A Grey- Fuzzy Approach to the Customer Perception ...

A Grey- Fuzzy Approach to the Customer Perception of In-Flight Service Quality in Domestic Airlines, Taiwan Ming Lang Tseng 1and Anthony SF Chiu

Abstract. This research uses a grey- fuzzy method based to deal with study objective. This study is aimed to present a perception approach to deal with domestic airline in-flight service quality ranking with uncertainty. The ranking of best in-flight service quality might be a key strategic direction of other domestic airlines. In general, these considering criteria are self-structured. The solving procedure is as follows, (i) the weights of criteria and alternatives are described in triangular fuzzy numbers; (ii) using a grey possibility degree to result the ranking order for all alternatives; (iii) an empirical example of in-flight service quality ranking problem in customer perspective was used to resolve with this proposed method approach and indicates that Airline A5 (Far Eastern Air Transport) is the best domestic airline in terms of in-flight service quality.

Keywords: grey theory, triangular fuzzy numbers, in-flight service quality, linguistic

1. INTRODUCTION

are initially used as the primary competitive weapons. Airlines realize that competition on

Airline providing high service quality to

price alone represents a no-win situation in the

passenger is important, because the competition

long term. This implies that airline’s competitive

is ever increasing as airline firm try to acquire

advantage based on price alone is not sustainable.

and retain customers. Price and service quality

Airline’s competitive advantage lies in service

________________________________________ † : Corresponding Author

722

APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference quality perceived by customers. The rapid growth

mathematical function. In marketing research,

of alternative transportation in Taiwan, the

most questionnaires use Likert scales to measure

airlines’ management needs to make important

respondents’

efforts for improving their customers’ satisfaction.

description. In the past, some statistical methods

Since passengers probably spend most of their

have been employed to analyze the in the

time airborne, the quality of in flight service

domestic airline industry, using some n-point

deserves more attention by the airline. And yet,

Likert scale to weight the importance of different

the evaluation of in-flight service quality in the

criteria. This research applies the Triangular

domestic airline is an on-going process that

fuzzy numbers (TFNs) that has been general

requires continuous monitoring to maintain high

applied in the field of management science

levels of in-flight service quality across a number

(Hutchinson, 1998, Xia et al., 2000).

of different service criteria. The

rapid

transportation

in

growth

attitude,

which

is

linguistic

The evaluation ranking problem in real of

Taiwan,

alternative

the

airlines’

world systems are very often in uncertainty or lack

information.

Grey

theory

is

a

management needs to make important efforts for

multidisciplinary theory dealing with multi-

improving

their

criteria systems for which lack information. It is

Employed

fuzzy

customers’

satisfaction.

numbers is an

adequate

one of the methods that are used to study

methodology to overcome the ambiguity of

uncertainty, is superior in theoretical analysis of

concepts that are associated with human being’s

systems

subjective judgments. When solving real-life

incomplete samples. In-flight service quality is

service quality problems, linguistic information

measured to assess service performance, diagnose

usually appears as an important output of the

service problems, and manage service delivery

process. This information is frankly more

(Parasuraman, 1995). The advantage of grey-

difficult to measure throughout a classical

fuzzy combination is that grey theory considers

with

imprecise

information

and

Nusa Dua, Bali – INDONESIA December 3rd – 5th, 2008 723

APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference the condition of the fuzziness and deal flexibly

2. Literature review

with fuzziness situation (Bellman and Zadeh, 1970 and Deng, 1982).

The section aims to identify the theoretical

This study presents a grey possibility degree

composition that considers in this study objective.

to rank the domestic airlines in uncertainty. The

The term service quality has been used to explain

research procedure is briefly as follows: (i) the

by the customers evaluated the quality of service,

weight and rating of criteria for five alternatives

numerous contributions in the literature have

are described by linguistic information; (ii) a

attempted to establish which criteria or factors

degree of grey possibility is proposed to

they consider when evaluating service quality.

