterior: The consumer is satisfied only by the look of the product which they purchase. It should be attractive and satisfy their needs. It deals with the model, colour, style, decoration and length.

5

Dealer: Most consumers were not aware of selecting the best car; to overcome these difficulties they seek the advice from the experts of the same field. It can be categorised into four parts, namely: expertise, belief, attitude and visit.

6

Warranty: Another aspect which the consumers look for during the purchase of a car model. It is analysed through four sub criteria, namely: spare, service, repair and satisfaction.

7

Convenience: This aspect deals with the attitude of the consumer’s convenient mode and analysed through six sub criteria, namely: operating, fittings, visibility, inside width, loading and audio.

8

Emission: The important aspect which the consumer fails to consider during the purchase. The pollutants which cause atmospheric pollution, cause damage to all living beings. The emissions categorised are NOx, smoke, hydro carbons and carbon monoxide.

65


Decision hierarchy Selection of best car model

Safety Seat belt Body Alarm Impact

ABS

Performance Speed Torque

Braking

Economic

Dealer

Exterior Model

Resale

Expertise

Style

Belief

Colour

Attitude

Visibility

Visit

Insidewidth

Price Insurance

Comfort

Fuel

Length

Warranty

Emission

Spares

NOx

Service

Smoke

Satisfaction

HC

Repair

CO

Operating Fittings

Decoration Noise

Convenience

Loading

Equipment

Audio

Cornering Airbags

Model 2

Model 1

Table 3 Goal Selection of best car

Model 4

Model 3

Identified potential of the best car model Criteria

Indices (sub criteria)

Safety

Performance

Options Model 1

Model 2

Model 3

Model 4

I1 Seat belt

Excellent 0.9

Good 0.7

Moderate 0.5

Moderate 0.5

I2 Body

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I3 Alarm

Excellent 0.9

Good 0.7

Poor 0.3

Moderate 0.5

I4 Impact

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I5 ABS

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I6 Airbag

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I7 Speed

Excellent 0.9

Poor 0.3

Moderate 0.5

Good 0.7

I8 Torque

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I9 Braking

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I10 Noise

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I11 Comfort

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

66

G. Sakthivel et al.


Identified potential of the best car model (continued) Options


Model 1

Model 2

Model 3

Model 4

Performance

I12 Cornering

Excellent 0.9

Good 0.7

Poor 0.3

Moderate 0.5

Economic aspect

I13 Resale

Poor 0.3

Moder ate 0.5

Good 0.7

Excellent 0.9

I14 Price

Poor 0.3

Moder ate 0.5

Good 0.7

Excellent 0.9

I15 Insurance

Poor 0.3

Moder ate 0.5

Good 0.7

Excellent 0.9

I16 Fuel

Excellent 0.9

Moder ate 0.5

Moderate 0.5

Poor 0.3

I17 Equipment

Poor 0.3

Moder ate 0.5

Good 0.7

Excellent 0.9

I18 Model

Excellent 0.9

Moder ate 0.5

Poor 0.3

Good 0.7

I19 Style

Excellent 0.9

Moder ate 0.5

Poor 0.3

Good 0.7

I20 Colour

Excellent 0.9

Moder ate 0.5

Poor 0.3

Good 0.7

I21 Decoration

Excellent 0.9

Moder ate 0.5

Poor 0.3

Good 0.7

I22 Length

Excellent 0.9

Moder ate 0.5

Poor 0.3

Good 0.7

I23 Expert

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I24 Belief

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I25 Attitude

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I26 Visit

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I27 Spares

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I28 Repair

Excellent 0.9

Good 0.7

Moderate 0.5

Moderate 0.5

I29 Satisfaction

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I30 Service

Good 0.7

Excell ent 0.9

Moderate 0.5

Poor 0.3

I31 Operating

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I32 Fittings

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

Criteria

Exterior

Dealer

Warranty

Convenience

A hybrid MCDM approach for evaluating an automobile purchase model Table 3 Goal Selection of best car

67

Identified potential of the best car model (continued) Criteria


Convenience

Emission

Options Model 1

Model 2

Model 3

Model 4

I33 Visibility

Excellent 0.9

Good 0.7

Moderate 0.5

Moderate 0.5

I34 Inside width

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I35 Loading

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I36 Audio

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I37 NOx

Excellent 0.9

Good 0.7

Poor 0.3

Moderate 0.5

I38 Smoke

Excellent 0.9

Good 0.7

Poor 0.3

Moderate 0.5

I39 Hydro carbons

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

I40 Carbon monoxide

Excellent 0.9

Good 0.7

Moderate 0.5

Poor 0.3

5.2 FAHP computations As a result of decision makers’ perception, eight main criteria and forty sub-criteria are used in the selection process of the technology and the decision hierarchy diagram has been established accordingly. The decision model consists of four levels, namely, the objective of the problem, main criteria, sub-criteria and alternatives, which are positioned at the high level, second level, third level and the final level respectively. After the construction of the hierarchy diagram for the problem as mentioned, the FAHP methodology requires the pair-wise comparison of the main criteria and sub-criteria in order to determine their relative weights. In this stage, questionnaire design is given to the car users and managers to furnish the details based on their experiences. The questionnaire design is given in Appendix 1. The pair-wise comparison matrices, relative weight and consistency ratio for the main criteria are shown in Table 4.

