A hybrid approach based on fuzzy AHP and 2-tuple fuzzy linguistic method for evaluation in-flight service quality

Journal of Air Transport Management 60 (2017) 49e64

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Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman

A hybrid approach based on fuzzy AHP and 2-tuple fuzzy linguistic method for evaluation in-flight service quality Wenhua Li*, Suihuai Yu, Huining Pei, Chuan Zhao, Baozhen Tian Shaanxi Engineering Laboratory for Industrial Design, Northwestern Polytechnical University, No. 127, Youyi Road(West), Beilin District, Xi'an 710072, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 September 2016 Received in revised form 19 January 2017 Accepted 23 January 2017 Available online 3 February 2017

The in-flight service is one of the most important parts in the whole air travel service process. In order to better understand the passengers' preference and obtain their perception for service quality, the paper proposed a hybrid approach based on fuzzy AHP and 2-tuple fuzzy linguistic method to evaluate in-flight service quality. This study is comprised of three stages. In the first stage, the modified version of SERVQUAL instrument was used and a hierarchy of the evaluation index system for in-flight service quality was constructed. In the second stage we use fuzzy AHP to analyze the structure of the in-flight service evaluation problem. Using linguistic variables, pairwise comparisons for evaluation criteria and sub-criteria are made to determine the weights of criteria and sub-criteria. In the third stage, the ratings of sub-criteria are assessed in linguistic values to express the qualitative evaluation of passengers' subjective opinions, and then the linguistic values are transformed into 2-tuples and the 2-tuple linguistic arithmetic mean operator is utilized to obtain the average ratings of 100 respondents. Using the 2tuple linguistic weighted average operator to compute the aggregated ratings of criteria and the overall in-flight service quality of alternatives. Finally, we demonstrated the validity and feasibility of the proposed approach by conducting an application study of the comprehensive performance of three airlines' in-flight service quality in China. © 2017 Elsevier Ltd. All rights reserved.

Keywords: In-flight service Service quality SERVQUAL Fuzzy AHP 2-Tuple fuzzy linguistic method

1. Introduction Over the last few years, the performance evaluation of public transport is shifting from managers' perspective (Hensher and Daniels, 1995; Pullen, 1993) based on the cost efficiency and cost effectiveness to passengers' perspective based on service quality and passenger satisfaction (C. C. Chou et al., 2011; Eboli and Mazzulla, 2009; Gilbert and Wong, 2003). The companies with this strategy to improve their service quality are very profitable, because an improvement of the supplied service quality can attract further users, increase the customer satisfaction and loyalty (Eboli and Mazzulla, 2007). With the quickening pace of life and the improvement of transport infrastructure, more and more people prefer to travel by airplane. Based on 60th Edition of the World Air Transport Statistics (WATS) released by the International Air Transport Association (IATA), the airlines safely carried 3.6 billion

* Corresponding author. E-mail addresses: [email protected], (W. Li). http://dx.doi.org/10.1016/j.jairtraman.2017.01.006 0969-6997/© 2017 Elsevier Ltd. All rights reserved.

[email protected]

passengersdthe equivalent of 48% of the Earth's population in 2015. There was an increase of 7.2% over 2014, representing an additional 240 million air trips. The competition in the airline industry become more and more fierce because the emergence of the low cost carriers (Pearson et al., 2015). The airline industry is undergoing a very difficult time and many companies are in search of service segmentation strategies that will satisfy different target market segments (Gilbert and Wong, 2003). Passengers often cannot choose airports in some countries, but they can select reasonable flight among many different airlines. In addition, the passengers' demand for in-flight service keeps rising. The service quality of flight is a big factor when passengers choose a flight. The extant research suggested that delivering superior service quality is a prerequisite for success and survival in today's competitive business environment (Gilbert and Wong, 2003). Service quality and passenger satisfaction is increasingly recognized a critical determinant of business performance and a strategic tool for gaining competitive advantage. There is a considerable amount of related research on its practical applications. The traditional approach implies that the higher the

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W. Li et al. / Journal of Air Transport Management 60 (2017) 49e64

perceived service quality, the higher the customer's satisfaction (Basfirinci and Mitra, 2015). In addition, the studies draw a conclusion that the relationship between the dimensions of service quality and customer satisfaction may show a nonlinear pattern. Thus, determining the relative importance of dimensions of service quality is required. From a process prospective, air travel is divided into two stages: ground service and in-flight service (Chen and Chang, 2005), and it was believed that passengers' expectations of service quality may vary at different stages in the service process. Service quality at the ground and in-flight service stages should investigated separately. In-flight service stage includes on board security services, on board comfort preparations, in-flight entertainment materials and programs, in-flight telecommunications such as internet/e-mail/fax/ phone facilities, in-flight snack service, seat facilities, internal cleaning services, cabin crew and flight attendants responses, and taking off and landing procedures. The ground service is provided by airport and passengers have other alternatives to choose. However, passenger can choose their favorite flights which offer the superior in-flight service. Therefore, in-flight service quality is only researched in this article. The concern for a better understanding of factors affecting ser~ a and de vice quality in the public transport is increasing (de On ~ a, 2015). Many researchers had explored many approaches to On obtain the factors affecting the passengers' satisfaction and to assess to the performance of company service quality. The method of SERVQUAL developed by Parasuraman et al. (1988) is one of the most popular methods. It proposed a gap analysis method defined service quality as the degree and direction of difference between customers' expectations and perceptions in five dimensions. It has been widely used by many researchers and practitioners to measure service quality in a variety of fields, such as hospital, public transport, hotel, telecommunication, and bank (Altuntas et al., 2012; Daniel and Berinyuy, 2010; Kelley and Turley, 2001; Stefano et al., 2015; Toloie-Eshlaghy et al., 2011). SERVPERF is an instrument developed by Cronin and Taylor (1992), which is now widely used in measuring customer evaluations of service quality. A panel data approach is utilized to analyze the passenger satisfaction of a public transport service (Anna et al., 2014). The research measured and compared differences in passengers' expectations of the desired airline service quality in terms of the dimensions of reliability; assurance; facilities; employees; flight patterns; customization and responsiveness (Gilbert and Wong, 2003). To attract more passengers, airlines make a big effort to provide distinguished and high-quality service to meet passengers' demands and bring passengers comfortable flight experience, evaluation in-flight service quality from the passenger perspective is necessary. We proposed a hybrid approach that combines Fuzzy Analytic Hierarchy Process (Fuzzy AHP) and 2-tuple fuzzy linguistic method to evaluate in-flight service quality. There are several reasons that we select Fuzzy AHP and 2-tuple fuzzy linguistic method. AHP is a widely used method for solving multi-criteria problems in practical situations. Considering the intangibility, perishability, inseparability, and heterogeneous nature of the service industry, it becomes difficult for people to describe and measure service quality (Chen and Chang, 2005). Humans and preference judgments are often vague and cannot estimate their preference with an exact numerical value. Conventional measurement makes use of cardinal or ordinal scales to measure the quality of service, this scale used crisp number is difficult to represent the customer's preference. Fuzzy set theory is an appropriate method for dealing with uncertainty. Fuzzy logic provides tools able to capture vague information, generally described in a natural language, and convert it to a numeric format.

