Evaluating Airline Service Quality Using Fuzzy DEMATEL and ANP

A hybrid fuzzy MADM method is proposed in this paper for evaluating airline service quality. Fuzzy set theory is used since it helps in measuring the ambiguity of concepts associated with human being’s subjective judgment. After reviewing service quality evaluation models especially in airline industry, SSQAI model was adopted as a construct for evaluating airline service quality in Iran. Fuzzy DEMATEL was applied to determine the degree of influence and impact of criteria on each other and extract cause and effect relations between them that helped in ranking criteria based on degree of relationship. Then, ANP network map was constructed based on the relation map generated from Fuzzy DEMATEL analysis. Fuzzy ANP approach assisted in prioritizing criteria based on the need for improvement and enabled in a more accurate measurement in decision making process taking the advantage of using linguistic variables. Fuzzy DEMATEL results demonstrates that expertise, Problem-solving, and conduct has the most influence on other factors and in opposite Valence, Waiting Time, Comfort are the factors which get the most impact from other factors and according to Fuzzy ANP analysis Valence, Convenience, Problem-solving, and Safety&Security are the factors with most priorities that need improvement.


Introduction
Nowadays, delivery of high-quality service has become a marketing requirement among air carriers as a result of competitive pressure (Ostrowski, O'Brien and Gordon, 1993). In recent years, competition between Iranian airlines has increased, since the airlines try to gain more or at least not to lose their market share of passenger air transportation and significant advances in communication and transportation technology has changed the world into a global village and let to raise of air travel rates. So researches in airline service quality, has obtained a major significance. Although a lot of researches has been conducted in airline service quality in different countries, there is still a little research concerning airline service quality in Iran.
Delivering high-quality service leads to satisfaction and loyalty of the airline passengers (Kotler, 1991) and enhances airlines to stay up in competitive environment of passenger transportation (Nathanail, 2008). Airlines are required to keep the essential services and minimize efforts spent on the less important services while still maintaining passenger perceptions of airline service quality (Liou, Hsu, Yeh and Lin, 2011) in an accepted level and they have to understand what passengers expect from their services in order to better serve their needs.
With different daily decision making problems of diverse intensity in airline service quality evaluation, the results can be misleading if the fuzziness of human decision-making is not taken into account. This study get the advantage of fuzzy decision-making theory, considering the possible fuzzy subjective judgment of evaluators during airline service quality evaluation.

Literature Review
In today's competitive environment, delivering desirable service quality is vital for the airline's survival, competitiveness, profitability and sustained growth. High quality service results in retaining existing passengers and enticing passengers from other airlines which leads to differentiate airline image from competitors. Promoting high quality service plays a key role in generating profits (Zeithaml, Berry, Parasuraman, 1996). Offering high quality services will increase customer satisfaction, leading to consumer retention and encouraging recommendations (Nadiri and Hussain, 2005). Quality is not a singular but a multi-dimensional phenomenon. Moreover, the utility value of "service quality" determinants are situationdependent (Ghobadian, Speller and Jones, 1996). Parasuraman, Zeithaml and Berry (1985) defined the concept of service quality as a comparison between customers' expectations and actual service performance.
Park, Robertson, and Wu (2006) indicate that many airlines have difficulty in using a proper scale to evaluate service quality in order to appropriately assess and improve their service performance. Pakdil and Aydin (2007) modified SERVQUAL and proposed 34 criteria classified in eight dimensions to measure service quality in the airline industry. They used factor analysis to extract the eight dimensions that are: employees, tangibles, responsiveness, reliability and assurance, flight patterns, availability, image and empathy. Liou and Tzeng (2007) mentioned employees service, Safety and reliability, On-board service, Schedule, Ontime performance Frequent Flyer Program as airline service quality factors. Gilbert and Wong (2003) found incorporating measures of reliability, assurance, facilities, employees, flight patterns, customization and responsiveness as service quality factors. They used a 26-item questionnaire to compare passengers' expectations to their actual perceived airline service quality. Kuo and Liang (2011) used Costs of processing time, Convenience, Comfort, Information visibility, Courtesy of staff, Security, Reaction capacity in airline service quality measurement.
MCDM methods have attracted many researchers to measure airlines integrated service quality level based on hierarchical concept and to make suggestions for improvement (Chang and Yeh, 2002;Liou and Tzeng, 2007;Tsaur, Chang and Yeh, 2002;Liou et al., 2011). Brady and Cronin (2001) believe that customers form their service quality perceptions on the basis of evaluating performance at multiple levels and ultimately combine these evaluations to arrive at an overall service quality perception. Dabholkar, Thorpe and Rentz (1996) and Brady & Cronin (2001) Suggest that service quality should be based on a hierarchical concept. A review of some airline service quality measurements is shown in Table. 1.