determine the ranking order of all alternatives; in

Researchers have been described it into strategic,

the alternative ranking process, the degree of

inter-organization and internal service quality

uncertainty of criteria has to be taken into

perspective

account. This approach is more suitable for multi

competitiveness (Farmer 1997, Harland et al.,

criteria decision making system’s more uncertain

1999, Stanley and Wisner, 2001). The study of

environment than other approaches. The study

Grönroos (1984) presents that the perceived

objective is to ranking the domestic airlines based

quality of a given service will be the result of an

on in flight service quality criteria. This paper is

evaluation

organized as follows, section 2 discusses the

compares his expectations with his perception of

review of literatures, section 3 describes research

the service received. Grönroos (1993) suggested

method

and

that measuring customer experiences of service

reliability, grey theory and grey numbers, section

quality is a theoretically valid way of measuring

4 the proposed approach applies to domestic

perceived quality. Tsaur et al. (2002) proposed a

airlines ranking problem. Finally, conclusions are

five dimensional measurement of service quality

drawn in section 5.

that includes tangible, reliability, responsiveness,

includes

instruments’

validity

in

order

process,

to

where

improve

the

firm’s

consumer


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference assurance and empathy.

between the criteria weight and performance ratings of airlines. Gilbert and Wong (2003)

2.1 Airline service quality

developed

26

attributes

model considering

reliability, assurance, facilities, employees, flight In the passenger airline is difficult to

patterns,

customization to

measure

and and

responsiveness

describe and measure the service quality due to

dimensions

compare

the

its heterogeneity, intangible and inseparability.

differences in passenger’s expectations of desired

Quite a few studies devoted to investigate the

airlines service quality.

service quality issues in passenger airline industry.

developed a conceptual model to understand of

An empirical study by Ostrowski et al. (1993)

air passenger’s decision making process, the

presents that continuing to provide perceived

model considers service expectation, service

high quality service would help airline acquire

perception, service value, passenger satisfaction,

and retain customer loyalty. An airline would lead

airline image and behavioral intentions in

the market if they offer superior quality service

analysis of Korean international air passengers,

relatively to their competitors. It is strategic

the result shows that service value, passenger

importance for airlines to understand their

satisfaction and airline image have direct impact

competitive advantages on service quality.

on passenger decision making process. Chen and

Park et al. (2004)

Some recent empirical studies show the

Chang (2005) examined airline service quality

different way of approaching to airline service

from a process perspective by first examine the

quality. Chang and Yeh (2002) using fuzzy multi-

gap between passenger’s service expectations and

criteria analysis modeling to formulate the

the actual service received, and the gaps

service quality of airlines due to the hardness of

associated with passenger service expectations,

evaluation approaches. They applied Fuzzy set

perceptions of these expectations by frontline

theory was used to describe the ambiguity

manager

and

employees.

Importance-


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference performance analysis was then used to construct

quality

service attribute evaluation map to identify areas

perceptions of airline service quality are quite

for improvement. Gursoy et al. (2005) considered

diverse. Those studies imply that service quality

15 attributes of service quality when explore 10

criteria are context dependent and should be

major US airlines using canonical analysis to

selected to reflect the business environment

further establish a positioning map using the data

investigated. The definition of service quality and

in the US department of transportation’s air travel

its influential characteristics continues to be

consumer report. Pakdil and Aydin (2007)

important research issues. This research is

measures airline service quality in 8 dimensions

focusing on the in-flight service quality, which is

which are employees, tangibles, responsiveness,

most concerning and stay longer time with the

reliability

passengers and it is rare to be studied by the

and

assurance,

flight

patterns,

availability, image and empathy using factor

suggests

that

the

definitions

and

previous studies.

analysis to present the result that responsiveness and availability are most important dimensions in

3. Research method

Turkish airline. Liou and Tzeng (2007) developed a non-additive model for evaluating the service

This section is aimed to operationalize the

quality of airlines the measurement dimension

service quality by developing a multi-item five-

included employees service, safety and reliability,

point measurement scale to evaluate the different

on board service, schedule, on time performance

evaluation criteria of in-flight service quality with

and free ticket and upgrading using factor

regard to the domestic airline in Taiwan. To help

analysis, fuzzy integral and grey relation analysis

support scale generalization for in-flight service

to ranking among the six dimension which is

quality customers, it is important to collect data

important for the other competitors.

and

The result of existing studies on service

survey instrument

composition.

