E-SERVICE QUALITY OF INTERNET BASED BANKING USING COMBINED FUZZY AHP AND FUZZY TOPSIS

Original scientific paper Many researchers have used service quality scales for measuring service quality of banking sector including e-banking. Technology and technological tools are rapidly changed and every household has computers, pads and smartphones. They also get used to make banking operations with computers, pads or smartphones. In this study, we employed a fuzzy based prioritization using AHP and TOPSIS methods to the e-banking service quality indicators. The survey was carried out with the banking specialists and managers in both public and private banks inTurkey. The results provide helpful information for both web designers and internet users for developing and using the e-banking.


Introduction
Services are located in all areas of our lives.For instance, we use communication and transportation service almost every day.Also we go to the bank for financial operation or go to the supermarket to meet daily needs and so on.All of these services and others are widely used depending on developments in information technology; the importance of services in our lives is increasing every day.On the other hand, in the service industry, the performance indicators are very important such as productivity, quality, efficiency, customer satisfaction.However, measurement of performance in service businesses because of the characteristics of services is not very easy.
For competitive survival, companies are focusing on areas in their operations that might give them an edge over their competitors.A key area has been the delivery of high levels of service quality [12].During the past few decades service quality has become a major area of attention to practitioners, managers and researchers owing to its strong impact on business performance, lower costs, customer satisfaction, customer loyalty and profitability [6, 8, 13÷17].Many researchers have defined the service quality and they identified the construct of it.In the literature the subject on how consumers perceive the service a company provides has been studied extensively, as evidenced by the research literature [11].From an academic perspective McKenzie [11] cited in the literature from Cronin et al. (1994) and Zeithaml (2000) that has explored the theoretical framework and conceptualization of the construct, and from a practitioner standpoint, the linkages between providing high quality service and attaining superior firm performance.In this study, the service quality models are listed and explained.In the following sections, the employed methodology as the Fuzzy AHP and TOPSIS and the hierarchical model are explained with the numerical example and then the results are discussed in the final section.

Service quality models
Measuring service quality has so many difficulties for service providers.The reason for these difficulties is the unique characteristics of service such as inseparability, intangibility, perishability and heterogeneity.Many of researchers have developed the scales for measuring the quality of retail service.Seth et al. [14] discuss these scales in their study.These scales are listed in Tab. 1.

Methodology used
Many of the researchers measure the service quality by using these scales; especially SERVQUAL has been used in a number of studies [1,9,10,18].In this paper, a systematic and practical methodology is developed and presented for the assessment of internet banking among many alternatives based on fuzzy models using linguistic variables.
The sample study of the methodology has been carried out with internet bank specialists.First of all a literature review is done on the criteria for the evaluation of internet banking.Hierarchical E-Servqual model has been used for evaluation.
Moreover, the list of banks is gathered and a question form is prepared asking the pair wise comparison and evaluation of each criterion for each bank based on fuzzy AHP and fuzzy TOPSIS, respectively.
The first phase of the methodology consists of weighting the hierarchical criteria set via fuzzy-AHP method so that the weights are calculated in a pair wise comparison manner which is the advantage of AHP method.In the second phase, the alternative banks are evaluated by considering each criterion in the bottom level of the criteria set.The evaluation process is carried out according to TOPSIS methodology which depends on linguistic variables and fuzzy logic.
TOPSIS methodology concerns the distances of each alternative evaluation from negative ideal solution and positive ideal solution.Thus, the results of the solution show the closeness of each alternative that represents the importance among others.There exist two reasons to use TOPSIS model in the evaluation phase instead of any AHP method; when there are so many alternatives to be compared, then AHP method may generate inconsistency problem which is approved by so many studies in literature.The second reason is the complexity of comparison process; because alternatives should be evaluated more often than criteria set, the higher the number of alternatives, the higher the complexity.Instead of that, it would be more practical to use TOPSIS which includes linguistic evaluations based on fuzzy logic.The purpose of this model is to identify the dimensions associated with service quality in a traditional managerial framework of planning, implementation and control.

Cronin and Taylor, 1992 Performance only model
The authors investigated the conceptualization and measurement of service quality and its relationship with consumer satisfaction and purchase intentions.

Mattson, 1992
Ideal value model of service quality This model identified that the expectation is treated as belief about having desired attributes as the standard for evaluation.

Teas, 1993 Evaluated performance and normed quality model
The author proposed two frameworks for service quality.One of them is evaluated performance and other is normed quality model.