Pakdil and Aydin (2007)
Factor Analysis, Weighted SERVQUAL and Convenience (C11). Some of the models dimensions and criteria, based on Wu and Cheng (2013) are described to reduce ambiguity as follows: Interaction quality dimension; focuses on interaction between customers and employees in the service industry Conduct; includes the meaning of attitude and behavior. Expertise; is identified as the degree to which the interaction is affected by the employee's task-oriented skills; outcome dimension; focuses on outcome of the service act and indices what customers gain from service; Valence; focuses on the attributes dominating whatever customers accept the service or not. Physical environment quality dimension refers to the physical features of the service production process. Access quality; refers to the ease and speed with which people reach their desired information and locations. Information is referred to the feasibility of obtaining up-to-date information about service variety using phone and internet in an easy and comfortable way. The Convenience is based on something that is intended to save resources (i.e., time, energy) or frustration.

Methodology
By consulting Iranian airline experts, we found eleventh criteria in airline service quality proposed by Wu and Cheng (2013) as SSQAI model which is a performance-based measurement scale in a hierarchical structure specialized in measuring airline service quality.
First, Fuzzy DEMATEL was performed to find out relation of criteria with each other. Direct relation matrix generated in Fuzzy DEMATEL is used as an input in Fuzzy ANP. Then, Fuzzy ANP technique was used to determine need for improvement importance of each evaluation criteria, with calculating criteria rank due to expert's opinions. Sum of criteria in each cluster demonstrates weight of that cluster. The SSQAI model construct used in this paper is shown in Fig. 1. Our respondents involved 45 experts consists of 12 airline managers, 16 Aviation specialists, 17 Frequent fliers of major Iranian airlines of Mahan, IranAir and Aseman that participated in evaluating criteria of airline service quality that helped us with filling fuzzy DEMATEL and ANP questionnaires.

Fuzzy Set Theory
The terms of expressions ''Not very clear'', ''probably so'', ''very likely'', can be heard very often in daily life, and their commonality is that they are more or less tainted with uncertainty. It is very difficult for conventional quantification to express reasonably those situations that are overtly complex or hard to define; thus, notion of a linguistic variable is necessary in such situations (Zadeh, 1975). Fuzzy Theory firstly was introduced by Zadeh (1965). Fuzzy set theory is basically a theory of classes with non-sharp boundaries. This theory is a mathematical theory designed to model the vagueness or imprecision of human cognitive processes (Ayag and Ozdemir, 2012). Bellman and Zadeh (1970) described the decisionmaking method in fuzzy environments. Since then an increasing number of studies have dealt with uncertain fuzzy problems by applying fuzzy set theory. A triangular fuzzy number is shown in Fig. 2. Figure 2. A triangular fuzzy number

Fuzzy DEMATEL
All factors in a complex system may be either directly or indirectly related; therefore, it is difficult for a decision maker to evaluate a single effect from a single factor while avoiding interference from the rest of the system (Liou and Tzeng, 2007). DEMATEL technique is based on graph theory. It enables decision-makers to separate multiple measurement criteria into a cause and effect group to realize causal relationships more easily. In addition, directed graphs, called digraphs, represent a communication network or a domination relationship among entities and their groupings (Chen and Chen, 2010). This paper uses Fuzzy DEMATEL method in classifying and analyzing structural relationship of criteria in airline service quality. The steps of fuzzy DEMTEL are as follows:

Defining Fuzzy Linguistic Scale
For dealing with the vagueness of experts' opinions and expressions in decision making, linguistic ambiguities are represented through the conversion of linguistic variables into fuzzy numbers. The linguistic variable scale with triangular fuzzy numbers used here is seen in Table.2. This fuzzy linguistic scale formerly was applied in a fuzzy DEMATEL analysis by Wu and Lee (2007).

