An evaluation of airline service quality using the fuzzy weighted SERVQUAL method

Applied Soft Computing 11 (2011) 2117–2128

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Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc

An evaluation of airline service quality using the fuzzy weighted SERVQUAL method Chien-Chang Chou a,∗ , Li-Jen Liu b , Sue-Fen Huang c , Jeng-Ming Yih d , Tzeu-Chen Han b a

Department of Shipping Technology, National Kaohsiung Marine University, Taiwan, ROC Department of Shipping and Transportation Management, National Penghu University, Taiwan, ROC Department of Information Management, National Yunlin University of Science and Technology, Taiwan, ROC d Department of Mathematics Education, National Taichung University, Taiwan, ROC b c

a r t i c l e

i n f o

Article history: Received 21 January 2008 Received in revised form 10 May 2009 Accepted 25 July 2010 Available online 14 August 2010 Keywords: Service quality Airline SERVQUAL method Fuzzy sets theory Transportation

a b s t r a c t The airline service quality is an important issue in the international air travel transportation industry. Although a number of studies focus on the subject of airline service quality evaluation in the past, most of these studies applied the SERVQUAL method to evaluate the airline service quality. But only few have attempted to evaluate the airline service quality using the weighted SERVQUAL method. Furthermore, human judgments are often vague and it is not easy for passengers to express the weights of evaluation criteria and the satisfaction of airline service quality using an exact numerical value. It is more realistic to use linguistic terms to describe the expectation value, perception value and important weight of evaluation criteria. Due to this type of existing fuzziness in the airline service quality evaluation, fuzzy set theory is an appropriate method for dealing with uncertainty. The subjective evaluation data can be more adequately expressed in linguistic variables. Thus this article attempts to fill this gap in the current literature by establishing a fuzzy weighted SERVQUAL model for evaluating the airline service quality. A case study of Taiwanese airline is conduced to demonstrate the effectiveness of the fuzzy weighted SERVQUAL model. Finally, some interesting conclusions and useful suggestions are given to airlines to improve the service quality. © 2010 Elsevier B.V. All rights reserved.

1. Introduction In recent years, the airlines have been experiencing great competition due to both the deregulation and the increasing of passenger’s awareness of service quality. In today’s highly competitive air transportation environment, airlines not only attempt to establish more convenient routes and increase the frequency of flights, but also introduce more promotional incentives. However, the marginal benefits of these marketing strategies gradually reduce because most of airlines applied the same marketing strategies [79,26]. Thus the airlines now tend to focus on how to improve the service quality. Understanding, maintaining and improving the service quality are the main concerns of airlines today. In the past, although many researchers evaluated the airline service quality using the SERVQUAL method, few of these researchers applied the weighted SERVQUAL method to evaluate the airline service quality. Pakdil and Aydin [65] indicated that most of previous SERVQUAL questionnaire based on empirical studies of airline

∗ Corresponding author. E-mail address: [email protected] (C.-C. Chou). 1568-4946/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2010.07.010

service quality were performed on the basis of the respondents’ mean scores built on the Likert scaling. The categories in ordinal scales are ranked through their properties. As it is a ranking, frequencies or percentages are more appropriate statistics than means and standard deviations for meaningful interpretations. If means or standard deviations are preferred, passengers’ raw scores should be transformed into quantitative interval scores. To perform this transformation, factor loads produced through factor analysis might be used as an alternative tool. In factor analysis, the factor load on an observed variable is conceptualized as a properly weighted and summed combination of the scores on factors that underlie it [76]. Pakdil and Aydin [65] focus on measuring airline service quality from the point of view of international passengers by using weighted SERVQUAL scores as a calculation method. Service quality can be regarded as a composite of various attributes. It is not only consists of tangible attributes, but also intangible and subjective attributes such as safety, comfort and satisfaction, which are difficult to measure accurately. Different passenger usually has wide range of perceptions toward quality service. To measure the service quality, conventional measurement tools are devised on cardinal or ordinal scales. Most of the criticism about scale based on measurement is that scores do not necessarily represent user preference. This is because respondents have

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to internally convert preference to scores and the conversion may introduce distortion of the preference being captured [79]. Since human judgments and preference are often vague and can not estimate his preference with an exact numerical value. It is more realistic to use linguistic terms to describe the desired value and important weight of criteria, e.g. “very low”, “low”, “fair”, “high”, “very high”, etc. [5,39]. Due to this type of existing fuzziness in the process, fuzzy set theory is an appropriate method for dealing with uncertainty. The subjective evaluation data can be more adequately expressed in linguistic variables [87,42,52,21,19]. Thus the fuzzy set theory is an appropriate method for measuring passenger’s perception and evaluating the service quality provided by the airline. The aim of this paper is to construct a fuzzy weighted SERVQUAL method to evaluate and understand the airline service quality. This assessment model is tested by a case of Taiwanese airline. Finally, some interesting findings and useful suggestions are given to airlines to maintain and improve their service quality. The rest of this paper is organized as follows. Section 2 is the literature review. The fuzzy set theory is introduced in Section 3. In Section 4, a case study of Taiwanese airline service quality is shown. Finally, some interesting conclusions and useful suggestions are given in Section 5.

2. Literature review 2.1. SERVQUAL method Understanding exactly what customers expect and want is the most crucial step in defining and delivering the high-quality service [90,89]. The problem in the airline sector is whether management can correctly perceive what customers want and expect. Expectations serve as a major determinant of a consumer’s service quality evaluation and satisfaction [61]. At this point, the “voice of the customer” should be taken into the design process using advanced techniques, such as the experimental design, quality function development, and value engineering. After delivering services, service providers should monitor how well the customers’ expectations have been met. For this task, the SERVQUAL method proposed by Parasuraman et al. [66] is one of the best evaluation methods for assessing the expectations and perceptions. SERVQUAL method has five dimensions to measure service quality, including the tangibles, reliability, responsiveness, assurance and empathy [90]. Customers evaluate the service quality by determining whether there is any gap between their expectations and perceptions. SERVQUAL is based on the idea that quality is a subjective customer evaluation, as service is not a physical item, but an experience [66,36]. According to Zeithaml [88] means end chain approach to understanding the cognitive structure of consumers, service information is retained in memory at four levels of abstraction as Fig. 1. This approach considers four different levels to assess a service. In the lowest level, we have the attribute level (simple service attributes). This level is followed by the quality level. Then, we have the third level, the value level and, finally, the personal value level. We will now briefly describe each one of these four levels. At the first (lowest) level, service attributes refer to functional benefits or concrete service attributes. At the second level, a significant contribution was already given to the field of service marketing through the development of SERVQUAL [66]. Service quality is defined as the discrepancy between consumer’s perceptions of service offered by a particular firm and their expectations about firms offering such services. At the third level, service value is another construct found in the literature, defined as a cognitive tradeoff between perceptions of quality and sacrifice or as Zeithaml

Fig. 1. Service personal value and means-end chain approach.