The systems are based on fuzzy reasoning ability similar to the human form. In addition, 2-tuple representation model was used for processing of human's qualitative ratings, and has an advantage of allowing data processing without information loss (Herrera et al., 1999). The combination of AHP with fuzzy set and 2-tuple representation model can deal with human judgments under fuzzy environment and has no information loss. The research framework of this paper is shown in Fig. 1. The objectives of this study were to: 1) construct the evaluation index system of in-flight service quality; 2) propose an approach combining fuzzy AHP and 2-tuple fuzzy linguistic approach to computation of overall service quality and benchmarking. This research paper focuses on the computation of the weights of factor affecting in-flight service quality. The remainder of this paper is organized as follows. Section 2 makes an introduction to the tools and methods for measuring service quality. Section 3 reviews the fuzzy AHP and 2-tuple fuzzy linguistic method used in this study, and explains the proposed approach. A case study of China is given in Section 4. Finally, a brief conclusion is drawn and limitations for further research are descripted. 2. Literature review 2.1. The nature of service quality The service has three properties: intangibility, heterogeneity, and inseparability (Carman, 1990; Parasuraman et al., 1988). The service attributes make the service quality complex, fuzzy and ~ a et al., 2012). Some scholars (Gronroos, 1988; abstract (De On Parasuraman et al., 1985) think the perception of service quality is a comparison of customer expectation with actual service performance. Other scholars only concern the passengers' perception and do not take customer expectation into consideration (Eboli and Mazzulla, 2011; Nathanail, 2008). 2.2. Methods for analyzing service quality The assessment of airline in-flight service is a systemic and enormous project, which involve many factors, from staff, aircraft's equipment, facilities, cabin environment to the intangible service and so on. Many scholars study the airplane service quality from different aspects. Vink et al. (2005) studied service quality from the comfort perspective, he divided the comfort during flight experience into seven phases. Vink et al. (2012) researched the 10,032 passengers' trip reports and found the six descriptors strongly associated with comfort for all subjects, they are intention to fly again with this airline, enough/much legroom, cleanliness of the interior, nice crew and good seat. Eboli and Mazzulla (2009) proposed ordinal logistic regression model to analyze passenger satisfaction about airport. Ali et al. (2016) categorized the international airport's physical environment into 4 items, which include layout accessibility, facility ambience & aesthetic, functionality and cleanliness, and analyzed the effect of physical environment on passenger delight and satisfaction. When computations the customer satisfaction with a specific criterion or attribute, multicriteria analysis (MA) is a popular and widely used approach. And it is usually combined with a fuzzy approach (Kuo et al., 2007; Kuo, 2011). There are two main widely used methods to analyze the service quality. (1) Performance perception and expectation. Parasuraman et al. (1985) proposed that service quality is a function of the differences between expectation and performance from customers' rates. (2) Only performance perception approach. Cronin and Taylor (1992) were in favor of only perceptions models based on the

W. Li et al. / Journal of Air Transport Management 60 (2017) 49e64

51

Fig. 1. Research framework.

notion that performance perceptions are already the result of customers' comparison of the expected and actual service. They revealed that SERVPERF explained more variation in the measurement of service quality in all the four service industries. Therefore, SERVPERF is adopted in this study to evaluate the in-flight service quality. Parasuraman et al. (1985) does not help to set priorities for service attributes, it means that all attributes are equally important, which does not accord with the fact. The subsequent studies take the importance of each attribute into consideration. Pakdil et al. (2007) used a weighted SERVQUAL for analyzing airline service quality. C. C. Chou et al. (2011) included fuzziness in service quality evaluation by using a fuzzy weighted SERVQUAL to evaluate airlines. Although SERVQUAL is widely used in different service industries, its general nature has led to criticism regarding its ability to precisely measure an industry's service quality (Park et al., 2004). The evaluation of service quality is essentially multi-criteria decision making (MCDM) problem in the presence of many criteria and sub-criteria. Some of widely used MCDM methods € zkan et al., 2011; include analytic hierarchy process (AHP) (Büyüko Delbari et al., 2016; Liou and Tzeng, 2007), analytic network process (ANP) (Chen, 2016; Lin and Huang, 2015), TOPSIS (Awasthi et al., €zkan and Çifçi, 2012; Tang et al., 2011; Toloie2011; Büyüko Eshlaghy et al., 2011) and grey relation method(Chen et al., 2011; James and Liou Chao-Che Hsu, 2011). Since the subjective evaluation of service quality is difficult to be expressed in number, there is existence of uncertainty. The use of Fuzzy theory can be more realistic in assessing service quality as perception of passengers can be expressed in linguistic term. Tsaura et al. (2002) combined fuzzy set theory with AHP to evaluate the service quality of hospitals. Chen (2016) proposed a combined MCDM method based on DEMATEL and ANP to identify critical service quality improvement criteria with the goal of increasing the competitive advantages of airlines. In addition, 2-tuple linguistic model was developed by Herrera and Martínez (2000) and has been applied in different domains, including performance appraisal (Espinilla et al., 2013), product development (Wang, 2009), evaluation of hotel services (Carrasco et al., 2012).

2.3. Identification criteria and sub-criteria of in-flight service quality The facilities and environment of airplane, the crew work on the airplane, and safety and so on, are services that must be given the importance they deserve. It is clear that the aircraft itself is not the single factor that attracts the passengers. In addition, the general services and the quality satisfaction are more important indicators. Therefore, the airline must constantly understand the needs of the passengers and provide all the services needed in order to attract them. The communication skills and the problem solving ability have a positive effect on the passenger satisfaction. Being able to provide high quality service is of a great importance for the passengers and the way they feel, in this way the satisfaction increases. The common dimensions in the existing literature are shown in Table 1. Parasuraman proposed SERVQUAL, which consist of five dimensions and 22 items for measuring consumer perceptions of service quality. Gilbert and Wong (2003) proposed 7 dimensions based on the SERVQUAL to measure service quality. Pakdil et al. (2007) proposed eight dimensions combined the SERVQUAL with Gilbert and Wong's study, adding the image dimension into study. The dimension of image in the study included three items, which is image of the airline company, external appearance of the airplane and employees' foreign language level. The authors thought the image of the airline company is a comprehensive item; it cannot alone assess the specific service quality. The second and third item should be sorted into the tangible dimension and employee dimension. Hussain et al. (2015) proposed a six dimensions' airline service quality construct, the major difference is the identification of two additional dimensions, security and safety and communication. Although the issue of security and safety is considered to be an important factor of affecting passengers' travel decision, security checks belong to ground service. It is beyond the scope of in-flight service. Communication can be sorted into the criteria of employees. The evaluation structure used in this study is presented in Table 2. Some of measurement items were adapted from the existing literature. Measurements of service quality about airplane were taken from the previous studies (Gilbert and Wong, 2003; Han, 2013; Hussain et al., 2015; Pakdil et al., 2007; Parasuraman et al., 1988). The current study extends the scholars' research

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W. Li et al. / Journal of Air Transport Management 60 (2017) 49e64

Table 1 The dimensions in the previous studies on the service quality. SERVQUAL (1988)

Gilbert and Wong's study (2003)

Pakdil and Aydin's study (2007)

Hussain's study (2015)

Reliability Responsiveness Assurance Empathy Tangibles

Employees Facilities Responsiveness Reliability Flight patterns Assurance Customization

Employees Tangibles Responsiveness Reliability and assurance Flight patterns Availability Image Empathy

Reliability Responsiveness Assurance Tangibility Security and safety Communication

framework and concluded main criteria that are specific to the inflight service. The main criteria consist of employees, facilities, flight schedule and information, supporting service, and physical environment. The first two criteria are consistent with the Gilbert and Wong's model. Fight schedule and information is based on the flight pattern in the Gilbert and Wong's model and added information, which is related to assurance. The criterion of supporting service is adapted from Pakdil et al. (2007). The last criterion is referred to the air quality, temperature and noise in the aircraft cabin. The dimensions and sub-dimensions are now explained. 2.3.1. Employees Under the employees' dimension, there are five indicators: neat, tidy and graceful crew; courtesy and helpfulness of crew; knowledge and work skill of crew; understanding of passengers' specific needs and crew's approach against unexpected situations. This dimension mainly reflects the quality of a passenger's interaction with the service providers. During the whole flight, all service delivery is performed by the frontline workers. The existing research has shown that a positive interaction between a customer and a frontline employee has a positive impact on service quality (Dabholkar, 1996), customer satisfaction (Bitner et al., 1990), customer loyalty (Vesel and Zabkar, 2010), and positive word-ofmouth (Keaveney, 1995). Neat, tidy and graceful crew, which was a primary quality, refers to good appearance and dress of employees, it was taken as a indicator in many existing studies (Jeeradist et al., 2016; Kuo, 2011; Lin and Huang, 2015; Pakdil et al., 2007; Stefano et al., 2015; Wang et al., 2011). The second subcriterion of employees refers to behavior and attitude of employees. Unfriendly crew is one of the top factors that would have a negative impact on someone's future booking decisions (Waguespack and Rhoades, 2014). Knowledge and work skill of crew refers to the competence to provide accurate and timely service to passengers. Passengers may be more concerned with the cabin crew's professional knowledge and service skills than their physical appearance (Chen and Chang, 2005). Understanding of passengers' specific needs is most crucial step in defining and delivering high-quality service (Zeithaml et al., 1996). Meeting these expectations would raise the level of passenger satisfaction and value perception, and consequently the delivering process of the airline service quality performance level viability. Crew is more likely to experience unexpected issues and situations when serving passengers on a daily basis. This sub-criteria of crew's approach against unexpected situations refers to problem-solving ability, which is identified by Dabholkar (1996). The in-flight crew needs to handle various unexpected emergency situations. 2.3.2. Facilities The criterion of facilities includes aircraft itself and facilities in the cabin. People prefer to choose the newly airplane, because the newly airplane are normally equipped with the various basic and advanced facilities and mechanisms, can provide the passengers