5.3 PROMETHEE computations The PROMETHEE method is proposed for the selection of a suitable car. The obtained data are tabulated in Table 3 and are normalised using equations 5 or 6 depending upon the indices. The normalised data are tabulated in Table 6. The calculation of preference functions for all the alternatives using equations (7) and (8) are tabulated in Table 7. The resulting aggregated preference function values are tabulated in Table 8 by using equation (9). The calculation of leaving and entering flows by using equations (10) and (11) are tabulated in Table 9. Finally, the net outranking flow values for each alternative are calculated by using equation (12) and then relative rankings are tabulated in Table 10.

(1/8 1/7 1/6)

(1/8 1/7 1/6)

(1/9 1/9 1/8)

(1/9 1/9 1/8)

(1/9 1/9 1/8)

Exterior

Dealer

Warranty

Convenience

Emission

(1 1 1)

(1/6 1/5 1/4)

Economic

Performance

Safety

(1 1 1)

(1/9 1/9 1/8)

(1/9 1/9 1/8)

(1/8 1/7 1/6)

(1/8 1/7 1/6)

(1/6 1/5 1/4)

(1/4 1/3 1/2)

(1 1 1)

(1 1 1)

Performance

(1/9 1/9 1/9)

(1/8 1/7 1/6)

(1/8 1/7 1/6)

(1/6 1/5 1/4)

(1/4 1/3 1/2)

(1 1 1)

(2 3 4)

(4 5 6)

Economic

(1/6 1/5 1/4)

(1/4 1/3 1/2)

(1/6 1/5 1/4)

(1/4 1/3 1/2)

(1 1 1)

(2 3 4)

(4 5 6)

(6 7 8)

Exterior

(1/4 1/3 1/2)

(1/4 1/3 1/2)

(1/4 1/3 1/2)

(1 1 1)

(2 3 4)

(4 5 6)

(6 7 8)

(6 7 8)

Dealer

(1/4 1/3 1/2)

(1/4 1/3 1/2)

(1 1 1)

(2 3 4)

(4 5 6)

(6 7 8)

(6 7 8)

(8 9 9)

Warranty

(1 1 1)

(1 1 1)

(2 3 4)

(2 3 4)

(2 3 4)

(6 7 8)

(8 9 9)

(8 9 9)

Convenience

(1 1 1)

(1 1 1)

(2 3 4)

(2 3 4)

(4 5 6)

(8 9 9)

(8 9 9)

(8 9 9)

Emission

λmax 8.94

CI 0.134

CR 0.095

Table 4

Safety

68 G. Sakthivel et al.

Pair wise comparison matrix, relative weights and consistency ratio for the main criterion

1.000

1.000

1.000

1.000

Warranty

Convenience

Emissions

1.000

Economic

1.000

1.000

Performance

Dealer

1.000

Safety

Exterior

Opt 0

1

1

1

1

1

0.4

1

1

Model 1

0.601

0.601

0.601

0.601

0.397

0.465

0.334

0.601

Model 2

0.429

0.429

0.429

0.429

0.583

0.606

0.601

0.334

Model 3

0.334

0.343

0.362

0.383

0.373

0.973

0.429

0.429

Model 4

Weighted primary grey relational coefficients δ Ck (i )

1

1

1

1

1

0.411

1

1

Model 1

0.601

0.601

0.601

0.601

0.397

0.477

0.334

0.601

Model 2

0.429

0.429

0.429

0.429

0.583

0.623

0.601

0.334

Model 3

0.334

0.343

0.362

0.383

0.373

0.973

0.429

0.429

Model 4

Normalized weighted primary grey relational coefficients δ C′ k (i )

1

1

0.34

0.39

1

0.36

1

1

Model 1

0.46

0.50

0.38

0.36

0.43

0.385

0.39

0.49

Model 2

0.37

0.44

0.43

0.45

0.39

0.46

0.44

0.43

Model 3

0.33

0.48

1

1

0.33

1

0.33

0.51

Model 4

Secondary grey relational coefficients ξCk (i )

Table 5

Criteria

A hybrid MCDM approach for evaluating an automobile purchase model Secondary grey relational coefficients