[88] states, between the perception of what is received and given. Finally, at the fourth level, we have service personal values. Personal values are beliefs or conceptions about end-goals or desirable endstates, classified by Rokeach [70] as terminal values. They are key central elements in consumers’ cognitive structure, meaning that by understanding and acting on consumer personal values, it may be possible to better understand consumer behavior. However, there is a clear research gap at the highest level, probably because this last level is more individual and complex than all of the other three [88]. Lages and Fernandes [47] contributed to the services marketing literature by providing the SERPVAL scale, a new services scale at the personal value level. But our research only focuses on the second level-service quality. 2.2. Airline service quality To delivery better services to passengers, airlines have to understand passengers’ needs and expectations [3]. Only the customer can truly define the service quality in the airline service industry [10]. The delivery of high-quality service became an important requirement among airlines as a result of competitive pressure [62]. Empirical studies of demand for airline services show that service quality is central of the choice of airline for both business and leisure travelers (Bureau of Transport and Communications Economics [9]). Various studies for defining service quality dimensions have been proposed from the perspective of passengers. Most of these studies are presented as quality measures for examining the relationships between service quality and related issues such as airline choice [69,31,83], customer satisfaction [4], customer loyalty [62,85], passenger type [4,84], airline type [44], airline class [31,4], aircraft type [77], productivity [64], changes in quality levels over time (Bureau of Transport and Communications Economics [8]), total transportation service offering [59], assessment group [35] and attribute dependency [30]. Tsaur et al. [79] argued that quality in airline services is difficult to describe and measure due to its heterogeneity, intangibility and inseparability. It is in this context that SERVQUAL has been proposed as a valid and reliable evaluation method in airline service quality studies [33,68].

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In addition to SERVQUAL-related airline service studies, many scholars measured the airline service quality through various quality dimensions. For example, Gourdin [34] categorized airline service quality in terms of three items including the price, safety and timeliness. Most air passengers are sensitive to airline ticket price and airlines thus use pricing to differentiate market segments based on elasticity of demand [73]. Prices are determined based on different fare sensitivities of business and leisure passengers, although modern yield management and practices also allow for much more sensitive dynamic price discrimination. Service quality also affects passengers’ choices but is in many ways subjective, often being seen as referring to passengers’ overall impressions of the relative quality of airlines and their services. It can influence an airline’s competitive advantage [59]. Price is initially used as the primary competitive weapon. However, airlines soon realize that competition on price alone represents a no-win situation in the long term. This is mainly due to the fact that airlines are relatively efficient in responding to competitor’s price changes [45]. In addition, the regulators of the airline transportation system may interfere in the price competition as it often results in declined service quality and may affect flight safety. This implies that airlines’ competitive advantages based on the price alone are not sustainable. In a highly competitive environment of Taiwan’s domestic airline market, where all airlines have comparable fares and matching frequency flyer programs, airlines’ competitive advantages lie in the service quality perceived by passengers [14,1]. Abrahams [1] provides empirical support for the theory of service quality competition in the airline industry. Elliott and Roach [30] proposed timeliness luggage transport, food and beverage service quality, seat comfort, the check-in process and in-flight service dimensions. Ostrowski et al. [62] measured the service quality with timeliness, food and beverage quality, and comfort of seat dimensions. Truitt and Haynes [77] used the check-in process, the convenience of transit, the processing of luggage, timeliness, seat cleanliness, food and beverage quality, and the handing of customer complaints as the standards of service quality. Bowen and Headley [6] indicated on-time arrival, mishandled baggage, being denied boarding, and airline safety. They also added passenger complaints on items such as the flight, reservation, ticketing and boarding problems, fares, refunds, customer service, advertising, and frequent flyer programs. In addition, the US Department of Commerce monitors schedule, non-stop flight availability, safety reputation, on-time reputation, in-flight service reputation and frequent flyer program as variables affecting international air travelers’ choice. Sultan and Simpson [75] examined the importance of the relationships between the airline service quality, passenger satisfaction and behavioral intentions. Park et al. [68] seek to improve the understanding of air passengers’ decision-making processes by testing a conceptual model that considers service expectation, service perception, service value, passenger satisfaction, airline image and behavioral intentions simultaneously. The results show that service value, passenger satisfaction and airline image are each found to have a direct effect on air passengers’ decision-making processes. Park [67] found that passenger perceptions are significantly different across airlines, seat classes and usage frequencies. Pakdil and Aydin [65] measured the airline service quality based on data collected at a Turkey airline using SERVQUAL scores weighted by loadings derived from factor analysis. Passengers, regardless of the type of trip, consider reliability and safety-related matters as the top priority. In previous studies, the reliability was identified as the most important service quality dimension and the tangibles appeared as the least important one [90,75]. Especially, the safety-related service quality issues became increasingly important for passengers, after the September 11, 2001 incident in USA.

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Fig. 2. The graded mean h-level of fuzzy number A.

Oyewole [63] and Aksoy et al. [3] identified the educational level of passenger as a significant influence on passenger expectations and satisfaction with airline services.

2.3. Methods for evaluating the service quality A lot of fuzzy methods for evaluating the service quality have been proposed and applied to solving the real world problems. For example, Mikhailov and Tsvetinov [56] proposed a new fuzzy analytic hierarchy process (FAHP) approach for tackling the uncertainty and imprecision of the service evaluation process. Chang et al. [13] proposed a novel fuzzy analytic hierarchy process (FAHP) approach for addressing uncertainty and imprecision in service evaluation during pre-negotiation stages, where comparative judgments of decision makers are represented as triangular fuzzy numbers. Conventionally designed questionnaire frequently use the Likert Scale to gauge the feeling of respondents. Owing to the fuzziness of human thinking, this approach is inadequate and too simple to rule subject’s way and measure complex human thinking and cognition. Tsai et al. [78] proposed a fuzzy SERVQUAL approach to clarify the positioning of service quality in the department store market and proposed implementation priorities for different service strategies. Fuzzy multiple criteria decision-making (FMCDM) and fuzzy multiple attribute decision-making (FMADM) approaches have been proposed and applied to the evaluation of service quality [41,72,27]. Fuzzy quality function deployment (FQFD) models have been introduced and used to solve service quality evaluation problems [51,50,74]. In addition, some integrated algorithms also were applied to the evaluation of service quality in the soft computing field [58,15].

3. Fuzzy set theory The fuzzy set theory was introduced by Zadeh [86]. Fuzzy numbers are a fuzzy subset of real numbers, and they present the expansion of the idea of confidence interval. Fuzzy set theory was developed exactly based on the premise that the key elements in human thinking are not numbers, but linguistic terms or labels of fuzzy sets [5,86,93]. Fuzzy set theory has been applied to solve many decision-making problems. This study will propose a fuzzy weighted SERVQUAL method for evaluating the airline service quality.

3.1. The basic concept of fuzzy number First we introduce briefly the concept of fuzzy number. Let A = (c, a, b, d) be a trapezoidal fuzzy number as Fig. 2. Suppose the mem-

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Fig. 3. The subtraction operation on fuzzy numbers.

bership function of A is fA (x).

fA (x) =

Many types of membership functions in fuzzy set have been proposed in the past. But it is difficult and inappropriate for passengers to totally understand complex membership functions and answer quickly questionnaires in the interview survey. Thus, we interviewed passengers and obtained expectations and perceptions by linear membership functions.