good ambience and function during a flight. There are five subcriteria under the criterion of facilities: comfort and clean interior/seat, in-flight newspaper, magazines and books, in-flight facilities condition (internet/email/fax/phone/washroom), quality of food and beverage, in-flight entertainment facilities/programs. The seat comfort and interior design play an important role in air travel, especially for the long-haul flight (Vink et al., 2012), and it is related to passenger's satisfaction and the willingness to use the system again (Richards, 1980). In-flight newspaper, magazines and books and in-flight entertainment facilities/programs are effective service to help passengers kill time and distract them from tedious journey. In-flight entertainment system reduce the passenger's physical and psychological negative stress and boredom intelligently and effectively (Liu, 2007), it also contributes greatly to passengers' satisfaction with airline services (Alamdari, 1999). In-flight facilities in cabin are tangible and oriented to passengers, which have a direct effect on passengers' perception. The research has shown that catering is a key attribute for a customer's satisfaction with airline service quality (Messner, 2016). The in-flight food and beverage service is a major determinant of the in-flight service (An and Noh, 2009).

2.3.3. Flight schedule and information Under the criterion of flight schedule and information, there are four items: on-time departure and arrival, clear and precise cabin announcements, cabin safety demonstration, flight pattern (Nonstop, Direct, and Connecting). Flight delay is one of common complaints from passengers, which generate strong negative impacts on passenger emotion (Kim and Park, 2016). On-time departure and arrival, which has a direct effect on passengers' schedule, is a critical factor for passengers. The cabin announcements is a form of communication, it informs passengers about delivery of services, and keeps them updated in case of any modification in the flight schedule. Cabin safety demonstration is a necessary step which can give passenger the perception of safety and reliability. There are three flight patterns: nonstop, direct and connecting. Connecting flights are always the least desirable in terms of convenience and time. Direct and Connecting flight pattern take longer time than nonstop.

2.3.4. Supporting service Supporting service in this study refers to services from travelrelated partners, e.g. car rental, hotels, pick-up service, etc. These travel-related services have gradually been popular in airlines and have attracted more passengers' attention. These services which can be conducted onboard provide passengers more convenience and save their time after landing. The existing research (Abdlla et al., 2007; Eboli and Mazzulla, 2009; Gilbert and Wong, 2003; Han, 2013; Liou et al., 2010) mentioned this criterion to evaluating the service quality of airline.

Table 2 The criteria of in-flight service quality in current study. The criteria

The sub-criteria

References

The in-flight service quality

Employees (B1)

Neat, tidy and graceful crew (C11)

(Hussain et al., 2015; Jeeradist et al., 2016; Pakdil et al., 2007; Park, 2007; Wang et al., 2011) (Dabholkar et al., 1996; Pandey, 2016; Yeh and Kuo, 2003) (Chen and Chang, 2005; Miller and Bures, 2015; Sivilevi cius and  naite, 2010) Maskeliu (Abdlla et al., 2007; C. C. Chou et al., 2011; Pakdil et al., 2007) (C. C. Chou et al., 2011; Jeeradist et al., 2016; Pakdil et al., 2007) (Chen and Chang, 2005; Hu and Hsiao, 2016; Hussain et al., 2015; Lin and Huang, 2015; Wu and Cheng, 2013) (C. C. Chou et al., 2011; Han, 2013; Han et al., 2012; Wang et al., 2011) (Abdlla et al., 2007; C. C. Chou et al., 2011; Hu and Hsiao, 2016; Jeeradist et al., 2016; Pakdil et al., 2007) (Abdlla et al., 2007; An and Noh, 2009; Chen, 2008; C. C. Chou et al., lu et al., 2016; Messner, 2016) 2011; Han et al., 2012; Kurtulmus¸og (Abdlla et al., 2007; Han et al., 2012; Hussain et al., 2015; Leong et al., 2015; Pakdil et al., 2007; Park, 2007) (An and Noh, 2009; C. C. Chou et al., 2011; Gilbert and Wong, 2003; Liou et al., 2011; Pakdil et al., 2007) (Chen and Chang, 2005; Chen et al., 2011; Hussain et al., 2015) (Chen and Chang, 2005; Chen et al., 2011; James and Liou Chao-Che Hsu, lu et al., 2016) 2011; Kurtulmus¸og (Chen et al., 2011; Gilbert and Wong, 2003; Liou and Tzeng, 2007; Pakdil et al., 2007) (Abdlla et al., 2007; Gilbert and Wong, 2003; Liou et al., 2010)

Courtesy and helpfulness of crew (C12) Knowledge and work skill of crew (C13)

Facilities (B2)

Understanding of passengers' specific needs (C14) Crew's approach against unexpected situations (C15) Comfort and clean interior/seat(C21) In-flight newspaper, magazines and books (C22) In-flight facilities condition(internet/email/fax/phone/ washroom) (C23) Quality of food and beverage (C24) In-flight entertainment facilities/programs (C25)

Flight schedule and information (B3)

On-time departure and arrival(C31) Clear and precise cabin announcements(C32) Cabin safety demonstration(C33) Flight pattern (Nonstop,Direct,Connecting)(C34)

Supporting service(B4) Physical environment (B5)

Travel service related partners car rentals, hotels and airport pick-up(C41) Air quality (C51) Thermal comfort(C52) Sound comfort(C53)

W. Li et al. / Journal of Air Transport Management 60 (2017) 49e64

The goal

(Brundrett, 2001; Giaconia et al., 2013; Han, 2013; Hinninghofen and  naite, 2010) Enck, 2006; Sivilevi cius and Maskeliu ~ a et al., 2013; Sivilevi  naite, (An and Noh, 2009; De On cius and Maskeliu 2010; Wu and Cheng, 2013)  naite, (Jen and Hu, 2003; Pennig et al., 2012; Sivilevi cius and Maskeliu 2010; Vink and van Mastrigt, 2011; Wu and Cheng, 2013)

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W. Li et al. / Journal of Air Transport Management 60 (2017) 49e64

3.2. Fuzzy AHP

2.3.5. Physical environment There are three items under the criterion of physical environment: air quality, thermal comfort, and sound comfort. Han (2013) conducted studies to indicate that good ambient conditions significantly induce favorable cognitive and affective evaluations and satisfaction, thereby influencing passengers' positive behavioral intentions. Scholars have focused on a number of attributes of the physical environment. This atmospheric criteria, which is the background characteristics of the environment, is generally comprised of such elements as air quality (e.g., dust-free, easy of breathe, air freshness, odor), temperature (e.g., dryness, moisture/ humidity, cold/hot), and sound factor (e.g., noise, sound level, music). In-flight environmental factors appear very important in inducing cognitive evaluation of airline image and value (Han, 2013). These three items have an effect on passengers' comfort (Brundrett, 2001; Cui et al., 2014; Park et al., 2011; Pennig et al., 2012; Variables et al., 2014).