69

70

G. Sakthivel et al.


Normalised data of PROMETHEE Criteria


Alternatives Model 1

Model 2

Model 3

Model 4

I1 Seat belt

1

0.5

0

0

I2 Body

1

0.667

0.333

0

Safety

I3 Alarm

1

0.667

0

0.333

I4 Impact

1

0.667

0.333

0

I5 ABS

1

0.667

0.333

0

I6 Airbag

1

0.667

0.333

0

I7 Speed

1

0

0.333

0.667

I8 Torque

1

0.667

0.333

0

I9 Braking

1

0.667

0.333

0

Performance

I10 Noise

1

0.667

0.333

0

I11 Comfort

1

0.667

0.333

0

I12 Cornering

1

0.667

0

0.333

I13 Resale

0

0.333

0.667

1

I14 Price

0

0.333

0.667

1

Economic aspect

I15 Insurance

0

0.333

0.667

1

I16 Fuel

1

0.333

0.333

0

I17 Equipment

0

0.333

0.667

1

I18 Model

1

0.333

0

0.667

I19 Style

1

0.333

0

0.667

Exterior

I20 Colour

1

0.333

0

0.667

I21 Decoration

1

0.333

0

0.667

I22 Length

1

0.333

0

0.667

I23 Expert

1

0.667

0.333

0

I24 Belief

1

0.667

0.333

0

Dealer

I25 Attitude

1

0.667

0.333

0

I26 Visit

1

0.667

0.333

0

I27 Spares

1

0.667

0.333

0

I28 Repair

1

0.5

0

0

Warranty

I29 Satisfaction

1

0.667

0.333

0

I30 Service

0.667

1

0.333

0

I31 Operating

1

0.667

0.333

0

I32 Fittings

1

0.667

0.333

0

I33 Visibility

1

0.5

0

0

71

A hybrid MCDM approach for evaluating an automobile purchase model Table 6 Goal

Normalised data of PROMETHEE (continued) Criteria


Alternatives Model 1

Model 2

Model 3

Model 4

Convenience

I34 Inside width

1

0.667

0.333

0

I35 Loading

1

0.667

0.333

0

I36 Audio

1

0.667

0.333

0

I37 NOx

1

0.667

0

0.333

Emission

I38 Smoke

1

0.667

0

0.333

I39 HC

1

0.667

0.333

0

I40 CO

1

0.667

0.333

0

5.4 GRA computations In this section, hierarchy GRA method is projected for the selection of a suitable car among the alternatives. The questionnaire design for GRA model is given in Appendix 2. The first step of hierarchy GRA is to find out the normalised data depending on cost and benefit indices as shown in Table 3. The primary grey relational coefficient is calculated by using equations (13) to (17). The secondary grey relational coefficients are computed by using equations (18) to (24). The obtained results are tabulated in Table 5. Finally, the integrated grey relational grade for each alternative is obtained by multiplying the result of secondary grey relational coefficient matrix by weighing the vector for the criteria level with respect to the overall objective. The obtained results are tabulated in Table 10.

6

Results and discussion

The results of proposed methodology are tabulated in Table 10. Alternative Model 1 which has the highest performance value is selected as the best car using FAHP-GRA methodology. The ranking order of the alternatives with proposed FAHP-GRA is Model 1 > Model 4 > Model 3 > Model 2. To validate the results of proposed methodology, FAHP-PROMETHEE is applied and the obtained results are tabulated in Table 10. It shows that Model 1 has the best alternative like FAHP-GRA and ranking order is Model 1 > Model 2 > Model 3 > Model 4. The first ranking of both the models are similar but the preorders are changed. To show the impact of fuzzy numbers in the decision making process, the AHP-GRA is applied to the same numerical example and results obtained are tabulated in Table 10. The relative weights of the main criteria and the sub-criteria are shown in Figures 4 and 5 respectively. Figure 5 shows that the relative weights of a few criteria deviate from the AHP results. Similarly, in Figure 4, the main criteria relative weights are not matched with AHP which shows the impact of fuzzy set theory during the pair wise comparison process. However, compared with the AHP-GRA, the proposed methodologies produce better modelling during the pair-wise comparison process.

1

0.333

0.333

0.333

0.333

0.333

I8 Torque

I9 Braking

I10 Noise

I11 Comfort

I12 Cornering

0.667

0.667

0.667

I1 9 Style

I20 Colour

0

0.667

0

I18 Model

I17 Equipment

I16 Fuel

I15 Insurance

1

0.667

0.667

0.667

0.667

0.667

0.667

1

1

1

0

0.667

0

0

0.333

I6 Airbag

I7 Speed

0.667

0.667

0

0.333

0

0.333

I4 Impact

I5 ABS

1

0.667

1

(P1,P3)

0

0.333

I3 Alarm

I13 Resale

0.5

0.333

I2 Body

(P1,P2)

0.333

0.333

0.333

0

0

0

0

0

0.667

1

1

1

1

0.333

1

1

1

0.667

1

1

(P1,P4)

0

0

0

0

0.667

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

(P2,P1)

0.333

0.333

0.333

0

0

0

0

0

0.667

0.334

0.334

0.334

0.334

0

0.334

0.334

0.334

0.667

0.334

0.5

(P2,P3)

0

0

0

0

0

0

0

0

0.334

0.667

0.667

0.667

0.667

0

0.667

0.667

0.667

0.334

0.667

0.5

(P2,P4)

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

(P3,P1)

0

0

0

0

0

0

0

0

0

0

0

0

0

0.333

0

0

0

0

0

0

(P3,P2)

0

0

0

0

0

0

0

0

0

0.333

0.333

0.333

0.333

0

0.333

0.333

0.333

0

0.333

0

(P3,P4

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

(P4,P1)

0.334

0.334

0.334

0

0

0

0

0

0

0

0

0

0

0.667

0

0

0

0

0

0

(P4,P2)

0.667

0.667

0.667

0

0

0

0

0

0.333

0

0

0

0

0.334

0

0

0

0.333

0

0

(P4,P3)