⎧ (x − c) ⎪ ⎪ , c ≤ x ≤ a, ⎪ (a ⎪ ⎨ − c)

a ≤ x ≤ b,

1,

(x − d) ⎪ , b ≤ x ≤ d, ⎪ ⎪ ⎪ ⎩ (b − d) 0,

otherwise.

3.2. The basic arithmetic operations on fuzzy numbers

LA (x) =

(x − c) , (a − c)

c ≤ x ≤ a,

LA−1 (h) = c + (a − c)h,

RA (x) =

(x − d) , (b − d)

b ≤ x ≤ d,

RA−1 (h) = d + (b − d)h,

0 ≤ h ≤ 1.

0 ≤ h ≤ 1.

LA (x) and RA (x) are the function L and the function R of the trapezoidal fuzzy number A, respectively. LA−1 (h) and RA−1 (h) are the inverse functions of the function LA (x)and the function RA (x) at h-level, respectively. Chen and Hsieh [20] proposed the graded mean integration representation method for presenting the representation of one fuzzy number, based on the integral value of graded mean h-level of fuzzy number. Here we describe the meaning as follows. Let the graded mean h-level value of fuzzy number A is h(LA−1 (h) + RA−1 (h))/2 as Fig. 2. Then the graded mean integration representation of A is P(A).



1

P(A) = 0

 =

0

1

h(L−1 (h) + R−1 (h)) dh/ 2



1

hdh 0

h(c + (a − c)h + d + (b − d)h) dh/ 2



1

A1 ⊕ A2 = (c1 + c2 , a1 + a2 , b1 + b2 )

(2)

where c1 , c2 , a1 , a2 , b1 , b2 are real numbers. The above addition operation on fuzzy numbers will be applied to evaluate the service quality of airline in this study. For example, the subjective expectation from the passenger 1 is “fair”. The linguistic variable “fair” can be expressed in a triangular fuzzy number A1 = (2, 3, 4). And the subjective expectation from the passenger 2 is “high”. The linguistic variable “high” can be expressed in a triangular fuzzy number A2 = (3, 4, 5). By above formula (2), we can obtain easily the total subjective expectation from the passenger 1 and passenger 2. A1 ⊕ A2 = (2 + 3, 3 + 4, 4 + 5) = (5, 7, 9) (b) The subtraction operation on A1 and A2

The triangular fuzzy number Y = (c, a, b) is a special case of generalized trapezoidal fuzzy number. The graded mean integration representation of triangular fuzzy number Y becomes 1 (c + 4a + b) 6

(a) The addition operation on A1 and A2

hdh 0

1 = (c + 2a + 2b + d) 6

P(Y ) =

The basic fuzzy arithmetic operations on fuzzy numbers have been proposed in previous literature [57,29,60,2,11,46,54,38,28,55,49]. The basic arithmetic operations on fuzzy numbers are introduced as follows. Suppose A1 = (c1 , a1 , b1 ) is a triangular fuzzy number and A2 = (c2 , a2 , b2 ) is also a triangular fuzzy number.

(1)

Passenger’s subjective satisfaction can be expressed in linguistic variables in the context of this study. For example, the passenger’s subjective perception is “fair”. The linguistic variable “fair” can be expressed in a triangular fuzzy number Y = (c, a, b) = (2, 3, 4). By formula (1), P(Y ) = 16 (2 + 12 + 4) = 3. Various types of membership functions were used in fuzzy linear programming problem and its application such as a linear membership function [91,92,32], a tangent type of a membership function [48], an interval linear membership function [37], an exponential membership function [12], inverse tangent membership function [71], logistic type of membership function [82], concave piecewise linear membership function [43], piecewise linear membership function [40], dynamics membership function [7], S-curve membership function [80], and modified flexible S-curve membership function [81].

A1 A2 = (c1 − b2 , a1 − a2 , b1 − c2 )

(3)

For example, the passenger’s subjective perception is “fair”. The linguistic variable “fair” can be expressed in a triangular fuzzy number A1 = (2, 3, 4) as shown in Fig. 3. On the other hand, the passenger’s subjective expectation is “high”. The “high” linguistic variable can be expressed in a triangular fuzzy number A2 = (3, 4, 5). The service quality gap between the expectation and perception from the passenger is A1 A2 . By formula (3), we can obtain A1 A2 = (2 − 5, 3 − 4, 4 − 3) = (−3, −1, 1) This means there is a service quality gap between the expectation and perception from the passenger. In other words, the passenger is not satisfactory with the service quality provided by the airline. (c) The division operation on A and any real number r A = r

c r

,

a , r

b r



where r is a real number.

(4)

C.-C. Chou et al. / Applied Soft Computing 11 (2011) 2117–2128 Table 1 The SERVQUAL questionnaire for airline service.

For example, the total subjective expectation from two passengers is a fuzzy number A = (5, 7, 9). By formula (4), we can obtain the average subjective expectation of two passengers.



Tangibles Comfort and cleanness of seat Quality of food and beverage In-flight newspapers, magazines and books In-flight washroom facility In-flight entertainment facilities and programs Availability of waiting lounges Size of airplane



A 5 7 9 = , , 2 2 2 2 = (2.5, 3.5, 4.5) 3.3. The multiplication operation on fuzzy numbers

Responsiveness Courtesy of crew Handling of delay Efficient check-in/baggage handling services Crew’s speed handling request Quality of the reservation services Crew’s approach against unexpected situations Crew’s willingness to help Appearance of crew

Although many fuzzy arithmetic methods proposed in the previous literature, few of these papers presented the representation of multiplication operation on two or more fuzzy numbers. But Chen [17,18,19] proposed the Function Principle and the Graded Mean Integration Representation method for operation and ranking of fuzzy numbers. Chou [22] proposed the canonical representation of multiplication operation on two triangular fuzzy numbers by the Graded Multiple Integration Representation Method. Chou [23] further propose the canonical representation of multiplication operation on multiple trapezoidal fuzzy numbers based on the Inverse Function Arithmetic Representation Method, and then this canonical representation is applied to solve the multiple criteria decision-making problems [24,25]. First we introduce briefly the Inverse Function Arithmetic Representation Method. Suppose A1 = (c1 , a1 , b1 , d1 ) is a trapezoidal −1 −1 fuzzy number. LA1 (h) and RA1 (h) are the inverse functions of the function LA1 (x)and the function RA1 (x)of A1 at h-level, respectively. And the membership function of A1 is

fA1 (x) =

Reliability and assurance Safety On-time departure and arrival Consistent ground/in-flight services Empathy Crew’s behavior to delayed passenger Individual attention to passenger Understanding of passenger’s specific needs Extent travel services Convenient ticketing process Customer complaint handling Flight pattern Flight problems Convenient flight schedules Frequency of flight Non-stop flight

⎧ (x − c1 ) ⎪ ⎪ , c1 ≤ x ≤ a1 , ⎪ (a ⎪ ⎨ 1 − c1 )

a1 ≤ x ≤ b1 ,

1,

(x − d1 ) ⎪ , b1 ≤ x ≤ d1 , ⎪ ⎪ ⎪ ⎩ (b1 − d1 ) 0,

otherwise

Since

Since (x − c1 ) LA1 (x) = , (a1 − c1 ) RA1 (x) =

LA2 (x) =

(x − c2 ) , (a2 − c2 )

c2 ≤ x ≤ a 2 ,

RA2 (x) =

(x − d2 ) , (b2 − d2 )

b2 ≤ x ≤ d2 ,

c1 ≤ x ≤ a 1 ,

(x − d1 ) , (b1 − d1 )

b1 ≤ x ≤ d 1 ,

and −1 (h) = c2 + (a2 − c2 )h, LA2

and −1 LA1 (h) = c1 + (a1 − c1 )h, −1 RA1 (h) = d1 + (b1 − d1 )h,

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0 ≤ h ≤ 1,

−1 RA2 (h) = d2 + (b2 − d2 )h,

0 ≤ h ≤ 1, 0 ≤ h ≤ 1.