AHP is a widely used method for solving multi-criteria problems in practical situations. AHP is firstly introduced by Myres and Alpert in 1968 and developed by Saaty in 1977. Although the goal of AHP is to evaluate the expert information, people's judgments and preferences are difficult to express in precise numbers due to the fuzziness of language. In addition, the mapping of the decision maker's perception to crisp values is AHP's another drawback. To address these problems, Chang (1996) proposed fuzzy AHP and its extension to tackle alternative selection and justification problems. The steps of Chang's approach to handling fuzzy AHP are explained below. Let U ¼ fu1 ; u2 ; /; um g be a goal set and X ¼ fx1 ; x2 ; /; xn g be an object set. In the following, each object is taken and extent analysis for each goal is performed, respectively. Thus, m extent analysis values for each goal can be obtained and shown as follows:

3. Methodology

Mg1 ; Mg2 ; /Mgm ; i ¼ 1; 2; /; n

In many practical situations, people cannot precisely express their preferences because of the complexity and vagueness of decision making problems. Zadeh (1965) first introduced the fuzzy set theory, which is suitable for subjective judgment and qualitative assessment in the evaluation processes of decision making. It was oriented to the rationality of uncertainty due to vagueness. 2-tuple linguistic approach is an effective method to solve the uncertainty information. In this section, some essential definitions of the fuzzy number, 2-tuple linguistic approach, and a proposed method combined FAHP and 2-tuple fuzzy linguistic approach are briefly described in the following sections.

3.1. Fuzzy sets and fuzzy numbers

the smallest possible value, the most promising value, and the largest possible value that describe a fuzzy event. A triangular ~ is described as Eq. (1). membership function of M

x
Step 1. The value of fuzzy synthetic extent with respect to the ith object is defined as Eq. (3):

Si ¼

m X

2 mjgi 54

n X m X

j¼1

31 mjgi 5

(3)

i¼1 j¼1

where 5 denotes the extended multiplication of two fuzzy numbers. P j In order to obtain m j¼1 mgi , perform the fuzzy addition operation

m X

0 mjgi

¼@

j¼1

m X

lj ;

j¼1

m X

mj ;

m X

j¼1

1 uj A

(4)

j¼1

P P j 1 and to obtain ½ ni¼1 m j¼1 mgi  , perform the fuzzy addition operation of Mgj i ðj ¼ 1; 2; /; mÞ values such that n X m X

0 j mgi

¼@

i¼1 j¼1

n X j¼1

lj ;

n X

mj ;

j¼1

n X

1 uj A

(5)

j¼1

And then compute the inverse of the vector in Eq. (5) such that

lxm (1) mxu x>u

The following are the operations that can be performed on triangular fuzzy numbers. ~ 1 ¼ ðl1 ; m1 ; u1 Þ and M ~ 2 ¼ ðl2 ; m2 ; u2 Þ then, Let M ~ ¼ ðl þ l ; m þ m ; u þ u Þ ~ þM (i) Addition: M 1 2 1 2 1 2 1 2 ~ M ~ ¼ ðl  l ; m  m ; u  u Þ (ii) Subtraction: M 1 2 1 2 1 2 1 2 ~ M ~ ¼ ðl  l ; m  m ; u  u Þ (iii) Multiplication: M 2 1 2 1 2 1 2 1 1 1 1 1 ~ (iv) Division: M 1 ¼ ; ; u 1 m1 l 1

j

where all the Mgi ðj ¼ 1; 2; /; mÞ are triangular fuzzy numbers and gi is the corresponding goal.

of m extent analysis values for a particular matrix such as

The concept of fuzzy set is introduced firstly by Zadeh (1965), a fuzzy set is a class of objects with a continuum of grades of membership ranging between zero and one. If the assigned value is zero, the element does not belong to the set and if the value assigned is one, then the element belongs completely to the set. Lastly, the value which lies between 0 and 1 belongs to the fuzzy set only partially. A triangular fuzzy number (TFN) is represented with three points as follows. ~ (l, m, u), where the parameters l, m, u, respectively, indicate M¼

8 0; > > > > > > x l > > ; < m l mM~ ðxÞ ¼ > ux > > ; > > >u  m > > : 0;

(2)

2 4

n X m X

31 mjgi 5

¼

i¼1 j¼1

1

Pn

j¼1 uj

1

; Pn

j¼1 mj

1

!

; Pn

j¼1 lj

Step 2. The degree of possibility m2 ¼ ðl1 ; m1 ; u1 Þ  m1 ¼ ðl1 ; m1 ; u1 Þ is defined as

Vðm2  m1 Þ ¼ sup½minðm1 ðxÞ; m2 ðyÞÞ yx

and can be equivalently expressed as below.

(6)

of

(7)

W. Li et al. / Journal of Air Transport Management 60 (2017) 49e64

Vðm2  m1 Þ ¼ hgtðm2 ∩m1 Þ ¼ m2 ðdÞ 8 1 if m2  m1 > > > > > > < 0 if l1  u2 > > > > l1  u 2 > > otherwise : ðm2  u2 Þ  ðm1  l1 Þ

D½0; g/S 

 1 1 ; ; 2g 2g

(8)

DðbÞ ¼ ðsi ; ai Þ;

Step 3. The possibility degree for a convex fuzzy number to be greater than k convex fuzzy numbers mi ði ¼ 1; 2; /; kÞ can be defined by

Vðm  m1 ; m2 ; /; mk Þ ¼ V½ðm  m1 Þandðm  m2 Þand/andðm  mk Þ  ¼ min Vðm  mi Þ; i ¼ 1; 2; /; k:

(9)

Assume that

8 > <

si ;

> : ai ¼ b  i;

i ¼ roundðb,gÞ   1 1 ; ai 2 2g 2g

where roundð$Þ is the usual rounding operation, si has the closest index label to b and a is the value of the symbolic translation. The interval of a is determined by the number of linguistic terms in S. Let S ¼ fsi ; i ¼ 0; 1; /; gg be a linguistic term set and ðsi ; ai Þ be a 2-tuple. There exists a function D1 , which is able to convert a 2tuple linguistic variable into its equivalent numerical value b 2 [0, 1]. The reverse function D1 is defined as follows.

D1 : S 

d0 ðAi Þ ¼ minVðSi  Sk Þ



55

   1 1 ; / 0; g ; 2g 2g



(10) i g

D1 ðsi ; ai Þ ¼ þ ai ¼ b: For k ¼ 1; 2; /; n; ksi, then the weight vector is given by T

w0 ¼ ðd0 ðA1 Þ; d0 ðA2 Þ; /; d0 ðAn ÞÞ

(11)

D1 ðs3 ; 0Þ ¼ 34 þ 0 ¼ 0:75, and if b ¼ 0:560, then convert it to a 2tuple, Dðs3 ; 0:060Þ ¼ 0:5 þ 0:060 ¼ 0:560. Graphically, the above

where Ai ði ¼ 1; 2; /; nÞ are n elements. Step 4. Via normalization, the normalized weight vector is

w ¼ ðdðA1 Þ; dðA2 Þ; /; dðAn ÞÞT

For example, if a linguistic term set S ¼ fs0 ; s1 ; s2; s3 ; s4 ; s5 g, then there has been that: g ¼ 6; a2½0:125; 0:125Þ,

(12)

where w is a non-fuzzy vector.

3.3. 2-Tuple linguistic variables This 2-tuple linguistic computational model was developed by Herrera and Martínez (2000), in order to improve the precision of the processes of computing with words. The 2-tuples linguistic information is composed by a linguistic term and the symbolic translation represented by a numeric value, expressed as ðsi ; aÞ, where si is a linguistic term and a is the symbolic translation of this term. In this way, the linguistic information is managed as a continuous range instead of a discrete one. This method has no loss of information when we apply it to computation with words processes. Let S ¼ fsi ; i ¼ 0; 1; /; gg be a linguistic term set with granularity gþ1, si represents a linguistic information variable, and b2½0; 1 is a value representing the result of a symbolic aggregation operation. Then the generalized translation function D used to obtain the 2-tuple linguistic variable equivalent to b can be defined as follows.

calculation results are represented in Fig. 2. It is noteworthy that the conversion of a linguistic term into a linguistic 2-tuple consists of adding a value 0 as symbolic translation si 2S0ðsi ; 0Þ. Let ðsi ; a1 Þ and ðsj ; a2 Þ be two 2-tuples, then: (1) If i < j then ðsi ; a1 Þ is smaller than ðsj ; a2 Þ; (2) If i ¼ j then (a) if a1 ¼ a2 then ðsi ; a1 Þ is equal to ðsj ; a2 Þ; (b) if a1 < a2then ðsi ; a1 Þ is smaller than ðsj ; a2 Þ; (c) if a1 > a2 then ðsi ; a1 Þ is bigger than ðsj ; a2 Þ. The arithmetic mean is a classical aggregation operator, its equivalent operator for linguistic 2-tuples is defined as Let x ¼ fðr1 ; a1 Þ; ðr2 ; a2 Þ; /ðrn ; an Þg be a set of 2-tuples, the 2tuples arithmetic mean is computed as

xe ¼ D

n X 1 i¼1

n

!