Table 7

I1 Seat belt

Alternative pair


Preference functions for all the pairs of alternatives

0.333

0.333

0.333

I38 Smoke

I39 Hydro Carbons

I40 Carbon monoxide

0.333

0.333

I37 NOx

0.333

I36 Audio

0.333

0.5

I33 Visibility

I35 Loading

0.333

I34 Inside width

0.333

I32 Fittings

0

I31 Operating

I30Service

0.333

0.5

I28 Repair

I29 Satisfaction

0.333

0.333

0.333

I25 Attitude

I27 Spares

0.333

I24 Belief

I26 Visit

0.667

0.333

I23 Expert

0.667

I21 Decoration

0.667

0.667

1

1

0.667

0.667

0.667

1

0.667

0.667

0.334

0.667

1

0.667

0.667

0.667

0.667

0.667

1

1

(P1,P3)

1

1

0.667

0.667

1

1

1

1

1

1

0.667

1

1

1

1

1

1

1

0.333

0.333

(P1,P4)

0

0

0

0

0

0

0

0

0

0

0.333

0

0

0

0

0

0

0

0

0

(P2,P1)

0.334

0.334

0.667

0.667

0.334

0.334

0.334

0.5

0.334

0.334

0.667

0.334

0.5

0.334

0.334

0.334

0.334

0.334

0.333

0.333

(P2,P3)

0.667

0.667

0.334

0.334

0.667

0.667

0.667

0.5

0.667

0.667

1

0.667

0.5

0.667

0.667

0.667

0.667

0.667

0

0

(P2,P4)

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

(P3,P1)

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

(P3,P2)

0.333

0.333

0

0

0.333

0.333

0.333

0

0.333

0.333

0.333

0.333

0

0.333

0.333

0.333

0.333

0.333

0

0

(P3,P4

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

(P4,P1)

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0.334

0.334

(P4,P2)

0

0

0.333

0.333

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0.667

0.667

(P4,P3)

Table 7

I22 Length

(P1,P2)

Alternative pair

A hybrid MCDM approach for evaluating an automobile purchase model Preference functions for all the pairs of alternatives (continued)

73

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G. Sakthivel et al.

Table 8

Aggregated preference function

Alternatives

Model 1 (P1)

Model 2 (P2)

Model 3 (P3)

Model 4 (P4)

Model 1 (P1)

-

3.293

5.98

6.064

Model 2 (P2)

0.073

-

2.85

3.482

Model 3(P3)

0

0.146

-

1.327

Model 4 (P4)

0

0.638

1.188

-

Table 9

Leaving and entering flows for different alternatives

Alternatives

Leaving flow (φ+)

Model 1 (P1)

5.1123

0.496

Model 2 (P2)

2.135

4.077

Model 3(P3)

0.491

3.340

Model 4 (P4)

0.6087

3.624

Table 10

Entering flow (φ-)

Ranking of alternatives with the use of AHP-GRA, FAHP-GRA and FAHP-PROMETHEE methodologies Results of AHP-GRA

Alternatives

Integrated grey Rank relational grade

Results of FAHP-PROMETHEE

Results of FAHP-GRA Integrated grey relational grade

Rank

Net outranking Rank flow (φ)

Model 1

0.83

1

1.00

1

5.088

1

Model 2

0.43

3

0.59

4

–1.942

2

Model 3

0.42

4

0.60

3

–2.848

3

Model 4

0.55

2

0.78

2

–3.0157

4

Figure 4

Relative weights of main criteria (see online version for colours)


7

75

Relative weights of sub-criteria (see online version for colours)

Conclusions

In this paper, a decision making methodology is proposed for car selection problem. The car selection problem involves various evaluation criteria to compare car model alternatives. FAHP integrated GRA and FAHP integrated with PROMETHEE decision making methods have been used in this proposed approach. FAHP is used to compute the evaluation criteria weights and hierarchical GRA is employed to determine the priorities of alternatives. Similarly, FAHP weights are taken as the input for PROMETHEE and the priorities of alternatives are determined. The numerical example is demonstrated to show the performance of the proposed approach. The proposed decision methods can help the decision makers to choose and analyse the best car model. In addition, the strength of the proposed decision making approach is to eliminate the uncertainty and vagueness during the pair wise comparison process using fuzzy set theory. The outranking methods are used for precise ranking results of alternatives. It is evident that the proposed approaches are different from the existing car selection literature. An AHP-GRA approach is also applied in the same numerical example to show the validity of the fuzzy set theory with AHP. For further research, group decision making approaches can be developed using various MCDM techniques such as Fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and Fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) for selecting the best car.