Using

purpose sampling method (α=0.05) a total of 340


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference customer’s responses were obtained. Samples for

faces for each evaluation criteria.

the study were collected from Airlines customers.

To be convinced that the question of this instrument is valid, this research applied the difference

3.1 Instrument reliability and validity

scores

between

perceptions

and

expectations to EFA of statistical method The

questionnaires

were

tested

using

(Parasuraman et al., 1988, Parasuraman et al.

reliability and followed by exploratory factor

1991). Similarly, the measurement of difference

analysis (EFA) (Lai et al., 2002). Initially, this

scores has also been used by some researchers

study presents 22 questions to assess the service

(Teas, 1993, Babakus and Boller, 1992).

quality evaluation from difference group, and yet

Reliability is frequently defined as the

from the item to total and EFA the 15 questions

degree of consistency of a measurement. Thus,

are remained. However, in the survey process,

the internal consistency of a set of measurement

two sets of linguistic terms (very low, low,

items refers to the degree to which items in the

medium, high, very high) (very poor, poor, fair,

set are homogeneous. Reliability analysis is a

good, very good) are used for assessing the

correlation-based procedure. Internal consistency

service

category

for the five elements was estimated using the

respectively. Each respondent is rating of each

reliability coefficient (Cronbach, 1951). Typically,

evaluation criteria by using one of the linguistic

reliability coefficients of 0.60 or higher are

terms defined in the corresponding term set. It is

considered adequate, with reliability cronbach’s α

important to remark that each of the linguistic

0.914. Hair et al. (1998) further stated that

terms is linked to some graphical expression of

permissible alpha values can be slightly lower

the human face that appears at the beginning of

(0.50) for newer scales. Using SPSS 12.0

the questionnaire, and that the respondent needs

reliability scale, an internal consistency analysis

to tick off below one of the expressions of the

was performed separately for each of the model

quality

of

each

criteria


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference elements shown in Tables 2. The analysis revealed that maximization of the cronbach’s α coefficient would require elimination of items for whole evaluation criteria. Tables 2 shows the revised construct and meet or exceed prevailing standards of reliability for survey instruments. The factor loading ranges from 0.760 to 0.661, total variance extracted 61.1 % and KMO sampling adequacy 0.929, thereby, presenting evidence of convergent validity. Each of the categories did form a “solid” construct, from both theoretical and statistical perspective.


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference Table 1. Factor loading of in-flight service quality of domestic airlines evaluation criteria

Item C1 C2 C3 C4 C5 C6

C7

C8 C9 C10 C11 C12 C13 C14 C15

In-flight service quality evaluation criteria Cronbach’s α(0.914) Clear and precise cabin announcements Cabin safety demonstration Pax guidance and information by cabin crew Cabin crew are proactive Cabin crew are courteous, polite and respectful Cabin crew’s ability to handle customer complaints Cabin crew’s ability to handle unexpected situations, consistently and dependably Cabin crews are willing and able to provide service in a timely manner Clean and pleasant interior Good cabin equipment conditions Appearance of crew member Speed at In-flight snack service Inspection of passenger’s seat belt Seat and space are comfortable In-flight entertainment materials and programs Total variance explained

Mean

Factor loading

3.368

0.760

3.364

0.748

3.683

0.723

3.618

0.723

3.432

0.717

3.443

0.709

3.394

0.694

3.408

0.693

3.462

0.689

3.358

0.687

3.608

0.684

3.717

0.678

3.591

0.674

3.585

0.667

2.911

0.661 61.10%


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference 3.2 Grey theory

1. Let X be the universal set. Then a grey set G of X is defined by its two mappings

G (x)

and

 G (x )

.