D1 ðri ; ai Þ ¼ D

n 1X b n i¼1 i

! (13)

Let x ¼ fðr1 ; a1 Þ; ðr2 ; a2 Þ; /ðrn ; an Þg be a set of 2-tuples and w ¼ fw1 ; w2 ; /wn g be their associated weights. The 2-tuple weighted average is

0 1 0 1 P P B n D1 ðr ; a Þ,w C B n b ,w C B B i¼1 i i C iC xe ¼ DB i¼1 Pn i i C ¼ DB P C n @ A @ A i¼1 wi i¼1 wi

(14)

3.4. The procedure of the proposed method

Fig. 2. Example of a symbolic translation computation.

The procedure of the proposed method was shown in Fig. 3, which consisted of four main steps. The following content gave the details of every step.

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Fig. 3. Research methodology. Table 3 Triangular fuzzy numbers for importance comparison of two criteria. Linguistic scales

Triangular fuzzy number

Reciprocal triangular fuzzy numbers

Absolutely more important Very strong strong Weak Equally important Just equal

(5/2,3,7/2) (2,5/2,3) (3/2,2,5/2) (1,3/2,2) (1/2,1,3/2) (1,1,1)

(2/7,1/3,2/5) (1/3,2/5,1/2) (2/5,1/2,2/3) (1/2,2/3,1) (2/3,1,2) (1,1,1)

Table 4 Linguistic variable and its semantics for rating the criteria. Linguistic scales

Triangular fuzzy number

Very low(VL) Low(L) Average(A) High(H) Very high(VH)

(0,0,0.25) (0. 0.25, 0.5) (0.25, 0.5,0.75) (0.5,0.75,1) (0.75,1,1)

3.4.1. The evaluation index system of in-flight service quality The hierarchy structure of in-flight service quality evaluation system consists of four levels, the first level is the goal level, the second level is criteria level, includes five criteria, the third level is sub-criteria, includes eighteen sub-criteria. The last level the option level, there are three options in this research. The hierarchy structure of in-flight service quality evaluation system was shown in Fig. 4. 3.4.2. Questionnaire design There are two types of questionnaires, one for experts to make pair-wise comparisons between criteria (sub-criteria), and one for passengers to give ratings for sub-criteria. Two questionnaires used in this study were presented in Appendix A and B, respectively. The expert questionnaire included series of questions, like “How important is Employees(B1) when it is compared with Facilities(B2)?”, which were required to finish with corresponding linguistic terms shown in Table 3 during interview. The importance of one criterion over another included five levels: absolutely more important, very strong, strong, weak, equally important. The graphical representation of triangular linguistic labels was show in Fig. 5. The passenger questionnaire consisted of three sections. Questions in the first section are basic information including demographic characteristics, travel frequency and purpose. Perceived in-flight service quality was measured through the question in the second section (see Appendix B). All the respondents were asked to rate each item of in-flight services on a five-point Likert scale anchored from Very low (1) to Very high (5). The linguistic terms and graphical representation of triangular linguistic labels was

show in Table 4 and Fig. 6. In addition, a rating on global service, in terms of in-flight service quality, was requested in the third section.

3.4.3. Sampling and data collection Rating data from China were collected in surveys of 3 airplanes from 3 airline companies on the same air route from Xi'an to Hong Kong. The questionnaire was shown in Appendix B. Before the main study was conducted, a pilot test was performed on a small scale in order to make sure that the questions were read and understood as intended. The survey lasted 2 weeks and a total of 105 respondents participated in the survey, yielding 100 usable responses. A pilot test showed that most of the respondents were regular users and many of them were heavy users of air travel services. The questionnaires test using reliability, SPSS 12.0 reliability scale and an internal consistency analysis was performed separately for each of the elements.

3.4.4. The detailed calculation procedure The proposed hybrid fuzzy approach consists of two stages. The purpose of the first stage is calculation the weight of the subcriteria via collecting experts' comparisons about criteria, subcriteria, and the purpose of the second stage is measurement of the in-flight service quality of alternatives. The detailed procedure is as follows. Step 1. Organize a team of the experts who is experienced in the scope of this study. Step 2. Construct the AHP model hierarchically based on the criteria and sub-criteria. Step 3. Collect the experts' opinions on the criteria's importance via pair-wise comparisons. The experts are asked to compare five main criteria and the corresponding sub-criteria under the main criteria (Table 2). The expert team needs to finish a pairwise comparison matrix about criteria and six pairwise comparison matrices about sub-criteria. The experts use the linguistic scales expressed the relative importance of one criterion over another.

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57

Fig. 4. The hierarchy structure of in-flight service quality evaluation system.

Fig. 5. Linguistic scale for relative importance.

Step 4. The pairwise comparison matrices analyzed by using FAHP method are presented in this section. The weights of the sub-criteria are obtained used Eqs. (3e12). Step 5. Collect respondents' ratings for each item of in-flight services. Transform the ratings from respondents into 2tuples, and then sort these data. Step 6. The aggregated ratings of each sub-criteria from 100 respondents are computed by Eq. (13). Step 7. The aggregated ratings of each criterion are computed by Eq. (14). Step 8. The aggregated ratings of alternatives are computed by Eq. (14), and then rank them. 4. The application of in-flight service quality evaluation method To better understand the in-flight service quality of airlines in China, this study selected three well-known airlines. Take the flight line from Xi'an to Hong Kong for study case, we evaluated three airlines' in-flight service quality. Four stages are involved in the evaluation procedure for evaluating the in-flight service quality. The four stages include interview survey, calculation weights of criteria, the questionnaire design and collection of data, and measurement of service quality.

Fig. 6. Linguistic term set of five labels with its semantics.

4.1. Experts interview A commission consisting of 3 airline managers and 2 frontline employees on airplane, all of whom had more than 5 years'

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W. Li et al. / Journal of Air Transport Management 60 (2017) 49e64

Table 5 Pair-wise comparison matrix of criteria and local weights.

Employees(B1) Facilities(B2) flight schedule and information(B3) supporting service(B4) Physical environment(B5)

B1

B2

B3

B4

B5

Weight

(1,1,1) (1,1.5,2) (1,1.5,2) (1/2,2/3,1) (2/5,1/2,2/3)

(1/2,2/3,1) (1,1,1) (1/2,2/3,1) (2/5,1/2,2/3) (2/5,1/2,2/3)

(1/2,2/3,1) (1,1.5,2) (1,1,1) (1/2,2/3,1) (1/2,2/3,1)

(1,1.5,2) (3/2,2,5/2) (1,1.5,2) (1,1,1) (1/2,1,3/2)

(3/2,2,5/2) (3/2,2,5/2) (1,1.5,2) (2/3,1, 2) (1,1,1)

0.23 0.25 0.33 0.12 0.07

Table 6 Pair-wise comparison matrix of employees' sub-criteria and local weights.

Neat, tidy and graceful crew (C11) Courtesy and helpfulness of crew (C12) Knowledge and work skill of crew (C13) Understanding of passengers' specific needs (C14) Crew's approach against unexpected situations (C15)

C11

C12

C13

C14

C15

weight

(1,1,1) (1,3/2,2) (3/2,2,5/2) (3/2,2,5/2) (3/2,2,5/2)

(1/2,2/3,1) (1,1,1) (1,3/2,2) (1/2,1,3/2) (1,3/2,2)

(2/5,1/2,2/3) (1/2,2/3,1) (1,1,1) (1/2,1,3/2) (1/2,1,3/2)

(2/5,1/2,2/3) (2/3,1,2) (2/3,1,2) (1,1,1) (1/2,1,3/2)

(2/5,1/2,2/3) (1/2,2/3,1) (2/3,1,2) (2/3,1,2) (1,1,1)

0.09 0.20 0.24 0.23 0.24

Table 7 Pair-wise comparison matrix of facilities' sub-criteria and local weights.