The Inverse Function Arithmetic Representation Method is as follows.

0 ≤ h ≤ 1.

Definition 1.

Let P(A1 ⊗A2 ) be the representation of A1 ⊗A2 .

1 1 P(A1 ⊗ A2 ) =

0

−1 −1 −1 −1 −1 −1 −1 −1 1 {[hA1 LA1 (h) × hA2 LA2 (h)] + [hA1 LA1 (h) × hA2 RA2 (h)] + [hA1 RA1 (h) × hA2 LA2 (h)] + [hA1 RA1 (h) × hA2 RA2 (h)]}dhA1 dhA2 0 4 1 1 h dhA1 × 0 hA2 dhA2 0 A1



Similarly, suppose the membership function of A2 = (c2 , a2 , b2 , d2 ) is

fA2 (x) =

⎧ (x − c2 ) ⎪ ⎪ , c2 ≤ x ≤ a2 ⎪ ⎪ (a2 − c2 ) ⎨ 1, (x − d2 ) ⎪ , ⎪ ⎪ (b ⎪ ⎩ 2 − d2 ) 0,

a2 ≤ x ≤ b2

b2 ≤ x ≤ d2 otherwise





Now we can compute the representation of multiplication operation on Two trapezoidal fuzzy numbers. Table 2 Linguistic variables for expectation and perception. Very Poor Poor Fair Good Very Good

(0.0,1.0,2.0) (1.0,2.0,3.0) (2.0,3.0,4.0) (3.0,4.0,5.0) (4.5,5.0,5.0)

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By Definition 1, the representation of A1 ⊗A2 is P(A1 ⊗A2 ).

 1

P(A1 ⊗ A2 )

0

=

1

1 −1 −1 −1 −1 −1 −1 −1 −1 (h) × hA2 LA2 (h)] + [hA1 LA1 (h) × hA2 RA2 (h)] + [hA1 RA1 (h) × hA2 LA2 (h)] + [hA1 RA1 (h) × hA2 RA2 (h)]}dhA1 dhA2 {[hA1 LA1 4



0



1

hA1 dhA1 × 0

 1 0

1

0



1

hA2 dhA2 0

1 {[hA1 [c1 + (a1 − c1 )hA1 ] × hA2 [c2 + (a2 − c2 )hA2 ] + hA1 [c1 + (a1 − c1 )hA1 ] × hA2 [d2 + (b2 − d2 )hA2 ] + hA1 [d1 4

+ (b1 − d1 )hA1 ] × hA2 [c2 + (a2 − c2 )hA2 ] + hA1 [d1 + (b1 − d1 )hA1 ] × hA2 [d2 + (b2 − d2 )hA2 ]} × dhA1 dhA2



=



1



1

0

+ =



1

0

1 4

1



1

hA1 dhA1 ×

hA2 dhA2

0

0

1 1 1 1 [ h2A1 c1 + h3A1 (a1 − c1 )] × hA2 [c2 + (a2 − c2 )hA2 ] + [ h2A1 c1 + h3A1 (a1 − c1 )] × hA2 [d2 + (b2 − d2 )hA2 ] + [ h2A1 d1 2 3 2 3 2

1 3 1 1 h (b1 − d1 )] × hA2 [c2 + (a2 − c2 )hA2 ] + [ h2A1 d1 + h3A1 (b1 − d1 )] × hA2 [d2 + (b2 − d2 )hA2 ] 3 A1 2 3



1 4

1 2 h |× 2 A1



1



1

hA2 dhA2 0

1 1 1 1 1 [ c1 + (a1 − c1 )] × hA2 [c2 + (a2 − c2 )hA2 ] + [ c1 + (a1 − c1 )] × hA2 [d2 + (b2 − d2 )hA2 ] + [ d1 + (b1 − d1 )] 2 3 2 3 2 3

1 1 × hA2 [c2 + (a2 − c2 )hA2 ] + [ d1 + (b1 − d1 )] × hA2 [d2 + (b2 − d2 )hA2 ] 2 3



=

| dhA2

1

1 × 2





1

dhA2

hA2 dhA2 0

1 1 1 1 1 1 1 1 1 [ c1 + (a1 − c1 )] × [ h2A2 c2 + h3A2 (a2 − c2 )] + [ c1 + (a1 − c1 )] × [ h2A2 d2 + h3A2 (b2 − d2 )] + [ d1 + (b1 − d1 )] 2 3 2 3 2 3 2 3 2 3

1 1 1 1 1 1 × [ h2A2 c2 + h3A2 (a2 − c2 )] + [ d1 + (b1 − d1 )] × [ h2A2 d2 + h3A2 (b2 − d2 )] | 2 3 2 3 2 3 = 1 1  2 × hA2 | 2 2 1 1 1 1 1 1 1 1 1 1 1 [ c1 + (a1 − c1 )] × [ c2 + (a2 − c2 )] + [ c1 + (a1 − c1 )] × [ d2 + (b2 − d2 )] + [ d1 + (b1 − d1 )] 2 3 2 3 2 3 2 3 2 3 4

1 1 1 1 1 1 × [ c2 + (a2 − c2 )] + [ d1 + (b1 − d1 )] × [ d2 + h3A2 (b2 − d2 )] 2 3 2 3 2 3 = 1 1 × 2 2 1 1 = (c1 + 2a1 + 2b1 + d1 ) × (c2 + 2a2 + 2b2 + d2 ) 6 6 1 4

We have that P(A1 ⊗ A2 ) =

1 1 (c1 + 2a1 + 2b1 + d1 ) × (c2 + 2a2 + 2b2 + d2 ) 6 6

Triangular fuzzy numbers Y1 = (c1 , a1 , b1 ), Y2 = (c2 , a2 , b2 ) are special cases of generalized trapezoidal fuzzy number. The representation of multiplication operation on two triangular fuzzy numbers becomes P(Y1 ⊗ Y2 ) =

1 1 (c1 + 4a1 + b1 ) × (c2 + 4a2 + b2 ) 6 6

(5)