Grey theory is proposed by Deng (1982), is

G ( x) : x  [0,1] ……………………..(1)   G ( x) : x  [0,1]

a mathematical theory born out of the grey set. It is an effective method used to solve uncertainty problems with discrete data. In this research, we

G ( x)  G ( x), x  X , X  R, G ( x)

and

 G (x)

are the

apply basic definitions of grey systems with upper and lower membership functions in G TFNs, grey set and grey number in grey theory respectively. When

G (x)

=

G

(x)

, the grey set G

(Zhang et al., 2005, Chen and Tzeng, 2004). The becomes a fuzzy set. It shows the grey theory concept of a grey system is shown in Figure 1. considers the condition of the fuzziness and can deal flexibly with the fuzziness situation. The Figure grey number can be defined as a number with Grey system

uncertain information. For example, the rating of Input

Known information

Output

attributes are described by the TFNs, there will be Grey number …

…

a numerical interval expressing it. This numerical interval will contain uncertain information, the

Grey variables

Unknown information

Grey variables

grey number is as

 G , (G  G  ).

The lower and upper limit of G can be Figure 1. The concept of a grey system

possibly estimated and G is defined as a lower limit grey number.

A grey system is shown as a system containing uncertain information presented by a

 G  [G, )   G  (,G ]

…………...(2)

grey number and grey variables, shown in Figure


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference The lower and upper limits of G can be estimated and G is defined as an interval grey

 G2  [G 2 , G2 ]

, the possible degree of

 G1  G2

can

expressed as follows

number P  G1  G2

 G  [G , G ]



max(0, L *  max(0, G1  G2 ) L*

(6)

….…………..(3) Where

Grey number operation is an operation

, the positive relationship

L*  L(G1 )  L(G 2 )

between

 G1

and

 G2

is determined as follows:

and

G1  G2

, that

defined on sets of intervals, rather than real numbers. This research cited the basic operation laws of grey numbers.

 G  [G1 , G1 ]

and

 G  [G 2 , G2 ]

,

on intervals where the four basic grey number operations on the interval are the exact range of the corresponding real operation. In this research only apply the proofs of addition and subtraction formulas.

 G1  G2  [G1 G 2 , G1  G2 ] …….(4)   G1  G2  [G1 G 2 , G1  G2 ]

The length of grey number

 G is

If

G1  G2

 G1  G2

, then

P G1  G2 

=0.5 If If

G2  G1

, that

G2  G1

P G1  G2 

and

 G2  G1

, then

G1  G2

P G1  G2 

=1

 G2  G1

, that

, then

=0

If there is an intercrossing part in them, when P G1  G2 

>

P G1  G2 

< 0.5, that is

0.5,

that

is

 G2  G1

.

When

 G2  G1

3.3. Research approach

defined as

Grey- fuzzy approach bases on a grey possibility degree is proposed for ordering the

L (G ) =

[G  G ] ……(5)

preference of in flight service quality domestic airlines ranking. This approach is for ranking the

For the two grey numbers

 G1  [G1, G1 ]

and


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference decision making problem in uncertainty. Assume

Table 2. Linguistic scales for the importance

that A = {A1, A2, …. Am} is a discrete set of m

weight of criteria

domestic

airline

alternatives.

C

=

{C1,

C2,….Cn}is a set of n criteria of possible alternatives. independent

The

criteria

are

 w  { w1 , w2 ,........,  wn } is

additively the vector of

Linguistic

Corresponding TFNs

variable

( w)

Very low (VL)

(0.0,

0.3)

(0.3,

0.5)

(0.3,

0.7)

(0.5,

0.9)

(0.7,

1.0)

criteria weights. In this research, the criteria Low (L) weights and ratings of alternatives are considered as number scale, the number scale, criteria

Medium (M)

weights, can be expressed in fuzzy numbers by the TFNs scale, shown in Table 2. The criteria ratings  G can also be expressed in fuzzy numbers by TFNs scale, shown in Table 3. And

High (H)

Very high (VH)

build the expert opinions with TFNs following Eq.(1). The procedures are summarized as follows:


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference Note: this table is the linguistic scale and their

 wj 

1  w1j  w2j  .......   wkj …(7) K

Where

 w kj ( j  1, 2,......... .n )





corresponding fuzzy numbers defined by Wang and Chang (1995) and used in Chen (2000)

is the criteria weight of

Kth experts and can be described by grey number Table 3. Linguistic scales for the importance

k

k

 w kj  [ w j , w j ]

weight of alternative Linguistic

Corresponding TFNs

variable

(G)