Comfort and clean interior/seat(C21) In-flight newspaper, magazines and books (C22) In-flight facilities condition(internet/email/fax/phone/washroom) (C23) Quality of food and beverage (C24) In-flight entertainment facilities/programs (C25)

C21

C22

C23

C24

C25

weight

(1,1,1) (2/5,1/2,2/3) (1/2,2/3,1) (2/5,1/2,2/3) (2/5,1/2,2/3)

(3/2,2,5/2) (1,1,1) (1,3/2,2) (1,3/2,2) (1/2,1,3/2)

(1,3/2,2) (1/2,2/3,1) (1,1,1) (1/2,2/3,1) (1/2,2/3,1)

(3/2,2,5/2) (1/2,2/3,1) (1,3/2,2) (1,1,1) (1/2,1,3/2)

(3/2,2,5/2) (2/3,1,2) (1,3/2,2) (2/3,1,2) (1,1,1)

0.31 0.01 0.22 0.25 0.21

Table 8 Pair-wise comparison matrix of flight schedule and information's sub-criteria and local weights.

On-time departure and arrival(C31) Clear and precise cabin announcements(C32) Cabin safety demonstration(C33) Flight pattern (Nonstop,Direct,Connecting)(C34)

C31

C32

C33

C34

weight

(1,1,1) (2/5,1/2,2/3) (2/5,1/2,2/3) (2/3,1,2)

(3/2,2,5/2) (1,1,1) (1,3/2,2) (3/2,2,5/2)

(3/2,2,5/2) (1/2,2/3,1) (1,1,1) (3/2,2,5/2)

(1/2,1,3/2) (2/5,1/2,2/3) (2/5,1/2,2/3) (1,1,1)

0.38 0.07 0.17 0.38

Table 9 Pair-wise comparison matrix of physical environment's sub-criteria and local weights.

Air quality (C51) Thermal comfort(C52) Sound comfort(C53)

C51

C52

C53

weight

(1,1,1) (1/2,2/3,1) (1/2,2/3,1)

(1,3/2,2) (1,1,1) (1/2,1,3/2)

(1,3/2,2) (2/3,1,2) (1,1,1)

0.43 0.27 0.37

experience, was organized to have a deep interview and was asked to compare five main criteria and eighteen sub-criteria in the scope of this study. The questionnaire for experts was shown in Appendix A. These experts need to make pairwise comparisons of the relative importance of two criteria. Table 3 showed the linguistic scale and the triangular numbers used in this paper to express the relative importance of one criterion over another. 4.2. Calculation weights of the criteria The pair-wise comparison matrices collected from the experts were shown in Tables 5e9. We use Chang's extent analysis method and the fuzzy evaluation matrix of five criteria in Table 5 to calculation the local weights with response to the goal. First, using Eq. (3) to compute the value of fuzzy synthetic extent.

sB1 ¼ ð4:50; 5:83; 7:50Þ5ð1=35:33; 1=27:17; 1=20:67Þ zð0:13; 0:21; 0:36Þ

sB2 ¼ ð0:17; 0:29; 0:48Þ; sB3 ¼ ð0:13; 0:23; 0:39Þ; sB4 ¼ ð0:08; 0:13; 0:26Þ; sB5 ¼ ð0:08; 0:13; 0:22Þ Next using Eqs. (8) and (10), the degree of possibility of the every criteria over the others is obtained.

  0:17  0:36 ¼ 0:70; V SB1  SB2 ¼ ð0:21  0:36Þ  ð0:29  0:17Þ     V SB1  SB3 ¼ 1; V SB1  SB4 ¼ 1;   V SB1  SB5 ¼ 1:     V SB2  SB1 ¼ 1; V SB2  SB3 ¼ 1;     V SB2  SB4 ¼ 1; V SB2  SB5 ¼ 1:     V SB3  SB1 ¼ 0:74; V SB3  SB2 ¼ 1;   V SB3  SB4 ¼ 0:76;   V SB3  SB5 ¼ 1:     V SB4  SB1 ¼ 0:62; V SB4  SB2 ¼ 0:36;     V SB4  SB3 ¼ 0:58; V SB4  SB5 ¼ 1:

W. Li et al. / Journal of Air Transport Management 60 (2017) 49e64

59

Table 10 Global weights for sub-criteria. Criteria and weights

Sub-criteria

Local weights

Global weights

Employees(B1) (0.23)

Neat, tidy and graceful crew (C11) Courtesy and helpfulness of crew (C12) Knowledge and work skill of crew (C13) Understanding of passengers' specific needs (C14) Crew's approach against unexpected situations (C15) Comfort and clean interior/seat(C21) In-flight newspaper, magazines and books. (C22) In-flight facilities condition(internet/email/fax/phone/washroom) (C23) Quality of food and beverage(C24) In-flight entertainment facilities/programs(C25) On-time departure and arrival(C31) Clear and precise cabin announcements(C32) Cabin safety demonstration(C33) Flight pattern (Nonstop,Direct,Connecting)(C34) Travel service related partners car rentals, hotels and airport pick-up(C41) Air quality (C51) Thermal comfort(C52) Sound comfort(C53)

0.09 0.20 0.24 0.23 0.24 0.31 0.01 0.22 0.25 0.21 0.38 0.07 0.17 0.38 1.00 0.43 0.27 0.37

0.0207 0.046 0.0552 0.0529 0.0552 0.0775 0.0025 0.055 0.0625 0.0525 0.1254 0.0231 0.0561 0.1254 0.1200 0.0301 0.0189 0.0259

Facilities(B2)(0.25)

Flight schedule and information(B3)(0.33)

Supporting service(B4)(0.12) Physical environment(B5)(0.07)

Table 11 Linguistic evaluations of sub-criteria for different in-flight service alternatives. Sub-criteria

Very low(VL)

Employees(B1) Neat, tidy and graceful crew (C11) Courtesy and helpfulness of crew (C12) Knowledge and work skill of crew (C13) Understanding of passengers' specific needs (C14) Crew's approach against unexpected situations (C15) Facilities(B2) Comfort and clean interior/seat(C21) In-flight newspaper, magazines and books. (C22) In-flight facilities condition(internet/email/fax/phone/washroom) (C23) Quality of food and beverage(C24) In-flight entertainment facilities/programs(C25) Flight schedule and information(B3) On-time departure and arrival(C31) Clear and precise cabin announcements(C32) Cabin safety demonstration(C33) Flight pattern (Nonstop,Direct,Connecting)(C34) Supporting service(B4) Travel service related partners car rentals, hotels and airport pick-up(C41) Physical environment(B5) air quality (C51) Thermal comfort(C52) Sound comfort(C53)

Low(L)

Average(A)

High(H)

Very high(VH)

A1

A2

A3

A1

A2

A3

A1

A2

A3

A1

A2

A3

A1

A2

A3

0 0 0 0 0

0 0 0 0 0

0 0 0 0 1

2 7 3 14 15

0 2 8 20 20

1 13 2 19 18

56 46 50 55 56

48 38 62 59 63

59 45 56 62 70

32 30 36 23 19

50 45 21 16 14

35 32 31 10 10

10 17 11 8 10

2 15 9 5 3

5 10 11 9 1

0 0 0 0 0

0 0 1 0 0

0 0 0 0 0

20 10 13 17 11

25 15 20 10 13

16 8 15 18 17

68 68 56 48 42

56 60 53 56 36

65 59 64 60 39

5 19 21 23 35

6 15 15 19 41

13 24 15 13 29

7 3 10 12 12

13 10 11 15 10

6 9 6 9 15

0 0 0 0

1 0 0 0

0 0 0 0

10 2 25 0

14 10 15 0

19 6 27 78

50 64 57 35

45 58 61 40

55 72 51 13

25 20 8 20

18 21 15 32

15 13 17 4

15 14 10 45

22 11 9 28

11 9 5 5

0

0

0

11

23

25

25

39

40

39

20

20

25

18

15

0 0 0

0 0 0

0 0 0

5 3 25

12 10 19

3 2 20

68 70 48

70 69 50

61 62 52

12 11 24

8 9 23

20 18 22

15 16 3

10 12 8

16 18 6

The numbers denotes the frequency of the linguistic variable used by the respondents. A1 means the alternative 1, A2 means the alternative 2, A3 means the alternative 3.

Table 10.