Berkley and Gupta, 1994 IT alignment model
This model links the service and the information strategies of the organization.According to the model, relationship between service quality and information system is very important so that strategies for both must be tightly coordinated and aligned.The mathematical formulations for phase 1 and phase 2 are:

Phase 1: Criteria Importance Weighting: Fuzzy-AHP Methodology
To apply the process depending on the hierarchy, according to the method of Chang's (1992) extent analysis, each criterion is taken and extent analysis for each criterion, g i ; is performed.Therefore, m extent analysis values for each criterion can be obtained by using the following notation [7]: , where g i is the goal set (i = 1, 2, 3, 4, 5,..., n) and all the j g i M (j = 1, 2, 3, 4, 5,..., m) are Triangular Fuzzy Numbers (TFNs).The steps of Chang's analysis can be given as in the following: Step 1: The fuzzy synthetic extent value (S i ) with respect to the i th criterion is defined as the following Eq.(1).
To obtain Eq. ( 2): perform the "fuzzy addition operation" of m extent analysis values for a particular matrix given in Eq. ( 3) below, at the end step of calculation, new (l, m, u) set is obtained and used for the next: , , , where l is the lower limit value, m is the most promising value and u is the upper limit value.
To obtain the following Eq.( perform the "fuzzy addition operation" of j i g M (j = 1, 2, 3, 4, 5, ..., m) values given as Eq. ( 5): and then compute the inverse of the vector in the Eq. ( 6) Step 2: The degree of possibility of is defined as Eq. ( 7) and x and y are the values on the axis of membership function of each criterion.This expression can be equivalently written as given in Eq. ( 8) below: Figure 1 The intersection between M1 and M2 [19] where d is the highest intersection point m (see Fig. 1) [19].
Step 4.Via normalization, the normalized weight vectors are given in Eq. ( 12) below: , )) ( ..., ), ( ), ( ), ( ), ( ), ( ( where W is non-fuzzy numbers. To evaluate the questions, people only select the related linguistic variable, then for calculations they are converted to the following scale including triangular fuzzy numbers developed by [4] and generalized for such analysis as given in Tab. 2. By using these linguistic statements and given in Tab. 2, criteria set are evaluated with the equations given in phase 1 (Eqs.(1)÷( 12)) weight of each criterion is obtained and so that the weights can be used in TOPSIS methodology, they are converted to trapezoidal fuzzy number such as (a,a,a,a).

Phase 2: TOPSIS and Linguistic Variables for Ratings
By considering this main concept of TOPSIS model is implemented according to the following steps: 1) Normalize the evaluation matrix: x ij is the evaluation matrix R of alternative i under the evaluation criterion j.After normalization, the elements of matrix R are converted into r ij .Normalization is carried out by one of the methods which convert them into the numerical value, i.e. between 0÷1, according to the characteristics of the problem [2].
2) Construct the weighted normalization matrix according to the values determined for each criterion.These weights (w ij ) can be obtained by any method such as eigenvector, AHP, fuzzy numbers, linear programming models, etc., then these weight vector is multiplied by normalized matrix R to obtain the weighted normalized matrix v ij .
3) Determine the negative and positive ideal solutions.
4) Calculate the separation measure.This measure is selected among the measures for calculating the distances.This can be an Euclidean distance [3] or vertex distance [2].
5) Calculate the negative closeness to the ideal solution.The relative closeness of the i th alternative with respect to the ideal solution is calculated by negative distance over total distance.6) Rank the priority: a set of alternatives is sorted according to descending order of relative closeness.
Fuzzy triangular and trapezoidal numbers are used to evaluate each bank alternative.The linguistic variable for evaluation lies between "very poor" and "very good", the membership function set is given in Fig. 2, and as an example, the linguistic variable "Very Good (VG) " can be represented as (8, 9, 9, 10), the membership function of which is given in Eq. ( 13): Figure 2 Linguistic variables for ratings [2] In fact, evaluation of internet banking is a multiplecriteria decision-making problem, which may be described by means of the following sets [2]: (1) a set of K users called E = {D 1 ; D 2 ; ...; D K } (2) a set of m possible bank alternatives called A = {A 1 ; A 2 ; ...; A m } (3) a set of n criteria, C = {C 1 ; C 2 ; ...; C n } with which internet banking performances are measured; (4) a set of performance ratings of A i (i = 1; 2; ...; m) with respect to criteria C j (j = 1; 2; ...; n), called X = {x ij ; i = 1; 2; ...; m; j = 1; 2; ...; n} Assume that a decision group has K decision makers, and the fuzzy rating of each decision-maker D k (k = 1; 2; ..., K) can be represented as a positive trapezoidal fuzzy number k R ~(k = 1; 2; ...; K) with membership function . A good aggregation method should consider the range of fuzzy rating of each decision-maker.It means that the range of aggregated fuzzy rating must include the ranges of all decision-makers' fuzzy ratings.Let the fuzzy ratings of all decision makers be trapezoidal fuzzy numbers k R ~= (a k ; b k ; c k ; d k ), k = 1; 2; ...; K. Then the aggregated fuzzy rating can be defined as R ~= (a; b; c; d), k = 1; 2; ...; K. Eqs. ( 14) to (17) shows the detailed computations: where After the ratings are aggregated into one matrix normalized weighted matrix is constructed by calculating Eq. ( 18): As mentioned before, weight of each criterion is calculated using Fuzzy-AHP method which produces crisp weights through fuzzy numbers.Thus, in order to aggregate weights with ratings, weights are assumed as trapezoidal fuzzy numbers which have equal values (a = b = c = d).Then rating matrix is multiplied by weight matrix and finally weighted normalized matrix is obtained.
The distance of each alternative (internet banking) from A * and A -can be currently calculated with Eqs.
where d v (.,.) is the vertex distance measurement between two trapezoidal fuzzy numbers that is calculated by Eq. ( 23): . 4 In other words, bank A i is closer to the FPIS (A * ) and farther from FNIS (A − ) as CC i approaches to 1.According to the descending order of CC i , the ranking order of all banks is determined and the best one among a set of feasible banks is selected.For evaluation process, approval status for each alternative is defined in Tab. 3 which can also be used for further evaluation when a decision is required for any bank.
Table 3 Approval status [2] Closeness coefficient (CC i ) Evaluation status Do not recommend Recommend with high risk Recommend with low risk Approved and preferred