Step 2. Use TFNs for the rating to make a criteria rating value. The rating value can be

Very poor (VP)

(0,

3)

Poor (P)

(1,

5)

Fair (F)

(3,

7)

calculated as

1  Gij1  Gij2  .......  Gijk …(8) K



 Gij 

Good (G)

(5,

9)

Very good (VG)

(7,

10) Where

Note: this table is the linguistic scale and their corresponding fuzzy numbers defined by Wang



 Gijk (i  1,2,..... m; j  1, 2,......... .n )

is the criteria

weight of Kth experts and can be described by grey number

k

k

 G kj  [G j , G j ]

and Chang (1995) and used in Chen (2000) Step 3. Establish the grey decision matrix

Step 1. A sampling group of customer identified the criteria weights of airlines. Assume that a decision group has K sampling customers,

  G 11    G 21 D   ..   ..   G m1 

G G .. .. G

22

.. ..

.. ..

m2

.. .. ..

.. .. ..

12

 G1n    G2 n  ..   ..   Gmn 

the criteria weights wj can be calculated as (9)


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference Step 5. Establish the weighted normalized Where,

 Gij

are TFNs based in the grey

number.

grey decision matrix. Considering the different importance of each criteria, the weighted normalized

Step 4. Normalized the grey decision matrix

  G *11  *   G 21 D*   ..   ..   G *m1 

 G*12  G *22

.. ..

.. ..

..

..

..

..  G *m 2

.. ..

.. ..

 G1*n    G2*n  ..   ..  *   Gmn 

grey

decision

matrix

can

be

established as

 V  V D*   ..   .. V 

 V 12  V 22 .. ..  V m2

11 21

m1

.. .. .. .. ..

 V1n  V2 n .. ..  Vmn

.. .. .. .. ..

       

(10) Where,

for a benefit criteria,

 Gij*

(13)

is

expressed as Where,

 G ij G ij   Gij*   max , max  …..……………..(11)  G j G j 

 Vij  Gij*  w j

Step 6. Make the ideal alternative as a

G

max j

 

 max1 i  m G ij

for a criteria,

 Gij*

referential alternative. For m possible alternatives is set A = {A1, A2, …., Am} the ideal referential

expressed as

domestic min j

min j

G G  Gij*   ,  G ij G ij G min  min1i  m G ij  j

The

  ……..….……..(12)  normalization

is

airline





Amax   G1max ,G2max ,......... .......  Gnmax ,

to

Amax 

preserve the property that the ranges of the

alternative

can be obtained by

  max V , max V ,  max V , max V , ............. maxV , max V   1i m

i1

1i m

i1

1i m

i2

1i m

i2

1i m

in

1i m

in

(14)

normalized grey number belong to [0, 1] Step 7. Calculate the grey possibility degree


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference between compared domestic airline alternatives

Daily Air (A1), Uni-Air (A2), Trans Asia Airway

set A = {A1, A2, …. Am} and ideal airline

(A3), Mandarin-Airlines (A4) and Far Eastern

alternative Amax.

Air Transport (A5). The fifteen criteria are show in Table 1. The criteria are additively independent.





P Ai  Amax 

1 n p Vij  G max  j n j 1



 ...(15)

 w  {w1 , w1 ,w1....  wn }

is the vector of

criteria

weights. This research, the criteria weights and Step 8. Rank the order for domestic airline alternatives.

When



P Ai  Amax



is smaller,

the

ranking order of Ai is better. Or, the ranking order is worse. According to described procedures, this research is able to determine the ranking order of all domestic airline alternatives and select the

rating of alternatives are considered as linguistics variables. Here, these linguistic variables can be expressed in grey numbers by 5 point scale. The criteria rating  G can also be expressed in five point scale as well. The computational procedures are summarized as follows.

best from domestic airlines. Step 1- Make the weights of criteria Cj (j = 4. Empirical results

1,2,3….,15). 340 sampling respondents has been formed to express their prefences and to select

An approach based on a grey possibility degree is proposed for ordering the preference of airline by customer perception. This method is

their best domestic airline. From Eq. (7), the evaluation criteria weights can be obtained and results are summarized and shown in Table 4.

very suitable for solving this assess problem in an Step 2- Make criteria rating values for five

uncertain environment There are five alternatives Ai (i = 1,2,…5) against fifteen criteria Cj (j = 1,2,3….15)

which are five domestic airlines,

alternatives. According to Eq. (8), the results of criteria rating values are shown in Table 5.