    V SB5  SB1 ¼ 0:51; V SB5  SB2 ¼ 0:22;     V SB5  SB3 ¼ 0:48; V SB5  SB4 ¼ 0:96: Then

DðB1 Þ

¼ ¼



4.3. The questionnaire design and collection of the data 

min V SB1  SB2 ; SB3 ; SB4 ; SB5 minð0:70; 1:00; 1:00; 1:00Þ ¼ 0:70

DðB2 Þ ¼ 0:74; DðB3 Þ ¼ 1; DðB4 Þ ¼ 0:36; DðB5 Þ ¼ 0:22: Thus, the weight vector w ¼ ð0:70; 0:74; 1; 0:36; 0:22Þ In the next step, we perform normalization of weight vector. The normalized weight vector shown in Table 5 is calculated. w ¼ ð0:23; 0:25; 0:33; 0:12; 0:07Þ. Likewise, the local weights for the sub-criteria are calculated, the result is shown in Tables 6e9. Using weights of the criteria and local weights of sub-criteria, global weights for the sub-criteria are calculated in this step. Global sub-criteria weights are computed by multiplying local weights of the sub-criteria with the weights of the criteria to which it belongs. The global weights of all sub-criteria are shown in

The questionnaire about the in-flight service quality is shown in Appendix B. This survey lasted 2 weeks at Xianyang international airport in Xi'an. To save the passengers' time, we made the electronic questionnaire. They can enter the questionnaire website via using their phones to scan QR code. After finished their air travel, they answered the questionnaire. Every passenger will received an electronical coupon for paying phone bill. We got 100 responses from three flights, respectively. The data was shown in Table 11. 4.4. Performance measurement of in-flight service quality In this phase we already have the weights generated by the experts in the previous phase, which are applied to the overall answers provided in by the respondents to the survey form which was available in Appendix B.

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The frequency of every linguistic scale used to evaluate the ratings of sub-criteria was calculated, which was shown in Table 11. In this stage, we firstly transform the linguistic scales into 2-tuple linguistic variables according to Fig. 6. For example, the linguistic scale of VH is ðs4 ; 0Þ. Using Eq. (13), the aggregated rating of subcriteria was calculated. The result was shown in Table 12. In the next step, the aggregated ratings of each criterion were computed by Eq. (14). For example, the aggregated ratings of B1 for alternative A1 were computed as follows:

b1A1 ¼ D



Research has shown that catering is a key attribute for a customer's satisfaction with airline service quality (Messner, 2016). Knowledge and work skill of crew (C13) and Crew's approach against unexpected situations (C15) have the highest weights (0.0552) under the criterion of Employee. This suggests that airlines should concentrate on these two factors as the foundation of a good service rating. Employee's problem solving ability plays an important role in customers' expectations about the service quality. It is suggested that airlines should educate employees about the importance of their

 0:625  0:0207 þ 0:643  0:0460 þ 0:638  0:0562 þ 0:563  0:0529 þ 0:560  0:0552 0:0207 þ 0:0460 þ 0:0529 þ 0:0552

¼ Dð0:602Þ ¼ ðs2 ; 0:102Þ

The aggregated ratings of criteria for alternative 2 and 3 were shown in Table 13. The overall in-flight service quality of alternatives can be obtained by Eq. (14) in this step.

bA1 ¼ D



attitude towards service quality and examine employees' competence, it contributes to improve passengers' satisfaction. The findings of this study are likely to significantly help airlines learn to identify their strengths and weaknesses. It was shown that the levels of three airlines' in-flight service quality concerning every

0:602  0:23 þ 0:559  0:25 þ 0:675  0:33 þ 0:483  0:12 þ 0:607  0:07 0:23 þ 0:25 þ 0:33 þ 0:12 þ 0:07



¼ Dð0:595Þ ¼ ðs3 ; 0:095Þ

bA2 ¼ Dð0:541Þ ¼ ðs2 ; 0:041Þ; bA3 ¼ Dð0:500Þ ¼ ðs2 ; 0Þ According to the linguistic term set S, the in-flight service quality of Alternative 1(s3, 0.095) and 2(s3, 0.041) are more than “Average”, and the in-flight service quality of Alternative 3 (s3, 0) is “Average”. To sum up, the result above gives the top rank to Alternative 1 and the lowest rank to Alternative 3. The ranking order of alternatives by the proposed approach exactly matches with the comprehensive ratings obtained from respondents to the alternatives. Thus, it is a valid approach to deal with the fuzzy information under fuzzy environment. 5. Discussion and implications Although the criteria used in this study are all important, the results of the study show Flight schedule and information (0.33) Employees (0.23) and Facilities (0.25) are the most important criteria comparing with other criteria. Therefore, these criteria are the key factors that should be considered for in-flight service managers. The relatively low importance of physical environment, whose average weight is the smallest one (0.007), is in concordance with the fact that most passengers are content with in-flight physical environment, including temperature, air and noise. The results of sub-factors of flight schedule and information indicate that both on-time departure and arrival (C31) and flight pattern (Nonstop, Direct, Connecting) (C34) have the highest score (0.1254). It means that passengers hope their travel schedule can work as planned, and they don't spend long time on the plane. Long distance air travel will cause passengers both physiological and psychological discomfort and even stress. In addition, comfort and clean interior/seat (C21) has the highest weight (0.775) under the criterion of facilities. Passengers spend almost all their time in their seat with limited space, comfortable seat help to decrease the fatigue caused by long time sitting (Verver et al., 2005). The second highest weight (0.0625) is quality of food and beverage under the criterion of facilities.

criterion (Table 13). Although Alternative 1 is temporarily in the leading position in terms of overall in-flight service quality, there is still some room for improvement in the criteria of facilities(B2) and physical environment(B5) to maintain its leading status. On the other hand, other airlines should improve their weaknesses to catch up with competitors and attract more passengers. In terms of the managerial implications, the findings of this study benefit practitioners in airline managerial position. The proposed hierarchy structure allows the analysis of in-flight service quality at several levels of criteria. From the viewpoint of management, the hierarchical framework developed in this study provides an improved understanding of how passengers assess the inflight service quality of airline. The five main criteria contain the common aspects of in-flight service delivery system. These criteria can be applied to airlines in order to estimate the in-flight service quality and be aware of service level and passengers' perception. In addition, the developed hierarchical model in this study included 18 sub-criteria reflecting specific aspects of in-light service. Therefore, airline management practitioners can utilize these criteria to analyze their service process at different level, and this help practitioners to make management strategy and the specification of daily service process. This provides a more detailed and specific method of application to various levels of service quality of airline than the prior studies (SERVQUAL, SERVPERF, and SERVPEX). In short, the developed model offers practitioners a tool for performance evaluation and contributes them to make strategy for the improvement of service operation. The importance weight of criteria in the hierarchical framework can help practitioners identify the most and the least important dimensions in the in-flight service delivery process. Based on the detailed importance of criteria, practitioners can prioritize the service dimensions and reasonably allocate limited human and financial resource for the enhancement of service quality. In addition, the evaluation result can provide the practitioners the feedback of perceived service quality; practitioners should correct the management strategies timely and develop tactics to improve the service quality based on the results.