Calculating initial direct-relation average matrix
Based on groups of direct matrices from experts, we can generate an average matrix Z in which each element is mean of the corresponding elements in the experts' direct matrices. Zij is presented as the degree to which the criterion i affects the criterion j. Each part of triangular fuzzy number (l, m, u) is averaged. The average Matrix Z is calculated as follows:

Normalizing initial direct-relation matrix
To transform the various criteria scales into a comparable scale, the normalized directrelation matrix X = [Xij] can be obtained through Eq. (1) and (2), in which all Z fuzzy numbers are divided by r,

Acquiring total relation matrix T
Each part of the total-relation matrix T can be acquired through eq. (3), in which matrix I is denoted as the identity matrix. The element tij indicates the indirect effects factor i has on factor j, so the matrix T can reflect the total relationship between each pair of system factors. Matrix T is acquired as follows: For generating each item of matrix T these relations should be calculated:

Defuzzificating of matrix T
"Defuzzification" is selection of a specific crisp element based on the output fuzzy set and it also includes converting fuzzy numbers into crisp scores. The commonly used defuzzification method is centroid method commonly called as the Center of Area (COA) or center of gravity (COG) (Opricovic and Tzeng, 2003). The process of defuzzification has been proposed to locate the best non-fuzzy performance (BNP) value. Based on this method the following relation is formulated for converting a fuzzy number into crisp number Xcrisp.
For a triangular fuzzy number N= (l, m, u) best non fuzzy performance (BNP) value for triangular fuzzy performance score of COA method, can be derived from the following relation: This method is adopted in this paper since it has been widely used in the literature due to its simplicity and not requiring analyst's personal judgement. Defuzzificated Total influence matrix T is shown in Table. 3.

Setting a threshold value and Filtering data lower than the threshold value
It is necessary to set a threshold value to filter out negligible effects in matrix T because it helps explain the structural relation among factors while keeping the complexity of the whole system to a manageable level. After defining the threshold value as 'P', only the factors with greater effects than the threshold value in matrix T will be shown in an IRM. In setting threshold value, after defuzzificating matrix T, due to experts' opinions, the average of defuzzificated matrix T was adopted as the threshold value (P=0.1011).This filtered data (see Table. 4) will be used to construct ANP network relation map.

Calculating the cause and effect relation of criteria
To calculating the impact of criteria on each other and gain relation degree between criteria, we compute sum of each rows as Ri and sum of each column as Cj in matrix T through Eqs below. Respectively. R is generated as follows: Similarly, C is generated as follows: The sum of row i, which is denoted as Ri, represents all direct and indirect influence given by factor i to all other factors. Similarly, the sum of column j, which is denoted as Cj summarizes both direct and indirect impact received by factor j from all other factors.

Calculating impact-relation degree of criteria
Naturally, when i = j, Ri+Cj shows all effects given and received by factor i. That is, Ri+Cj indicates both, factor i's impact on the whole system and other system factors' impact on factor i. hence, the indicator Ri+Cj can represent the degree of interact that factor i has with other factors in the entire system.
On the contrary, again when i=j, the difference of the two, Ri-Cj shows the net effect and influence that factor i has on the system. Specifically, if the value of Ri-Cj is positive, the factor i is a net cause, exposing net causal effect on the system.
When Ri-Cj is negative, the factor is a net result clustered into effect group. Values of (D+R) and (D-R) are shown in Table. 5.

Obtaining crisp scores of (R+C) and (R-C)
We use BNP here for gaining crisp scores of (R+C) and (R-C) sinces it is needed for drawing impact-relation map.
Crisp values of (R+C) def and (R-C) def can be seen in Table. 6.

Drawing cause-effect relationship map based on (R + C) def and (R -C) def
A cause-effect diagram can be drawn by mapping the dataset of (R + C) def and (R-C) def . And the complex interrelationship among factors is visualized through the diagram construction process. Crisp scores are used to construct cause-effect relation diagram. The horizontal axis (R+C) is made by adding R to C and the vertical axis (R-C) is made by subtracting R from C. This diagram is shown in Fig. 3.