Model explanation
First step of our model is to determine the web site evaluation criteria of e-banking.In e-sq measurement of e-banking web sites, the objective is to determine the best e-banking service delivery performance among the most preferable public and private banks of Turkey.Figure 3 depicts the hierarchy of the e-banking website service quality model.According to the hierarchical model of our study, we have determined the web site prioritization weights of banks.Therefore, the pair-wise comparisons with linguistic and fuzzy terms are performed from the experts' judgments.At the end of the F-AHP process, the prioritization results of the e-service quality of internet based banking are obtained.
The following step after the prioritization of e-SERVQUAL criteria is to classify the web sites of the alternative internet based banking.The fuzzy scale is used the same as for the AHP and the decision matrix with alternatives and criteria is carried out.In this study there are 6 internet based banking web sites in which 3 public banks and 3 private banks alternatives which belong to L A = Vakifbank (www.vakifbank.com.tr),L B = Halkbank (www.halkbank.com.tr),L C = Ziraat Bank (www.ziraat.com.tr),L D = İs Bank (www.isbank.com.tr),L E = Yapi Kredi Bank (www.yapikredi.com.tr),L F = Garanti Bank (www.garanti.com.tr).In the finalization of the methodology, the ranking of the web sites is determined.

Computational results
According to the criteria set, hierarchy structure pair wise comparisons within Fuzzy-AHP local and global importance weights are obtained as given in Tab. 4.

Results
The objective of this research was to present a hybrid approach based on SERVQUAL and fuzzy TOPSIS for evaluating e-service quality of internet based banking alternatives in order to obtain to best qualified alternative that satisfies the needs and the expectations of e-users.The detailed literature and SERVQUAL scales are mentioned and then e-SERVQUAL framework was proposed for the internet based banking web sites.We develop a questionnaire for collecting data for evaluating the quality of internet based banking.After these steps, the questionnaire responses are aggregated to generate an overall performance score for measuring service quality using Fuzzy AHP and for ranking the alternatives using Fuzzy TOPSIS method.We perform AHP and TOPSIS methods in fuzzy environment for reducing the uncertainty of human decisions in assigning the evaluation of criteria.There are also many other multi criteria decision making techniques for selection of the best alternative as Analytic Network Process, DEMATEL, Electre etc.For further research, the application of techniques combined with these can be used for the service quality models and the selection of the best among the alternatives.The model proposed in this study also could be carried out to investigate the customer expectations and determine the web based service quality.

.
(21)÷(22): is defined to determine the ranking order of all possible s once * i d and − i d of each banks A i (i = 1; 2; ...; m) has been calculated.The closeness coefficient represents the distances to the fuzzy positive-ideal solution (A * ) and the fuzzy negative-ideal solution (A − ) simultaneously by taking the relative closeness to the fuzzy positive-ideal solution.The closeness coefficient (CC i ) of each alternative (banks) is calculated in Eq. (24):

Table 4
Fuzzy -AHP results for each criterion

Table 6
Distances between banks and FPIS with respect to each criterion

Table 7
Distances between Banks and FNIS with Respect To Each Criterion

Table 8
Computations of di*, di -and CCi