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference Step 3- Follows Eqs. (9) the grey decision matrix of alternatives can be obtained

Step 5- Follows Eqs. (12) and (13) the weighted normalized grey decision matrix can be obtained. For example, the grey number (0.203,

Step 4-Follows Eqs. (10) the normalized

0.730) of alternative A1 with respect to criteria

grey decision matrix can be obtained. The grey

C1 (see Table 7), where 0.203 = 0.43 x 0.472 and

normalized decision table is shown Table 6.

0.73 = 0.917 x 0.810


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference Table 4. Criteria weights for 5 alternatives Cj

D1

D2

…..

D 340

 w* j

 wj C1

M

H

…..

M

[0.425,

0.800]

[0.430,

0.810]

C2

H

VH

…..

H

[0.450,

0.837]

[0.456,

0.848]

C3

M

M

…..

M

[0.350,

0.725]

[0.354,

0.734]

C4

M

H

…..

L

[0.425,

0.800]

[0.430,

0.810]

C5

VH

VH

…..

VH

[0.600,

0.925]

[0.608,

0.937]

C6

H

H

…..

H

[0.500,

0.887]

[0.506,

0.899]

C7

H

VH

…..

H

[0.600,

0.950]

[0.608,

0.962]

C8

H

H

…..

H

[0.425,

0.825]

[0.430,

0.835]

C9

H

H

…..

H

[0.500,

0.900]

[0.506,

0.911]

C10

H

H

…..

H

[0.475,

0.875]

[0.481,

0.886]

C11

M

M

…..

VH

[0.400,

0.750]

[0.405,

0.759]

C12

H

H

…..

H

[0.475,

0.875]

[0.481,

0.886]

C13

H

H

…..

M

[0.375,

0.775]

[0.380,

0.785]

C14

M

M

…..

M

[0.375,

0.750]

[0.380,

0.759]

C15

H

VH

…..

VH

[0.675,

0.988]

[0.684,

1.000]


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference Table 5. Criteria rating value for alternatives Ci

AI

D1

D2

…..

C1

A1

G

G

…..

F

[4.25,

8.25]

A2

G

G

…..

G

[5.00,

9.00]

A3

G

G

…..

G

[5.00,

9.00]

A4

F

G

…..

G

[4.75,

8.75]

A5

G

G

…..

G

[4.00,

8.00]

A1

G

F

…..

F

[4.25,

8.25]

A2

G

G

…..

F

[4.00,

8.00]

A3

VG

G

…..

VG

[6.50,

9.75]

A4

G

G

…..

P

[4.25,

8.12]

A5

F

G

…..

G

[3.50,

7.50]

A1

G

F

…..

F

[3.75,

7.75]

A2

G

F

…..

F

[4.00,

8.00]

A3

F

F

…..

F

[3.00,

7.00]

A4

G

F

…..

F

[3.25,

7.25]

A5

G

G

…..

M

[5.75,

9.37]

A1

G

G

…..

F

[3.00,

7.00]

A2

G

G

…..

P

[3.25,

7.25]

A3

G

G

…..

P

[3.50,

7.50]

A4

F

G

…..

P

[3.25,

7.25]

A5

G

G

…..

G

[3.75,

7.75]

A1

F

G

…..

F

[3.50,

7.50]

A2

F

P

…..

P

[1.75,

5.75]

A3

G

G

…..

F

[4.75,

8.62]

A4

F

G

…..

F

[3.50,

7.50]

A5

P

F

…..

VG

[4.25,

8.00]

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

…..

C15

A1

G

G

…..

G

[4.00,

8.00]

A2

VG

G

…..