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References Albadvi, A., Sharafi, S.A. and Sarem, G.H. (2007) ‘Application of PROMETHEE for market targeting: a case study on the TV market in Iran’, Scientia Iranica, Vol. 14, No. 3, pp.221–229. Albayrak, E. and Erensal, Y.C. (2004) ‘Using analytic hierarchy process (AHP) to improve human performance: an application of multiple criteria decision making problem’, Journal of Intelligent Manufacturing, Vol. 15, No. 4, pp.491–503. Athawale, V.M. and Chakraborty, S. (2010) ‘Facility location selection using PROMETHEE II method’, International Conference on Industrial Engineering and Operations Management Dhaka, Bangladesh, pp.221–229. Ayag, Z. and Ozdemir, R.G. (2006) ‘A fuzzy AHP approach to evaluating machine tool alternatives’, Journal of Intelligent Manufacturing, Vol. 17, No. 2, pp.179–190. Behzadian, M., Kazemzadeh, R.B., Albadvi, A. and Aghdasi, M. (2010) ‘PROMETHEE: a comprehensive literature review on methodologies and applications’, European Journal of Operational Research, Vol. 200, No. 1, pp.198–215. Bellman, R.E. and Zadeh, L.A. (1970) ‘Decision making in a fuzzy environment’, Management Science, Vol. 17, No. 4, pp.141–164. Beynon, M.J. and Wells, P. (2008) ‘The lean improvement of the chemical emissions of motor vehicles based on preference ranking: a PROMETHEE uncertainty analysis’, Omega International Journal of Management Science, Vol. 36, No. 3, pp.384–394. Brans, J.P. and Vincke, PH. (1985) ‘A preference ranking organization method’, Management Science, Vol. 31, No. 6, pp.647–656. Brans, J.P., Vincke, P.H. and Mareschal, B. (1986) ‘How to select and how to rank projects: the PROMETHEE method’, European Journal of Operational Research, Vol. 24, No. 2, pp.228–238. Buckley, J.J. (1985) ‘Fuzzy hierarchical analysis’, Fuzzy Sets and Systems, Vol. 17, No. 2, pp.233–247. Byun, D.H. (2001) ‘The AHP approach for selecting an automobile purchase model’, International Journal of Information and Management, Vol. 38, No. 5, pp.289–297. Calef, D. and Goble, R. (2007) ‘The allure of technology: how France and California promoted electric and hybrid vehicles to reduce urban air pollution’, Springer Link Policy Science, Vol. 40, No. 1, pp.1–34. Cascales, M.S.G. and Lamata, M.T. (2009) ‘Selection of a cleaning system for engine maintenance based on the analytic hierarchy process’, Computers & Industrial Engineering, Vol. 56, No. 4, pp.1442–1451. Chan, F.T.S. (2003) ‘Interactive selection model for supplier selection process an AHP’, International Journal of Production Research, Vol. 41, No. 15, pp.3549–3579. Chang, C.K. and Lu, H.S. (2007) ‘Design optimization of cutting parameters for side milling operations with multiple performance characteristics’, International Journal of Advanced Manufacturing Technology, Vol. 32, Nos. 1–2, pp.18–26. Chang, C.L., Wei, C.C. and Lee, Y.H. (1999) ‘Failure mode and effects analysis using fuzzy method and grey theory’, Kybernetes, Vol. 28, No. 9, pp.1072–1080. Chang, S.H., Hwang, J.R. and Doong, J.L. (2000) ‘Optimization of the injection molding process of short glass fiber reinforced polycarbonate composites using grey relational analysis’, Journal of Materials Processing Technology, Vol. 97, Nos. 1–3, pp.186–193. Chang, Y.H. and Yeh, C.H. (2002) ‘A survey analysis of service quality for domestic airlines’, European Journal of Operational Research, Vol. 139, No. 1, pp.166–177. Chang, Y.H., Cheng, C.H. and Wang, T.C. (2003) ‘Performance evaluation of international airports in the region of East Asia’, Proceedings of Eastern Asia Society for Transportation Studies, Vol. 4, pp.213–230.