Fuzzy ANP
ANP incorporates feedback and interdependent relationships among decision attributes and alternatives (Saaty, 1996).conventional ANP seems inadequate to capture decision maker's requirements explicitly because of uncertainty in human preference. Fuzzy ANP approach allows a more accurate description of the decision making process. Fuzzy sets could be incorporated with the pairwise comparison as an extension of ANP (Ayag and Ozdemir, 2012).
The steps of the Fuzzy ANP analysis proposed in this study, developed based on (lee, Kang, Yang and Lin, 2010) is conducted as follows:

Defining Fuzzy Linguistic Scale
Fuzzy Linguistic scale adopted in this paper for analysing Fuzzy ANP (shown in Table. 7) Zhou (2012) has been used this fuzzy scale in Fuzzy ANP calculation.  Absolutely important (9,9,9) (

Constructing network structure and questionnaire
The problem is decomposed into a rational system like a network. The structure is obtained according to experts opinions through filtered total relation matrix of fuzzy DEMATEL analysis. The problem is composed into a network, as shown in Fig. 4. Base on the relation between criteria in network structure, the questionnaire is constructed.

Employing fuzzy pairwise comparisons and Checking consistency of comparison matrices
Decision makers are asked to pairwise compare the elements in a questionnaire. The scores of pairwise comparison of each part of the questionnaire from all experts are transformed into linguistic variables by the transformation concept listed in Table. 6 and for each decision maker, pairwise comparison Matrices are formed. For getting accurate results in our survey, adequate explanations on survey questions were given to experts, so the experts could understand the questionnaire clearly.
The quality of ultimate decision of the ANP process is strongly related to the consistency of judgments that decision makers demonstrate during the series of pairwise comparisons. When CR is less than 0.10, the comparisons are acceptable, otherwise not (Saaty, 1996).If the consistency test fails, the expert is asked to fill out the specific part of the questionnaire again. Since consistency ratio for all of comparisons filled by experts in the questionnaires is less than 0.1, the expert's judgment is consistent.

Making aggregated pairwise comparison matrix
When all pairwise comparison matrices of the experts have passed the consistency test, we can aggregate expert's opinions with making aggregated pairwise comparison matrix. For doing this, the fuzzy pairwise comparison matrices with respect to the same element are aggregated into one single fuzzy pairwise comparison matrix through the geometric mean method. If there are k experts, every pairwise comparison between criteria has k positive reciprocal triangular fuzzy numbers. Geometric average approach is employed to aggregate decision-makers' responses.

Defuzzificating aggregated fuzzy pairwise comparison matrix
Applying the Center of Area (COA) method, fuzzy aggregated pairwise comparison matrix is defuzzified into an equivalent matrix with crisp data using best non fuzzy values.

Calculating priority vectors and forming unweighted super matrix
Derive priority vectors for all aggregated comparison matrices can be calculated as follows: Where A is the matrix of pairwise comparison, w is the eigenvector, and λmax is the largest eigenvalue of A. Saaty (1996) declares that for obtaining global priorities in a system with interdependent influences, the local priority vectors are entered in the appropriate columns of a matrix, known as an unweighted supermatrix, as follows: 21  In the supermatrix, w21 is a vector that represents the impact of the goal on the criteria, W32 is a matrix that represents the impact of criteria on sub-criteria, W22 indicates the interdependency of the criteria, W33 indicates the interdependency of the sub-criteria, and I is the identity matrix. Due to Priority vectors of aggregated comparison matrices, the unweighted supermatrix is calculated in Table. 8.

Transforming Unweighted Supermatrix into Weighted Supermatrix
For transforming an unweighted supermatrix to a weighted supermatrix, the supermatrix must be transformed first to make it stochastic; that is, each column of the matrix sums to unity. the relative importance of the clusters in the supermatrix with the column cluster (block) as the controlling component, should be determined (Saaty1996). Giving equal weights to the blocks in the same column makes each column sums to unity. The weighted supermatrix is shown in Table. 9. Table 9. Weighted supermatrix

Calculating the limit supermatrix
To achieve a convergence on importance weights, the weighted supermatrix is raised to powers to capture all interactions and to reach stability. The weighted supermatrix is raised to the power of 2k +1 to obtain the limit supermatrix. The entries in the same row are the global weights of each measurement criterion. Priorities generated from limit supermatrix are shown in Table. 10.
Raising a matrix to powers gives the long-term relative influences of the elements on each other.to achieve a convergence on the importance weights, the weighted supermatrix is raised to the power of 2k+1,where k is an arbitrarily large number, and this new matrix is called the limit supermatrix (saaty,1996).