P

[5.00,

8.87]

A3

G

G

…..

F

[6.00,

9.50]

A4

G

F

…..

G

[4.25,

8.25]

A5

G

G

F

[5.00,

9.00]

C2

C3

C4

C5

D 340

 Gij


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference Table 6. Grey normalized decision C1

C2

C3

C4

C5

A1

[0.472,

0.917]

[0.436,

0.846]

[0.400,

0.827]

[0.387,

0.903]

[0.313,

0.813]

A2

[0.556,

1.000]

[0.410,

0.821]

[0.427,

0.853]

[0.419,

0.935]

[0.344,

0.844]

A3

[0.556,

1.000]

[0.667,

1.000]

[0.320,

0.747]

[0.452,

0.968]

[0.344,

0.844]

A4

[0.528,

0.972]

[0.436,

0.833]

[0.347,

0.773]

[0.419,

0.935]

[0.344,

0.844]

A5

[0.444,

0.889]

[0.359,

0.769]

[0.613,

1.000]

[0.484,

1.000]

[0.500,

1.000]

C6

C7

C8

C9

C 10

A1

[0.353,

0.824]

[0.406,

0.870]

[0.529,

1.000]

[0.529,

0.838]

[0.278,

0.722]

A2

[0.353,

0.824]

[0.203,

0.667]

[0.529,

0.971]

[0.471,

0.941]

[0.361,

0.778]

A3

[0.500,

0.971]

[0.551,

1.000]

[0.529,

1.000]

[0.382,

0.853]

[0.278,

0.722]

A4

[0.529,

1.000]

[0.406,

0.870]

[0.441,

0.912]

[0.441,

0.912]

[0.611,

1.000]

A5

[0.529,

1.000]

[0.493,

0.928]

[0.500,

0.971]

[0.559,

1.000]

[0.500,

0.944]

C 11

C 12

C 13

C 14

C 15

A1

[0.556,

1.000]

[0.343,

0.800]

[0.528,

0.944]

[0.529,

1.000]

[0.421,

0.842]

A2

[0.333,

0.778]

[0.429,

0.886]

[0.278,

0.722]

[0.265,

0.735]

[0.526,

0.934]

A3

[0.417,

0.861]

[0.371,

0.829]

[0.361,

0.778]

[0.324,

0.794]

[0.632,

1.000]

A4

[0.444,

0.889]

[0.543,

1.000]

[0.278,

0.722]

[0.324,

0.794]

[0.447,

0.868]

A5

[0.556,

0.972]

[0.429,

0.886]

[0.611,

1.000]

[0.324,

0.794]

[0.526,

0.947 ]


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference Table 7. Grey weighted normalized decision table C1

C2

C3

C4

C5

A1

[0.2035,

0.743]

[0.199,

0.718]

[0.132,

0.607]

[0.157,

0.732]

[0.190,

0.782]

A2

[0.239 ,

0.810]

[0.187,

0.696]

[0.140,

0.626]

[0.170,

0.758]

[0.209,

0.812]

A3

[0.239,

0.810]

[0.304,

0.848]

[0.105,

0.548]

[0.183,

0.784]

[0.209,

0.812]

A4

[0.227,

0.788]

[0.199,

0.707]

[0.114,

0.568]

[0.170,

0.758]

[0.209,

0.812]

A5

[0.191,

0.720]

[0.164,

0.652]

[0.202,

0.734]

[0.196,

0.810]

[0.304,

0.962]

C6

C7

C8

C9

C 10

A1

[0.214,

0.792]

[0.236,

0.815]

[0.268,

0.899]

[0.322,

0.806]

[0.169,

0.695]

A2

[0.214,

0.792]

[0.118,

0.624]

[0.268,

0.872]

[0.286,

0.905]

[0.219,

0.748]

A3

[0.304,

0.934]

[0.321,

0.937]

[0.268,

0.899]

[0.232,

0.821]

[0.169,

0.695]

A4

[0.322,

0.962]

[0.236,

0.815]

[0.223,

0.819]

[0.268,

0.877]

[0.371,

0.962]

A5

[0.322,

0.962]

[0.287,

0.869]