77

Chang, Y.H., Yeh C.H. and Wang, S.Y. (2007) ‘A survey and optimization-based evaluation of development strategies for the air cargo industry’, International Journal of Production Economics, Vol. 106, No. 2, pp.550–562. Chen, G. and Pham, T.T. (2001) ‘Introduction to fuzzy sets fuzzy, logic and fuzzy control systems’, Applied Mechanics Reviews, Vol. 54, No. 6, pp.102–104. Chen, M.F. and Tzeng, G.H. (2004) ‘Combining grey relation and TOPSIS concepts for selecting an expatriate host country’, Mathematical and Computer Modeling, Vol. 40, No. 13, pp.1473–1490. Cheng, C.H., Yang, K.L. and Hwang, C.L. (1999) ‘Evaluating attack helicopters by AHP based on linguistic variable weight’, European Journal of Operational Research, Vol. 116, No. 2, pp.423–435. Chou, T.Y. and Liang, G.S. (2001) ‘Application of a fuzzy multi-criteria decision making model for shipping company performance evaluation’, Maritime Policy & Management, Vol. 28, No. 4, pp.375–392. Dagdeviren, M. (2008) ‘Decision making in equipment selection: an integrated approach with AHP and PROMETHEE’, Journal of Intelligent Manufacturing, Vol. 19, No. 4, pp.397–406. Deng, H. (1999) ‘Multi criteria analysis with fuzzy pair-wise comparison’, International Journal of Approximate Reasoning, Vol. 21, No. 3, pp.215–231. Deng, J.L. (1989) ‘Introduction to grey system theory’, Journal of Grey System, Vol. 1, No. 1, pp.1–24. Ding, J.F. and Liang, G.S. (2005) ‘Using fuzzy MCDM to select partners of strategic alliances for liner shipping’, Information Sciences, Vol. 173, Nos. 1–3, pp.197–225. Ertugrul, I. and Tus, A. (2007) ‘Interactive fuzzy linear programming and an application sample at a textile firm’, Fuzzy Optimum Decision Making, Vol. 6, No. 1, pp.29–49. Fu, C., Zheng, J., Zhao, J. and Xu, W. (2001) ‘Application of grey relational analysis for corrosion failure of oil tubes’, Corrosion Science, Vol. 43, No. 5, pp.881–889. Goumas, M. and Lygerou, V. (2000) ‘An extension of the PROMETHEE method for decision making in fuzzy environment: ranking of alternative energy exploitation projects’, European Journal of Operational Research, Vol. 123, No. 3, pp.606–613. Hsieh, T.Y., Lu, S.T. and Tzeng, G.H. (2004) ‘Fuzzy MCDM approach for planning and design tenders selection in public office buildings’, International Journal of Project Management, Vol. 22, No. 7, pp.573–584. Hsu, L.C. and Wang, C.H. (2009) ‘Forecasting integrated circuit output using multivariate grey model and grey relational analysis’, Expert Systems with Applications, Vol. 36, No. 2, pp.1403–1409. Huang, C.C., Chu, P.Y. and Chiang, Y.H. (2008) ‘A fuzzy AHP application in government-sponsored R&D project selection’, Omega the International Journal of Management Science, Vol. 36, No. 6, pp.1038–1052. Hwang, H.J. and Hwang, H.S. (2006) ‘Computer-aided fuzzy-AHP decision model and its application to school food service problem’, International Journal of Innovative Computing, Information and Control, Vol. 2, No. 1, pp.125–137. Hwang, H.S. and Ko, W.H. (2003) ‘A restaurant planning model based on fuzzy-AHP method’, ISAHP. Kahraman, C., Beskese, A. and Ruan, D. (2004) ‘Measuring flexibility of computer integrated manufacturing systems using fuzzy cash flow analysis’, Information Sciences, Vol. 168, Nos. 1–4, pp.77–94. Karsak, E.E. and Tolga, E. (2001) ‘Fuzzy multi-criteria decision-making procedure for evaluating advanced manufacturing system investments’, International Journal of Production Economics, Vol. 69, No. 1, pp.49–64. Khajeeh, M. (2010) ‘Water conservation in Kuwait: a fuzzy analysis approach’, International Journal of Industrial Engineering, Vol. 6, No. 10, pp.90–105.

78

G. Sakthivel et al.

Khoram, M.R, Shariat, M., Azar, A., Moharamnejad, N. and Mahjub, H. (2007) ‘Prioritizing the strategies and methods of treated wastewater reusing by fuzzy analytic hierarchy process (FAHP): a case study’, International Journal of Agriculture & Biology, Vol. 9, No. 2, pp.319–323. Khorasani, O. and Bafruei, M.K. (2011) ‘A fuzzy AHP approach for evaluating and selecting supplier in pharmaceutical industry’, International Journal of Academic Research, Vol. 3, No. 1, pp.346–352. Kulak, O., Durmusoglu, M.B. and Kahraman, C. (2005) ‘Fuzzy multi-attribute equipment selection based on information axiom’, Journal of Materials Processing Technology, Vol. 169, No. 3, pp.337–345. Kung, C.Y. and Wen, K.L. (2007) ‘Applying grey relational analysis and grey decision-making to evaluate the relationship between company attributes and its financial performance – a case study of venture capital enterprises in Taiwan’, Decision Support Systems, Vol. 43, No. 3, pp.842–852. Laarhoven, P.J.M.V. and Pedrycz, W. (1983) ‘A fuzzy extension of Saaty’s priority theory’, Fuzzy Sets and Systems, Vol. 11, Nos. 1–3, pp.199–227. Lai, H.H., Lin, Y.C. and Yeh, C.H. (2005) ‘Form design of product image using grey relational analysis and neural network models’, Computers & Operations Research, Vol. 32, No. 10, pp.2689–2711. Lai, Y.J. and Hwang, C.L. (1994) ‘Fuzzy multiple objective decision making: methods and applications’, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, New York. Lee, M.C. and Chang, T. (2010) ‘Linguistic variables and PROMETHEE method as tools in evaluation of quality of portal website service’, International Journal of Research and Reviews in Computer Science, Vol. 1, No. 3, pp.53–67. Lim, M.C.H., Ayoko, G.A., Morawska, L., Ristovski, Z.D. and Jayaratne, E.R. (2007) ‘The effects of fuel characteristics and engine operating conditions on the elemental composition of emissions from heavy duty diesel buses’, Fuel, Vol. 86, Nos. 12–13, pp.1831–1839. Lim, M.C.H., Ayoko, G.A., Morawska, L., Ristovski, Z.D., Jayaratne, E.R. and Kokot, S. (2006) ‘A comparative study of the elemental composition of the exhaust emissions of cars powered by liquefied petroleum gas and unleaded petrol’, Atmospheric Environment, Vol. 40, No. 17, pp.3111–3122. Lin, C.H. (2008) ‘Frequency-domain features for ECG beat discrimination using grey relational analysis-based classifier’, Computers and Mathematics with Applications, Vol. 55, No. 4, pp.680–690. Lin, J.L. and Lin, C.L. (2002) ‘The use of the orthogonal array with grey relational analysis to optimize the electrical discharge machining process with multiple performance characteristics’, International Journal of Machine Tools & Manufacture, Vol. 42, No. 2, pp.237–244. Lin, S.C., Liang, G.S. and Lee, K.L. (2006) ‘Applying fuzzy analytic hierarchy process in location mode of international logistics on airports competition evaluation’, Journal of Marine Science and Technology, Vol. 14, No. 1, pp.25–38. Lo, K.Y. (2008) ‘A novel grey relation method with analytic hierarchy process for stock selection’, Journal of Grey System, Vol. 11, No. 2, pp.97–106. Mayyas, A., Shen, Q., Mayyas, A., Abdelhamid, M., Shan, D., Qattawi, A. and Omar. M. (2011) ‘Using quality function deployment and analytical hierarchy process for material selection of body-in-white’, Materials and Design, Vol. 32, No. 5, pp.2771–2782. Mikhailov, L. (2003) ‘Deriving priorities from fuzzy pair wise comparison judgments’, Fuzzy Sets and Systems, Vol. 134, No. 3, pp.365–385. Nepal, B., Yadav, O.P. and Murat, A. (2010) ‘A fuzzy-AHP approach to prioritization of CS attributes in target planning for automotive product development’, Expert Systems with Applications, Vol. 37, No. 10, pp.6775–6786.