4. A case study of airline service quality Four stages are involved in the evaluation procedure for evaluating the airline service quality. The four stages include the questionnaire design, interview survey and collection of data, calculation of scores of expectations and perceptions, and analysis of service quality. Step 1: Questionnaire design This paper used a questionnaire based on the pervious literature [26]. The SERVQUAL and airline service quality dimensions were

taken into consideration under the inspiration of previous studies. Even though SERVQUAL presents general quality dimensions for service industries, it does not include the specific dimensions for each service industry, such as the airline service industry. Thus this paper summarized five major dimensions and 28 items in this SERVQUAL questionnaire for airline service quality as Table 1. The SERVQUAL questionnaire addressing expectations and perceptions are rated using linguistic variables scale. For example, the linguistic variables for passenger’s expectations and perceptions include “Very poor”, “Poor”, “Fair”, “Good” and “Very good”. The linguistic variables for importance weight of evaluation criteria include “Very low”, “Low”, “Fair”, “High” and “Very high”. The linguistic variables and the ratings for passenger’s expectations and perceptions are shown in Table 2. The linguistic variables and the ratings for importance weight of evaluation criteria are shown in Table 3. Step 2: Interview survey and collection of dataThe interview sample was taken from the passengers of an international airline that flies from International Airport of Kaohsiung in Taiwan. The airline volunteered to take part in this study is well known in the international airline industry. The survey was administered over 4 weeks. Questionnaires were distributed to the passengers and collected

C.-C. Chou et al. / Applied Soft Computing 11 (2011) 2117–2128 Table 3 Linguistic variables for importance weight of criteria. Very Low Low Fair High Very High

Similarly, according to the formulas (2) and (7), we can obtain easily the total service quality perception from all passengers under service item i. (b) Let fuzzy number MAei be the average service quality expectations from all passengers under service item i. Let fuzzy number MApi be the average service quality perceptions from all passengers under service item i.

(0.0,1.0,2.0,) (1.0,2.0,3.0) (2.0,3.0,4.0) (3.0,4.0,5.0) (4.5,5.0,5.0)

in the last hour of the flight. Participation was voluntary. The size of sample was 329. A thousand questionnaires were distributed with a response rate 32.9%. Step 3: Calculation of scores of expectations and perceptionsAfter collecting and calculating of data, the scores of expectations and perceptions, and the gap between expectation and perception from passengers are shown in Table 4. The computational procedure is shown as follows. (a) Let fuzzy number Aein be the service quality expectation from the nth passenger under service item i. Let fuzzy number Apin be the service quality perception from the nth passenger under service item i. Let fuzzy number TAei be the total service quality expectations from all passengers under service item i. Let fuzzy number TApi be the total service quality perceptions from all passengers under service item i. TAei =

N 

Aein

(6)

1

TApi =

N 

Apin

2123

(7)

1

According to the formulas (2) and (6), we can obtain easily the total service quality expectation from all passengers under service item i.

MAei = MApi =

TAei N

(8)

TApi

(9)

N

According to the formulas (4) and (8), we can obtain easily the average service quality expectation from all passengers under service item 1. MAe1 = (3.52, 4.31, 4.89) Similarly, according to the formulas (4) and (9), we can obtain easily the average service quality perception from all passengers under service item 1. MAp1 = (2.51, 3.51, 4.50) (c) Let fuzzy number Gapi be the service quality gap between the expectation and perception from all passengers under item i. Gapi = MApi MAei

(10)

According to the formulas (3) and (10), we can obtain easily the service quality gap between the expectation and perception from all passengers under service item 1. Gapi = (2.51, 3.51, 4.50)(3.52, 4.31, 4.89) = (2.51–4.89, 3.51–4.31, 4.50–3.52) = (−2.38, −0.80, 0.98) According to the formula (1), we can obtain the representation of fuzzy numbers MAe1 = 4.28, MAp1 = 3.51 and Gap1 = −0.77. This means passengers are not satisfactory with

Table 4 The scores of expectations and perceptions. Dimension

Fuzzy expectation

Fuzzy perceptions

Fuzzy gap

Expectation

Perceptions

Gap

Tangibles Comfort and cleanness of seat Quality of food and beverage In-flight newspapers, magazines and books In-flight washroom facility In-flight entertainment facilities and programs Availability of waiting lounges Size of airplane Responsiveness Courtesy of crew Handling of delay Efficient check-in/baggage handling services Crew’s speed handling request Quality of the reservation services Crew’s approach against unexpected situations Crew’s willingness to help Appearance of crew Reliability and assurance Safety On-time departure and arrival Consistent ground/in-flight services Empathy Crew’s behavior to delayed passenger Individual attention to passenger Understanding of passenger’s specific needs Extent travel services Convenient ticketing process Customer complaint handling Flight pattern Flight problems Convenient flight schedules Frequency of flight Non-stop flight

(3.20, 4.05, 4.75) (3.52, 4.31, 4.89) (3.26, 4.11, 4.82) (3.24, 4.09, 4.79) (3.19, 4.04, 4.75) (3.27, 4.12, 4.81) (3.03, 3.91, 4.67) (2.87, 3.76, 4.55) (3.27, 4.11, 4.78) (3.64, 4.42, 4.97) (3.35, 4.18, 4.82) (3.46, 4.27, 4.88) (3.32, 4.15, 4.81) (3.01, 3.89, 4.65) (3.47, 4.28, 4.89) (2.99, 3.87, 4.64) (2.91, 3.80, 4.60) (3.46, 4.25, 4.84) (3.73, 4.43, 4.84) (3.37, 4.20, 4.85) (3.29, 4.13, 4.82) (3.27, 4.10, 4.76) (3.28, 4.13, 4.83) (3.26, 4.12, 4.82) (3.05, 3.92, 4.65) (3.00, 3.87, 4.61) (3.37, 4.19, 4.83) (3.63, 4.36, 4.82) (3.10, 3.95, 4.66) (2.93, 3.82, 4.61) (3.28, 4.13, 4.81) (3.19, 4.03, 4.71) (3.01, 3.84, 4.52)

(2.61, 3.59, 4.55) (2.51, 3.51, 4.50) (2.36, 3.35, 4.35) (2.80, 3.77, 4.71) (2.86, 3.82, 4.75) (2.78, 3.74, 4.66) (2.64, 3.63, 4.60) (2.33, 3.32, 4.32) (2.95, 3.87, 4.71) (3.55, 4.33, 4.88) (2.79, 3.76, 4.70) (3.09, 3.97, 4.73) (2.89, 3.83, 4.71) (2.82, 3.77, 4.67) (2.88, 3.82, 4.70) (2.79, 3.74, 4.65) (2.82, 3.77, 4.68) (2.92, 3.85, 4.71) (2.92, 3.84, 4.67) (2.88, 3.82, 4.70) (2.97, 3.89, 4.74) (2.86, 3.79, 4.65) (3.12, 3.99, 4.73) (2.92, 3.85, 4.70) (2.83, 3.77, 4.65) (2.69, 3.64, 4.52) (2.92, 3.85, 4.70) (2.70, 3.65, 4.57) (2.75, 3.70, 4.62) (2.71, 3.67, 4.58) (2.75, 3.71, 4.62) (2.73, 3.69, 4.61) (2.79, 3.74, 4.65)