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Table 12 Value b and 2-tuple linguistic variable of sub-criteria for alternatives. Sub-criteria

Employees(B1) Neat, tidy and graceful crew (C11) Courtesy and helpfulness of crew (C12) Knowledge and work skill of crew (C13) Understanding of passengers' specific needs (C14) Crew's approach against unexpected situations (C15) Facilities(B2) Comfort and clean interior/seat In-flight newspaper, magazines and books. In-flight facilities condition(internet/email/fax/phone/washroom) Quality of food and beverage In-flight entertainment facilities/programs Flight schedule and information(B3) On-time departure and arrival(C31) Clear and precise cabin announcements(C32) Cabin safety demonstration(C33) Flight pattern (Nonstop,Direct,Connecting)(C34) Supporting service(B4) Travel service related partners car rentals, hotels and airport pick-up(C41) Physical environment(B5) Air quality (C51) Thermal comfort(C52) Sound comfort(C53)

Alternative 1

Alternative 2

Alternative 3

Value b and 2-tuple

Value b and 2-tuple

Value b and 2-tuple

0.625 0.643 0.638 0.563 0.560

(s2,0.125) (s3,0.107) (s3,0.112) (s2,0.065) (s2,0.060)

0.635 0.683 0.578 0.515 0.500

(s3,0.115) (s3,0.067) (s2,0.078) (s2,0.015) (s2,0)

0.610 0.598 0.628 0.523 0.480

(s2,0.110) (s2,0.098) (s3,0.122) (s2,0.023) (s2,0.020)

0.498 0.538 0.570 0.575 0.620

(s2,0.002) (s2,0.038) (s2,0.070) (s2,0.075) (s2,0.120)

0.518 0.550 0.538 0.598 0.620

(s2,0.018) (s2,0.050) (s2,0.038) (s2,0.098) (s2,0.120)

0.523 0.585 0.530 0.533 0.605

(s2,0.023) (s2,0.085) (s2,0.030) (s2,0.033) (s2,0.005)

0.613 0.615 0.508 0.775

(s2,0.113) (s2,0.115) (s2,0.008) (s3,0.025)

0.615 0.583 0.545 0.720

(s2,0.115) (s2,0.083) (s2,0.045) (s3,0.030)

0.545 0.563 0.500 0.340

(s2,0.045) (s2,0.063) (s2,0) (s1,0.090)

0.695

(s3,0.055)

0.583

(s2,0.083)

0.563

(s2,0.063)

0.593 0.600 0.513

(s2,0.093) (s2,0.100) (s2,0.013)

0.540 0.558 0.550

(s2,0.04) (s2,0.058) (s2,0.050)

0.623 0.630 0.535

(s2,0.123) (s3,0.120) (s2,0.035)

Table 13 2-tuple linguistic variable of criteria for alternatives.

Employees(B1) Facilities(B2) flight schedule and information(B3) supporting service(B4) Physical environment(B5) The overall in-flight service quality

Alternative 1

Alternative 2

Alternative 3

(s2,0.102)(1) (s2,0.059)(2) (s3,0.093)(1)

(s2,0.071)(2) (s2,0.061)(3) (s2,0.064)(1) (s2,0.045)(3) (s3,0.109)(3) (s2,0.093)(2)

(s2,0.017)(1) (s1,0.090)(2) (s1,0.067)(3) (s2,0.107)(3) (s1,0.018)(2) (s3,0.114)(1) (s2,0.095)(1) (s2,0.041)(2) (s2,0)(3)

6. Conclusion Airlines are becoming more customer-oriented and make efforts to improve their service quality, in order to attract more passengers. Therefore, identifying the factors affecting in-flight service and assessing the in-flight service quality is critical for airlines managers. In this paper, we present a hybrid approach based on fuzzy AHP and 2-tuple fuzzy linguistic method for evaluating the in-flight service quality. The proposed approach comprises of three steps. Firstly, we develop an evaluation index system of in-flight service quality. Using fuzzy AHP obtains the weights of criteria and sub-criteria. Secondly, we design the questionnaire and collect the response. The questionnaire responses are aggregated to generate an overall performance score for measuring service quality using 2-tuple fuzzy linguistic method. The alternative with the highest score is finally chosen. The proposed approach explicitly indicates the ranking index for alternatives. In summary, the contribution of this study is threefold. First, evaluation index system for in-flight service quality is constructed. Second, the key factors affecting in-flight service quality are identified. The last one is that a hybrid approach based on fuzzy AHP and 2-tuple fuzzy linguistic method for evaluating the in-flight service quality is proposed. This methodology helps to compare the in-flight service of different airlines and to select the highest one. 6.1. Limitations and suggestions for future research As with all studies, the present research is not without

limitations. First, the evaluation criteria of in-flight service quality were selected from the literature review and expert opinions, the criteria system is not inclusive of all influences on evaluation of inflight service quality and it may exclude some possible factors such as culture and social factor. Therefore, future studies will adopt different methodologies, such as surveys, in-depth interviews, and longitudinal studies to identify other factors influencing the inflight service quality and to enrich the research content. Second, determining the most appropriate sample size is a never-ending quandary for researchers, it is the same with this research. The results are obtained from relatively small samples, which may have resulted in sample selection bias. A larger sample that brings more explanatory power would have allowed more sophisticated evaluation analysis. In addition, people in different age, education, background have different opinions with the in-flight service criteria. In the follow-up studies, we expect to expand the sample range of ages, regions and culture of passengers, so that the relevant research might be more representative. Also future studies might adopt random sampling for different purposes. Finally, this study uses fuzzy AHP and 2-tuple fuzzy linguistic approach to develop an evaluation model which helps managers understand the critical factors in promoting in-flight service quality. Future studies can adopt additional multi-criteria decision-making approaches (such as TOPSIS method) to estimate the relative weights of the influences on in-flight service. The results of future studies can then be compared with those presented here.

Acknowledgement The authors sincerely thank the editors and the anonymous reviewers for their constructive comments and suggestions which are very helpful in improving the quality of the paper. The authors also express their thanks to the participating passengers and experts for their time and effort. The authors would like to acknowledge support for this work from National Key Technology R&D Program, China (Grant No. 2015BAH21F01). The study is partly supported by the 111 Project, Grant No.B13044.

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Appendix A

Table A.1 The importance comparison of criteria Criteria Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10

4

3

2

1

0

1

2

3

4

Employees(B1) Employees(B1) Employees(B1) Employees(B1) Facilities(B2) Facilities(B2) Facilities(B2) Flight schedule and information(B3) Flight schedule and information(B3) Supporting service(B4)

criteria Facilities(B2) Flight schedule and information(B3) Supporting service(B4) Physical environment(B5) Flight schedule and information(B3) Supporting service(B4) Physical environment(B5) Supporting service(B4) Physical environment(B5) Physical environment(B5)

Notes: The importance of the left criterion over the right one in the table included four levels: 4-absolutely more important, 3-very strong, 2-strong, 1-weak; the importance of the right criterion over the left criterion in the table included four levels: -4-absolutely more important, -3-very strong, -2-strong, -1-weak; 0 means the two criteria have equal importance level. An example of the importance comparisons of sub-criteria under the criterion of Physical environment(B5).

Table A.2 The importance comparison of sub-criteria under the criteria B5 Criteria Q1 Q2 Q3

4

3

2

1

0

1

2

3

Air quality(C51) Air quality(C51) Thermal comfort(C52)

4

criteria Thermal comfort(C52) Sound comfort(C53) Sound comfort(C53)

Notes: The importance of the left criterion over the right one in the table included four levels: 4-absolutely more important, 3-very strong, 2-strong, 1-weak; the importance of the right criterion over the left criterion in the table included four levels: -4-absolutely more important, -3-very strong, -2-strong, -1-weak; 0 means the two criteria have equal importance level.

Appendix B

Table B.1 The questions about each item of in-flight service No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Detailed questions Employees The staffs of the airline appear neat and tidy, have graceful behavior. The staffs of the airline are always polite and willing to help. The staffs of the airline have the knowledge to answer your questions and have good work competence. The staffs of the airline can understand the passengers' specific needs. The staffs of the airline always have good skill to deal with unexpected situations. Facilities The aircraft has clean and comfortable interiors and seats There are lot of in-flight newspaper, magazines and books, etc. The airline provides in-flight internet/email/fax/phone services. The airline provides high quality food and beverage. The airline has up-to-date in-flight entertainment facilities and programs. Flight schedule and information The flight departs and arrives at the time it promises. The aircraft has clear and precise cabin announcements. There are clear cabin safety demonstrations in the airplane. Flight pattern (Nonstop, Direct, and Connecting) is satisfactory. Supporting service There are travel service related partners car rentals, hotels and airport pick-up. Physical environment The air quality in this plane was appropriate. The temperature in the plane was comfortable. The noise level of the plane was acceptable.

Notes: A five-point Likert scale from 1 to 5 denotes the service quality level, 1-Very low, 2-Low, 3-Average, 4-High, 5-Very high.

Number scale 1 1 1 1 1

2 2 2 2 2

3 3 3 3 3

4 4 4 4 4

5 5 5 5 5

1 1 1 1 1

2 2 2 2 2

3 3 3 3 3

4 4 4 4 4

5 5 5 5 5

1 1 1 1

2 2 2 2

3 3 3 3

4 4 4 4

5 5 5 5

12345 12345 12345 12345

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