79

Rousis, K., Moustakas, K., Malamis, S., Papadopoulos, A. and Loizidou, M. (2008) ‘Multi-criteria analysis for the determination of the best WEEE management scenario in Cyprus’, Waste Management, Vol. 28, No. 10, pp.1941–1954. Saaty, T.L. (1980) The Analytic Hierarchy Process, McGraw-Hill, New York. Sapuan, S.M., Hambali, A., Ismail, N. and Nukman, Y. (2010) ‘Material selection of polymeric composite automotive bumper beam using analytical hierarchy process’, Springer link Journal of Central South University of Technology, Vol. 17, No. 2, pp.244–256. Taleb, M.F.A. and Mareschal, B. (1995) ‘Water resources planning in the Middle East: application of the PROMETHEE V multicriteria method’, European Journal of Operational Research, Vol. 81, No. 3, pp.500–511. Tang, Y.C. and Beynon, M.J. (2005) ‘Application and development of a fuzzy analytic hierarchy process within a capital investment study’, Journal of Economics and Management, Vol. 1, No. 2, pp.207–230. Tsaur, S.H., Chang, T.Y. and Yen, C.H. (2002) ‘The evaluation of airline service quality by fuzzy MCDM’, Tourism Management, Vol. 23, No. 2, pp.107–115. Tuzkaya, U.R. (2009) ‘Evaluating the environmental effects of transportation modes using an integrated methodology and an application’, International Journal of Environment Science and Technology, Vol. 6, No. 2, pp.277–290. Tzeng, G.H., Lin, C.W. and Opricovic, S. (2005) ‘Multi-criteria analysis of alternative-fuel buses for public transportation’, Energy Policy, Vol. 33, No. 11, pp.1373–1383. Wang, T.C., Chen, L.Y. and Chen, Y.H. (2008) ‘Applying fuzzy PROMETHEE method for evaluating IS outsourcing suppliers’, Fifth International Conference on Fuzzy Systems and Knowledge Discovery, pp.361–365. Xu, G., Tian, W., Qian, L. and Zhang, X. (2007) ‘A novel conflict reassignment method based on grey relational analysis (GRA)’, Pattern Recognition Letters, Vol. 28, No. 15, pp.2080–2087. Xu, Z.S. and Chen, J. (2007) ‘An interactive method for fuzzy multiple attributes group decision making’, Information Sciences, Vol. 177, No. 1, pp.248–263. Ye, Z.Y. (2003) ‘The selection of methods for the dimensionless standardization of index during the multi-index integral evaluation’, Zhejiang Statistics, Vol. 4, pp.24–25 (in Chinese). Zadeh, L.A. (1965) ‘Fuzzy sets’, Information and Control, Vol. 8, No. 3, pp.338–353. Zhang, K., Kluck, C. and Achari, G. (2009) ‘A comparative approach for ranking contaminated sites based on the risk assessment paradigm using Fuzzy PROMETHEE’, Environmental Management, Vol. 44, No. 5, pp.952–967. Zhou, D.Q. and Zhang, Y.H. (1995) ‘The normalization methods for economic index of the integral evaluation’, Statistics and Prediction, Vol. 6, pp.18–20 (in Chinese). Zimmerman, H.J. (1996) Fuzzy Sets Theory and its Applications, Kluwer Academic Publishers, Boston, London.

Websites http://www.siamindia.com/ (accessed on 10 March 2011).

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Appendix 1 Questionnaire design for development of FAHP model for selection of car model Read the following questions and put check marks on the pair wise comparison matrices. If a criterion on the left is more important than the matching one on the right, put the check mark to the left of the importance ‘equal’ under the importance level. If a criterion on the left is less important than the matching one on the right, put your check mark to the right of the importance ‘equal’ under the importance level.