(−2.14, −0.46, 1.36) (−2.38, −0.80, 0.98) (−2.46, −0.76, 1.08) (−1.99, −0.32, 1.47) (−1.89, −0.22, 1.56) (−2.03, −0.38, 1.39) (−2.03, −0.28, 1.57) (−2.22, −0.44, 1.45) (−1.83, −0.23, 1.44) (−1.42, −0.09, 1.24) (−2.03, −0.42, 1.34) (−1.79, −0.30, 1.27) (−1.92, −0.32, 1.39) (−1.83, −0.12, 1.66) (−2.02, −0.46, 1.23) (−1.84, −0.13, 1.66) (−1.77, −0.03, 1.77) (−1.91, −0.40, 1.25) (−1.92, −0.59, 0.95) (−1.97, −0.38, 1.33) (−1.85, −0.24, 1.46) (−1.90, −0.31, 1.38) (−1.72, −0.14, 1.45) (−1.90, −0.27, 1.44) (−1.82, −0.14, 1.61) (−1.92, −0.24, 1.52) (−1.90, −0.34, 1.33) (−2.12, −0.70, 0.94) (−1.92, −0.31, 1.38) (−1.90, −0.15, 1.65) (−2.06, −0.42, 1.34) (−1.97, −0.34, 1.42) (−1.74, −0.10, 1.65)

4.02 4.28(4) 4.09(14) 4.06(17) 4.02(18) 4.09(14) 3.89(20) 3.74(28) 4.08(2) 4.37(2) 4.15(9) 4.24(6) 4.12(10) 3.87(22) 4.25(5) 3.85(23) 3.79(27) 4.22(1) 4.38(1) 4.17(7) 4.10(12) 4.07(3) 4.11(11) 4.09(14) 3.89(20) 3.85(23) 4.16(8) 4.31(3) 3.93(5) 3.80(26) 4.10(12) 4.00(19) 3.81(25)

3.59 3.51(26) 3.35(27) 3.76(13) 3.82(8) 3.73(19) 3.62(25) 3.32(28) 3.86(1) 4.29(1) 3.75(16) 3.95(3) 3.82(8) 3.76(13) 3.81(10) 3.74(17) 3.77(12) 3.84(2) 3.83(7) 3.81(10) 3.88(4) 3.78(3) 3.97(2) 3.84(5) 3.76(13) 3.63(24) 3.84(5) 3.65(23) 3.70(4) 3.66(22) 3.70(20) 3.68(21) 3.74(17)

−0.44(1) −0.77(1) −0.73(2) −0.30(13) −0.20(20) −0.36(9) −0.27(16) −0.42(6) −0.22(5) −0.09(26) −0.39(8) −0.29(15) −0.30(13) −0.11(25) −0.44(5) −0.12(24) −0.02(28) −0.38(2) −0.56(4) −0.36(9) −0.22(18) −0.29(3) −0.14(21) −0.26(17) −0.13(23) −0.22(18) −0.32(11) −0.67(3) −0.23(4) −0.14(21) −0.40(7) −0.32(11) −0.08(27)

Mean

(3.25, 4.08, 4.76)

(2.82, 3.76, 4.64)

(−1.94, −0.33, 1.40)

4.06

3.75

−0.31

(4)

(5)

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the service quality provided by the airline. Similarly, we can obtain all fuzzy expectations, fuzzy perceptions, fuzzy gaps, expectations, perceptions and gaps shown in Table 4. (d) Let fuzzy number Awin be the importance weight of service item from the nth passenger under service item i. Let fuzzy number TAwi be the total importance weight from all passengers under service item i. TAwi =

N 

Awin

(11)

1

According to the formulas (2) and (11), we can obtain easily the total importance weight from all passengers under item i. (e) Let fuzzy number MAwi be the average importance weight from all passengers under service item i. MAwi =

TAwi N

(12)

According to the formulas (4) and (12), we can obtain easily the average importance weight from all passengers under service item 1. MAw1 = (2.53, 3.50, 4.43) According to the formula (1), we can obtain the representation of fuzzy number MAw1 = 3.49. Similarly, we can obtain fuzzy weights of all service items shown in Table 5. (f) Let fuzzy number WGapi be the fuzzy weighted service quality gap between the expectation and perception from all passengers under service item i. WGapi = MAwi ⊗ Gapi

(13)

According to the formulas (5) and (13), we can obtain easily the fuzzy weighted SERVQUAL gap of service item 1. WGap1 = (2.53, 3.50, 4.43) ⊗ (−2.38, −0.8, 0.98) = −2.68

Similarly, we can obtain fuzzy weights gaps of all service items shown in Table 6. Step 4: Analysis of service quality of airlineBased on the results in Tables 4, 5 and 6, this paper further analyzes the service quality of airline as follows. The service quality expectations, perceptions and gaps between the expectations and perceptions from passengers are listed in Table 4. In terms of the dimensions of service expectation, the first is the reliability and assurance (4.22 average scores), the second is the responsiveness (4.08 average scores), the third is the empathy (4.07 average scores), followed by the tangibles (4.02 average scores) and flight pattern (3.93 average scores). In terms of the items of service expectation, the first is the safety (4.38 scores), the second is the courtesy of crew (4.37 scores), the third is the customer complaint handling (4.31 scores), followed by the comfort and cleanness of seat (4.28 scores) and crew’s approach against unexpected situations (4.25 scores). In terms of the dimensions of service perception, the first is the responsiveness (3.86 average scores), the second is the reliabilities and assurance (3.84 average scores), the third is the empathy (3.78 average scores), followed by the flight pattern (3.70 average scores) and tangibles (3.59 average scores). In terms of the items of service perception, the first is the courtesy of crew (4.29 scores), the second is the crew’s behavior to delayed passenger (3.97 scores), the third is the efficient check-in/baggage handling service (3.95 scores), followed by the consistent ground/in-flight services (3.88 scores) and individual attention to passenger (3.84 scores), and convenient ticketing process (3.84 scores). Comparing the service quality expectations with perceptions, we can see the top 10 service quality gaps from passengers are the comfort and cleanness of seat, quality of food and beverage, customer complaint handling, safety, crew’s approach against unexpected situations, size of airplane, convenient of flight schedules, handling of delay, on-time departure and arrival, and in-flight entertainment facilities and programs. The list is in order of gap.

Table 5 The weights of service items. Dimension

Fuzzy weight

Defuzzied

Weight %

Tangibles Comfort and cleanness of seat Quality of food and beverage In-flight newspapers, magazines and books In-flight washroom facility In-flight entertainment facilities and programs Availability of waiting lounges Size of airplane Responsiveness Courtesy of crew Handling of delay Efficient check-in/baggage handling services Crew’s speed handling request Quality of the reservation services Crew’s approach against unexpected situations Crew’s willingness to help Appearance of crew Reliability and assurance Safety On-time departure and arrival Consistent ground/in-flight services Empathy Crew’s behavior to delayed passenger Individual attention to passenger Understanding of passenger’s specific needs Extent travel services Convenient ticketing process Customer complaint handling Flight pattern Flight problems Convenient flight schedules Frequency of flight Non-stop flight