[0.253,

0.872]

[0.340,

0.962]

[0.304,

0.909]

C 11

C 12

C 13

C 14

C 15

A1

[0.338,

0.962]

[0.208,

0.770]

[0.321,

0.909]

[0.322,

0.962]

[0.256,

0.810]

A2

[0.203,

0.748]

[0.260,

0.852]

[0.169,

0.695]

[0.161,

0.707]

[0.320,

0.899]

A3

[0.253,

0.828]

[0.226,

0.797]

[0.219,

0.748]

[0.197,

0.764]

[0.384,

0.962]

A4

[0.270,

0.855]

[0.330,

0.962]

[0.169,

0.695]

[0.197,

0.764]

[0.272,

0.835]

A5

[0.338,

0.935]

[0.260,

0.852]

[0.371,

0.962]

[0.197,

0.764]

[0.320,

0.911]


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference Step 6- Make the ideal alternative Amax a

result of ranking order as shown as follows:

referential alternative following Eq. (14), the ideal alternative Amax is shown as follows:

Amax

=

{[0.225,

A5 > A3 > A4 > A2 > A1

0.810],

This research can identify Airline 5 is the

[0.196, 0.810],

best domestic airline out of five. Airline 5 should

[0.321, 0.937], [0.268, 0.899], [0.340, 0.962],

be best alternative from the customer perception.

[0.371, 0.962], [0.304, 0.962], [0.322, 0.962],

The next alternative is A3. Because the grey-

[0.338, 0.962], [0.330, 0.962], [0.371, 0.962],

fuzzy possibility, degree of A5 and A3 against the

[0.322, 0.962], [0.384, 0.962]

ideal Amax are most equal.

[0.304,0.848],[0.202, 0.736],

Step 7- Calculate the grey possibility degree between the compared alternative of 5 domestic

5. Conclusions

airlines Ai (i= 1,2,3,4,5) and the ideal referential alternative Amax. According to Eq.(6) and (15),

The competition of domestic airline market

the results of the grey possibility degree are

is very intensive. The airlines must realize the

shown as follows:

key point of passenger service quality and read the customer’s mind in grey-fuzzy environment.

P(A1 ≦Amax) = 0.568 ; P(A2 ≦ Amax) =

To help airlines understand the importance of

0.567; P(A3 ≦ Amax) = 0.544; P(A4 ≦ Amax) =

customer-driven of in flight service quality, this

0.545; P(A5 ≦Amax) = 0.519

research developed the measurement instrument adopted the purposing sampling method from all

Step 8: Rank the order of five alternative

the passengers of domestic airlines, tested in

airlines Ai (i= 1,2,3,4,5) According to step 7, the

validity and reliability scale for further presenting


APIEMS 2008 Proceedings of the 9th Asia Pacific Industrial Engineering & Management Systems Conference that the measurement is solid constructed. However,

in

many

situations

scale, Journal of Business Research 24, 253ranking

268

judgments are often uncertain and can not be estimated by an exact numerical value. The

2.

Bellman, R.E. and Zadeh, L.A., 1970.

problem of justify the best domestic airline based

Decision making in a fuzzy environment,

on certain criteria has many uncertainties and

Management Science 17(4), 141-164

becomes more difficult. This research applied different perspective and look from a different angle at a real grey fuzzy world.

The advantage

3.

Chang, Y.H. and Yeh, C.H., 2002. A survey analysis of service quality for domestic

of grey-fuzzy combination is that grey theory

airlines, European Journal of Operational

considers the condition of the fuzziness and deal

Research 139, 166-177

flexibly with fuzziness situation. The rating of criteria are described by linguistic information that can be re-solved by TFNs, therefore airline

4.

Chen, CT., 2000.Extensions of the TOPSIS for group decision making under fuzzy

ranking can be viewed as a grey fuzzy process.

environment. Fuzzy Sets and Systems 114,1-9

The empirical result of domestic airline in Taiwan is presented the best airline; the result might be other airlines’ strategic benchmark in terms of in

5.

flight service quality.

Chen, F., and Chang, Y.H., 2005. Examining airline service quality from

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