With respect to safety (S) Q1 How important is the safety (C1) when it is compared with performance (C2)? Q2 How important is the safety (C1) when it is compared with economic (C3)? Q3 How important is the safety (C1) when it is compared with exterior (C4)? Q4 How important is the safety (C1) when it is compared with dealer (C5)? Q5 How important is the safety (C1) when it is compared with convenience (C6)? Q6 How important is the safety (C1) when it is compared with warranty (C7)? Q7 How important is the safety (C1) when it is compared with emission (C8)?

With respect to performance (P) Q8 How important is the performance (C2) when it is compared with economic (C3)? Q9 How important is the performance (C2) when it is compared with exterior (C4)? Q10 How important is the performance (C2) when it is compared with dealer (C5)? Q11 How important is the performance (C2) when it is compared with convenience (C6)? Q12 How important is the performance (C2) when it is compared with warranty (C7)? Q13 How important is the performance (C2) when it is compared with emission (C8)?


81

With respect to economic (E) Q14 How important is the economic (C3) when it is compared with exterior (C4)? Q15 How important is the economic (C3) when it is compared with dealer (C5)? Q16 How important is the economic (C3) when it is compared with convenience (C6)? Q17 How important is the economic (C3) when it is compared with warranty (C7)? Q18 How important is the economic (C3) when it is compared with emission (C8)?

With respect to exterior (R) Q19 How important is the exterior (C4) when it is compared with dealer (C5)? Q20 How important is the exterior (C4) when it is compared with convenience (C6)? Q21 How important is the exterior (C4) when it is compared with warranty (C7)? Q22 How important is the exterior (C4) when it is compared with emission (C8)?

With respect to dealer (D) Q23 How important is the dealer (C5) when it is compared with convenience (C6)? Q24 How important is the dealer (C5) when it is compared with warranty (C7)? Q25 How important is the dealer (C5) when it is compared with emission (C8)?

With respect to convenience (C) Q26 How important is the convenience (C6) when it is compared with warranty (C7)? Q27 How important is the convenience (C6) when it is compared with emission (C8)?

With respect to warranty (W) Q28 How important is the warranty (C7) when it is compared with emission (C8)?

Performance (c2)

Economic (c3)

Q13

Q14

Performance (c2)

Q10

Performance (c2)

Performance (c2)

Q9

Performance (c2)

Performance (c2)

Q8

Q12

Safety (c1)

Q7

Q11

Safety (c1)

Safety (c1)

Q4

Safety (c1)

Safety (c1)

Q3

Q6

Safety (c1)

Q5

Safety (c1)

Q2

Criteria

Q1

Que

With respect to best Extreme

Very strong Strong

Moderate Equal

Just equal Equal Moderate Strong

Very strong

Importance (or) preference of one criterion over another Extreme

Exterior (c4)

Emission (c8)

Warranty (c7)

Convenience (c6)

Dealer (c5)

Exterior (c4)

Economic (c3)

Emission (c8)

Warranty (c7)

Convenience (c6)

Dealer (c5)

Exterior (c4)

Economic (c3)

Performance (c2)

Criteria


Economic (c3)

Exterior (c4)

Q18

Q19

Dealer (c5)

Dealer (c5)

Convenience (c6)

Convenience (c6)

Warranty (c7)

Q25

Q26

Q27

Q28

Q23

Q24

Exterior (c4)

Dealer (c5)

Q22

Exterior (c4)

Economic (c3)

Q17

Exterior (c4)

Economic (c3)

Q16

Q21

Economic (c3)

Q15

Q20

Criteria

Que

With respect to best Extreme

Very strong Strong

Moderate Equal

Just equal Equal Moderate Strong

Very strong

Importance (or) preference of one criterion over another Extreme

Emission (c8)

Emission (c8)

Warranty (c7)

Emission (c8)

Warranty (c7)

Convenience (c6)

Emission (c8)

Warranty (c7)

Convenience (c6)

Dealer (c5)

Emission (c8)

Warranty (c7)

Convenience (c6)

Dealer (c5)

Criteria


83

Evaluation criteria

Performance of ABS feature

Impact protection systems

Seat belt flexibility

Body safety

Car function during speed driving

Braking capacity

Noise during driving

Cornering function

Seating comfort

Mileage

S. no.

1

2

3

4

5

6

7

8

9

10

Excellent

Moderate

Model – 1

Good

Poor

Moderate

Model – 2 Excellent Good

Poor

Moderate


Poor

Moderate


Poor


Appendix 2

Questionnaire design for development of GRA model for selection of car model

Evaluation criteria

Specific model

Style

Car colour

Interior decoration

Length of the car

Belief in dealer’s assurance

Dealer’s attitude

Dealer’s expertise

Ease of operating

S. no.

11

12

13

14

15

16

17

18

19

Excellent

Moderate

Model – 1

Good

Poor

Moderate


Poor

Excellent

Moderate

Model – 3 Good

Poor

Excellent

Moderate

Model – 4 Good

Poor


Questionnaire design for development of GRA model for selection of car model (continued)

85