(2.03, 2.99, 3.91) (2.53, 3.50, 4.43) (2.37, 3.32, 4.21) (1.90, 2.86, 3.79) (1.69, 2.64, 3.54) (2.19, 3.16, 4.10) (1.85, 2.84, 3.80) (1.68, 2.61, 3.48) (2.33, 3.27, 4.16) (2.75, 3.68, 4.53) (2.27, 3.25, 4.22) (2.49, 3.42, 4.29) (2.54, 3.47, 4.32) (1.81, 2.79, 3.74) (2.14, 3.07, 3.94) (2.55, 3.47, 4.30) (2.08, 3.04, 3.95) (2.78, 3.64, 4.36) (3.46, 4.20, 4.68) (2.76, 3.65, 4.42) (2.12, 3.07, 3.97) (2.25, 3.17, 4.01) (1.77, 2.71, 3.61) (2.46, 3.38, 4.21) (2.06, 3.02, 3.93) (1.78, 2.72, 3.60) (2.44, 3.34, 4.14) (2.96, 3.83, 4.57) (1.99, 2.96, 3.88) (2.00, 2.96, 3.90) (1.97, 2.94, 3.87) (2.07, 3.02, 3.93) (1.94, 2.91, 3.84)

2.98 3.49 3.31 2.85 2.63 3.16 2.83 2.60 3.26 3.67 3.25 3.41 3.45 2.78 3.06 3.45 3.03 3.62 4.16 3.63 3.06 3.15 2.71 3.36 3.01 2.71 3.33 3.81 2.95 2.96 2.93 3.01 2.90

3.37(4) 3.95(5) 3.73(11) 3.22(22) 2.97(27) 3.57(13) 3.20(23) 2.94(28) 3.69(2) 4.14(3) 3.67(12) 3.85(8) 3.90(6) 3.15(24) 3.46(14) 3.90(6) 3.42(16) 4.08(1) 4.68(1) 4.09(4) 3.46(14) 3.56(3) 3.05(26) 3.79(9) 3.40(17) 3.06(25) 3.75(10) 4.30(2) 3.33(5) 3.34(19) 3.31(20) 3.40(17) 3.28(21)

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Table 6 The result comparison of gap and weighted gap. Dimension

Gap

Rank

Weighted gap

Rank

%

Tangibles Comfort and cleanness of seat Quality of food and beverage In-flight newspapers, magazines and books In-flight washroom facility In-flight entertainment facilities and programs Availability of waiting lounges Size of airplane Responsiveness Courtesy of crew Handling of delay Efficient check-in/baggage handling services Crew’s speed handling request Quality of the reservation services Crew’s approach against unexpected situations Crew’s willingness to help Appearance of crew Reliability and assurance Safety On-time departure and arrival Consistent ground/in-flight services Empathy Crew’s behavior to delayed passenger Individual attention to passenger Understanding of passenger’s specific needs Extent travel services Convenient ticketing process Customer complaint handling Flight pattern Flight problems Convenient flight schedules Frequency of flight Non-stop flight

−0.44 −0.77 −0.73 −0.30 −0.20 −0.36 −0.27 −0.42 −0.22 −0.09 −0.39 −0.29 −0.30 −0.11 −0.44 −0.12 −0.02 −0.38 −0.56 −0.36 −0.22 −0.29 −0.14 −0.26 −0.13 −0.22 −0.32 −0.67 −0.23 −0.14 −0.40 −0.32 −0.08

(1) (1) (2)

−1.36 −2.68 −2.43 −0.85 −0.54 −1.15 −0.75 −1.09 −0.72 −0.33 −1.27 −0.97 −1.04 −0.30 −1.34 −0.40 −0.06 −1.43 −2.32 −1.29 −0.69 −0.97 −0.38 −0.86 −0.39 −0.60 −1.08 −2.53 −0.69 −0.43 −1.17 −0.95 −0.23

(2) (1) (3)

4.82 9.54 8.64 3.02 1.91 4.08 2.67 3.89 2.54 1.16 4.53 3.46 3.71 1.07 4.77 1.43 0.22 5.09 8.23 4.59 2.44 3.46 1.34 3.05 1.40 2.14 3.84 9.00 2.47 1.52 4.16 3.38 0.80

Based on the results in Table 5, in terms of the important weight of service dimensions, the first important dimension is the reliability and assurance (3.62 average scores), the second is the responsiveness (3.26 average scores), the third is the empathy (3.15 average scores), followed by the tangibles (2.98 average scores) and flight pattern (2.95 average scores). In terms of the important weight of service items, the first important service item is the safety (4.16 scores), the second is the customer complaint handling (3.81 scores), the third is the courtesy of crew (3.67 scores), followed by the on-time departure and arrival (3.63 scores) and comfort and cleanness of sat (3.49 scores). This paper also compared the fuzzy SERVQUAL gap with the fuzzy weighted SERVQUAL gap in Table 6. In terms of the service dimensions, the tangibles dimension, regardless of importance weight, is with the largest service quality gap (−0.44 average scores). The second is the reliability and assurance dimension (−0.38 average scores). The third is the empathy dimension (−0.29 average scores), followed by the flight pattern dimension (−0.23 average scores) and the responsiveness dimension (−0.22 average scores). The top 10 service items with large quality gap are the comfort and cleanness of seat, quality of food and beverage, customer complaint handling, safety, crew’s approach against unexpected situations, size of airplane, convenient of flight schedules, handling of delay, on-time departure and arrival, and in-flight entertainment facilities and programs. The list is in order of gap. On the other hand, the reliability and assurance dimension, regardful of importance weight, is with the largest service quality gap (−1.43 average scores). The second is the tangibles dimension (−1.36 average scores). The third is the empathy dimension (−0.97 average scores), followed by the responsiveness dimension (−0.72 average scores) and the flight pattern dimension (−0.69 average scores). The top 10 service items with large quality gap are the comfort and cleanness of seat, customer complaint han-

(9) (6) (5) (8)

(5)

(2) (4) (9) (3)

(3) (4) (7)

(9) (10) (4) (7)

(5)

(1) (4) (6) (3)

(2) (5) (8)

dling, quality of food and beverage, safety, crew’s approach against unexpected situations, on-time departure and arrival, handling of delay, convenient of flight schedules, in-flight entertainment facilities and programs, and the size of airplane. The list is in order of weighted gap. 5. Conclusions and future works The fuzzy weighted SERVQUAL model proposed in this paper is tested by a Taiwanese airline case. Finally, some interesting findings and useful suggestions are given as follows. In terms of the important weight of service dimensions, the first important dimension is the reliability and assurance, the second is the responsiveness, the third is the empathy, followed by the tangibles and flight pattern. In terms of the important weight of service items, the first important service item is the safety, the second is the customer complaint handling, the third is the courtesy of crew, followed by the on-time departure and arrival, and comfort and cleanness of seat. So far, we have seen that passengers consider reliability and assurance dimension, and the safety-related service items as the top priority. Previous studies provided the same empirical results [90,75,14,53]. On the other hand, the tangibles dimension and the flight pattern dimension appear as the least important service dimensions. The tangibles dimension was identified as the least important dimension in previous studies [90,75,14]. One of interesting findings in this paper is that passengers consider the comfort and cleanness of seat as an increasingly important service item in recent years. The same results were proposed in the recent empirical studies [16,53]. In addition, another interesting finding is that although the passenger complaint handling was not an important service item in the previous empirical studies [79,14], this service item has become increasingly an important service item