Conclusions
After reviewing the literature and different factors in evaluating airline service quality and according to experts' opinions, the SSQAI model with its eleven criteria was selected for evaluating Iran's airline industry in domestic flights. According to fuzzy DEMATEL results, factors with more influence and effective power on the other factors (positive R-C) include expertise, Problem-solving, conduct, tangibles, Information, and cleanliness, that are placed in cause factors category and the other factors which are impressed from other factors (negative R-C) involve Valence, Waiting Time, Comfort, Convenience, and Safety&Security that are placed in effect group. Getting advantage of fuzzy DEMATEL analysis we also ranked factors based on the degree of relationship (R+C) that sequentially are Problem-solving, Valence, Expertise, Comfort, Conduct, Convenience, Waiting Time, Safety & Security, Tangibles, Information and Cleanliness.
Since expertise and problem-solving have the most influence on other evaluation criteria in airline industry, it is suggested that airlines pay more attention on professional training methods for improving airline personnel Skills. So, they can better serve customers and passengers especially in critical circumstances. Also airline managers should take advantage of focus group meetings with involvement of managers and employees for finding suitable and proper solutions for decreasing passenger problems and subsequently increasing passenger's satisfaction of the airline services. after mentioning relation between criteria with fuzzy DEMATEL, fuzzy ANP was used to obtain weight and priorities of criteria.in fuzzy ANP analysis we first constructed evaluation criteria network map based on SSQAI scale, then we collected experts' opinions as linguistic variables to perform analysis in Fuzzy environment.
After checking consistency for each pairwise comparison matrix, Geometric mean of fuzzy data was calculated in excel software (2016). Superdecision (2.4.0) software was used to obtain criteria improvement priorities. Due to results, criteria weights which need improvement, in order to the most importance are: Valence, Convenience, Problem-solving, Safety&Security, Tangibles, Information, Expertise Comfort, Conduct, Waiting Time, Cleanliness that placed in first to eleventh rank, respectively. Results of this study, offer a clearer perspective for airline providers, enabling them in better strategic planning, identifying airline passengers' needs and gaining remarkable market share in airline industry.

Discussion and Recommendations
According to our findings valence is the most important factor in airline service quality evaluation. Similarly, previous studies stated that quality is positively related to customer satisfaction (Anderson and Sullivan, 1993;Cronin and Taylor, 1992) and corporate image (Grönroos, 1984). Results of our study about minor importance of Waiting time is inconsistent with the study of Suki (2014) who indicated that service quality is widely developed by providing uphold punctuality of the flight departures and arrivals. Also findings of Gilbert and Wong (2003) show passengers consistently ranked assurance as the most important service dimension.
In our study waiting time got minor importance for improvement of airline service quality. This is because some other criteria need more importance for improvement. This result is similar to findings of Chow (2014); and Andotra, Gupta and Pooja (2008) that indicated ontime performance of scheduled flights has no significant effect on the customer complaints and influencing on their choice of airlines. We found Convenience as the most important factor after valence which is inconsistent with Andotra et al. (2008) that stated ticket prices, in-flight services, facilities and ticketing procedures have not played key roles in determining airline service quality and influencing passengers' choice of airlines. Nadiri and Hussain (2005) found that consumers put less emphasis on aspects such as airline tangibles, because of insignificantly impact on customer, however in our study tangibles has an Intermediate importance among all criteria. Findings of Suki (2014) stated that attentiveness of in-flight cabin crews has great influence on costumer experience but his research Implied that airline tangible characteristics like cleanliness of airplane interior toilets, quality of catering and design of aircraft have little impact on the customers' level of satisfaction with airline service quality. As well, in our study Cleanliness has the least importance for improvement from expert views.