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in Taiwanese airline service industry recently. Recent studies provided empirical support for the importance of passenger complaint handling service [16,53]. In terms of the dimensions of service expectation, the first is the reliability and assurance, the second is the responsiveness, the third is the empathy, followed by the tangibles and flight pattern. In terms of the items of service expectation, the first is the safety, the second is the courtesy of crew, the third is the customer complaint handling, followed by the comfort and cleanness of seat and crew’s approach against unexpected situations. In terms of the dimensions of service perception, the first is the responsiveness, the second is the reliabilities and assurance, the third is the empathy, followed by the flight pattern and tangibles. In terms of the items of service perception, the first is the courtesy of crew, the second is the crew’s behavior to delayed passenger, the third is the efficient check-in/baggage handling service, followed by the consistent ground/in-flight services and individual attention to passenger, and convenient ticketing process. Comparing the service quality expectations with perceptions, we can see the top 10 service quality gaps from passengers are the comfort and cleanness of seat, quality of food and beverage, customer complaint handling, safety, crew’s approach against unexpected situations, size of airplane, convenient of flight schedules, handling of delay, on-time departure and arrival, and in-flight entertainment facilities and programs, respectively. The list is in order of gap. One of interesting findings is the service quality gap between the expectation and perception from passenger is increasingly large, in terms of the tangibles dimension and the comfort of seat service item in recent years. The same results were proposed in the recent empirical studies [16,53]. This paper also compared the fuzzy SERVQUAL gap with the fuzzy weighted SERVQUAL gap. In terms of the service dimensions, the tangibles dimension, regardless of importance weight, is with the largest service quality gap. The second is the reliability and assurance dimension. The third is the empathy dimension, followed by the flight pattern dimension and the responsiveness dimension. On the other hand, the reliability and assurance dimension, regardful of importance weight, is with the largest service quality gap. The second is the tangibles dimension. The third is the empathy dimension, followed by the responsiveness dimension and the flight pattern dimension. The top 10 service items with large quality gap are the comfort and cleanness of seat, customer complaint handling, quality of food and beverage, safety, crew’s approach against unexpected situations, on-time departure and arrival, handling of delay, convenient of flight schedules, in-flight entertainment facilities and programs, and the size of airplane. The list is in order of weighted gap. Another interesting finding in this study the manager of airline may be interested in is described as follows. The top 10 service items airline has to improve as soon as possible, regardless of the weight of service item, are the comfort and cleanness of seat, quality of food and beverage, customer complaint handling, safety, crew’s approach against unexpected situations, size of airplane, convenient of flight schedules, handling of delay, on-time departure and arrival, and in-flight entertainment facilities and programs. On the other hand, the top 10 service items airline has to improve as soon as possible, regardful of the weight of service item, become the comfort and cleanness of seat, customer complaint handling, quality of food and beverage, safety, crew’s approach against unexpected situations, on-time departure and arrival, handling of delay, convenient of flight schedules, in-flight entertainment facilities and programs, and the size of airplane. The list is in order of weighted gap. This research finding is given to the airline to decide the ranking order of service items which have to be improved as soon as possible.

In the past, although many researchers evaluated the airline service quality using the SERVQUAL method, few of these researchers applied the fuzzy theory to evaluate the airline service quality. Most of previous SERVQUAL questionnaires are based on accurate measure. Since human judgments and preference are often vague and can not estimate his preference with an exact numerical value. Thus, fuzzy sets theory is an appropriate method for measuring passenger’s perception. One of the major advantages of fuzzy weighted SERVQUAL method is that the fuzzy weighted SERVQUAL method is more appropriate than the SERVQUAL method to measure passenger’s perception. In addition, fuzzy MCDM approach only evaluates passenger’s perception. Fuzzy weighted SERVQUAL method not only evaluates passenger’s perception, but also the service quality gap between passenger’s perception and expectation. Thus, fuzzy weighted SERVQUAL method is more appropriate than fuzzy MCDM approach to evaluate, understand and improve the service quality of airline. Although a lot of works evaluated the service quality of airline, most of these researches evaluated the service quality either by using SERVQUAL method or by fuzzy sets theory. So far, none researcher evaluates the service quality by using the weighted fuzzy SERVQUAL method. Thus, this paper fills this gap in current literature through such the way of integrating fuzzy theory and SERVQUAL. In this scene, the manuscript offers something that making fuzzy theory a little better growing. The major disadvantage of fuzzy weighted SERVQUAL method is that it is difficult to justify appropriately and accurately the membership function of passenger’s perception and expectation. A hybrid fuzzy weighted SERVQUAL method for the evaluation of service quality of airline will be shown in future research work. Although a lot of researches on the evaluation of airline service quality have been proposed, none of these researches obtained passenger’s expectations and perceptions by using non-linear MF. Thus, an evaluation of airline service quality by using non-linear MF will be shown in future studies. References [1] M. Abrahams, A service quality model for air travel demand: an empirical study, Transportation Research Part A 17A (5) (1983) 385–393. [2] J.M. Adamo, Fuzzy decision trees, Fuzzy Sets and Systems 4 (1980) 207– 219. [3] S. Aksoy, E. Atilgan, S. Akinci, Airline services marketing by domestic and foreign firms: differences from the customers’ viewpoint, Journal of Air Transport Management 9 (2003) 343–351. [4] K.F. Alotaibi, An empirical investigation of passenger diversity, airline service quality, and passenger satisfaction, Ph.D. Dissertation, Arizona State University, 1992. [5] R.E. Bellman, L.A. Zadeh, Decision-making in a fuzzy environment, Management Science 17 (4) (1970) 141–164. [6] B. Bowen, D. Headley, Air Travel Consumer Report: The Airline Quality Rating 2000, US Department of Transportation, Washington, DC, 2000. [7] A. Buller, Fuzzy sets with dynamics membership functions, in: Proceedings of the 2002 1st International Conference on Fuzzy Systems and Knowledge Discovery; November, 2002, pp. 564–565. [8] Bureau of Transport and Communications Economics, Quality of Service in Australian Passenger Aviation, Australian Government Publishing Service, Canberra, 1992. [9] Bureau of Transport and Communications Economics, International Aviation Trends and Issues, Australian Government Publishing Service, Canberra, 1994. [10] G.F. Butler, M.R. Keller, The cost-constrained global airline industry environment: what is quality? Transportation Quarterly 46 (1992) 599–618. [11] L. Campos, J.L. Verdegay, Linear programming problems and ranking of fuzzy numbers, Fuzzy Sets and Systems 32 (1989) 1–11. [12] C. Carlsson, P. Korhonen, A parametric approach to fuzzy linear programming, Fuzzy Sets and Systems 20 (1986) 17–30. [13] C.W. Chang, C.R. Wu, H.L. Lin, Integrated fuzzy theory and hierarchy concepts to evaluate software quality, Software Quality Journal 16 (2) (2008) 263–276. [14] Y.H. Chang, C.H. Yeh, A survey analysis of service quality for domestic airlines, European Journal of Operational Research 139 (2002) 166–177. [15] S. Chandramathi, S.P.P. Raghuram, V.S. Srinivas, H. Satyajit Singh, Dynamic bandwidth allocation for 3G wireless systems: a fuzzy approach, Applied Soft Computing 8 (2008) 274–284.

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