INTEGRATION OF IMPORTANCEPERFORMANCE ANALYSIS AND FUZZY DEMATEL

International Journal of Computer Science & Information Technology (IJCSIT) Vol 10, No 3, June 2018
DOI: 10.5121/ijcsit.2018.10302 19
INTEGRATION OF IMPORTANCE-
PERFORMANCE ANALYSIS AND FUZZY
DEMATEL
Chin-Yi Chen1
, Tung-Shen Wu2*
, Mei-Lan Li3
and Ching-Tang Wang4
1
Department of Marine Leisure and Tourism, Taipei University of Maritime Technology,
No. 150, Sec. 3, Binhai Rd., Tamsui District, New Taipei City 251, Taiwan
2
Department of Physical Education Center, Hsiuping University of Science and
Technology, No.11, Gongye Rd., Dali Dist., Taichung City 412-80, Taiwan, R. O. C.
3
Department of Office of Academic Affairs, China University of Technology
4
Department of Sport Information & Communication, National Taiwan University of
Sport, No. 16, Sec. 1, Shuang-Shih Road, Taichung, 404, Taiwan, R. O. C.
ABSTRACT
The traditional Importance-Performance Analysis (IPA) assumes that quality attributes are independent
variables, and presupposes that explicit customers’ response data is used for assessing the importance and
performance of quality attributes. Under this supposition, when the quality attribute has explicit causation
data, the traditional IPA cannot correctly provide importance and priority of improvement. Moreover, the
influential degree of the traditional quality attributes is emphasized as maximum degree. This study
employs regression analysis and the fuzzy Decision Making Trial and Evaluation Laboratory (DEMATEL),
which consider the fuzziness of human thinking, to calculate the causal relationship and the influential
degree among each quality attribute, and then proposes a new methodology of decision analysis, which
modifies the traditional IPA and obtains the accurate importance and the improvement the quality
attributes. In this study, a Taiwanese bank is an empirical case study, which illustrates the application and
the effectiveness of integrating fuzzy DEMATEL and IPA.
KEYWORDS
Importance-Performance Analysis; Multiple Regression Analysis; Decision Making Trial and Evaluation
Laboratory; Fuzzy Theory
1. INTRODUCTION
Martilla and James [18] first used Importance-Performance Analysis (IPA) method in the
marketing strategy on development companies, which emphasized that the method is low-cost,
easy to apply, and with a better focus on strategies. The IPA method is easy to understand, and
companies can analyze their strengths and shortcomings from the results of the method in order to
confirm their business opportunities and strategic direction to improve, so the IPA not only has
been widely used in analyzing business strategies of every industry, but also has become an
important research tool for service quality attributes. For example, Xiuli and Chu [30] used IPA
approach for customer satisfaction evaluation supporting PSS design. Hu, Chiu, Cheng, and Yen

20
[8] applied the IPA and DEMATEL models to improve the order-winner criteria. Deng, Chen and
Pei [2] used IPA method to improve the management of the quality of hot spring hotels. Tonge
and Moore [27] used IPA method and gap analysis in assessment of marine environmental
protection management. Huang, Wu and Hsu [10] used IPA method to probe the national
highways’ the long-range passengers satisfaction of service quality attributes. Levenburg and
Magal [16] used IPA method to establish e-commerce strategies and resource allocation.
These scholars have contributed to IPA method in many ways. However, the design of the
traditional IPA survey locks consideration of the fuzziness of human thinking. The questionnaire
of the survey often asks respondents to choose one answer from the selected semantic wording,
which results in an integer value, the analyzed results are distorted, and leads to relationing errors.
Moreover, the traditional IPA presupposes that explicit customers’ response data is used for
assessing the importance and performance of quality characteristics and that each quality
characteristic is an independent variable, which does not take implicit phenomena of human
psychological decision-making behavior and causal relationship between the quality attributes in
the positive information into account, so the traditional IPA model cannot provide accurate
importance analysis and the priority ranking for improvement. This study proposes a new
methodology of decision analysis, in addition to the use of multiple regression analysis method to
establish the relationship between quality attributes and overall satisfaction and importance;
considering the fuzziness of human thinking, this study employs fuzzy Decision Making Trial and
Evaluation Laboratory (DEMATEL) to analyze the causal relationship between the quality
attributes and the degree of their mutual influence in order to in order to modify the importance of
quality attributes and the priority ranking for improvement based on the traditional IPA model,
which can be a reference for managers to deal with complicated practical issues. A Taiwanese
bank is an empirical case study in this research, which illustrates the application and the
effectiveness of integrating fuzzy DEMATEL and IPA.
2. IPA
2.1 IPA Review
IPA, proposed by Martilla and James [18], assists managers to confirm the quality attributes
which can achieve the results of high customer satisfaction, and then to develop effective
marketing strategies. IPA is a two-dimensional matrix based on customer-perceived importance
of quality attributes and attribute performance. In the matrix, quality attributes of performance
and importance are axis X and axis Y, and the split values axis X and axis Y are the total average
of each quality attributes’ performance and importance. Therefore, quality attributes are divided
into four quadrants, defined as: (1) Concentrate here: customers think highly of the quality
attributes, but they are not satisfied with the quality. (2) Keep up the good work: customers think
highly toward the importance of products or service quality attributes, and the level of
companies’ performance is high. (3) Low priority: the performance of companies’ products and
service quality attributes is low, and the importance of customers’ awareness is also low. (4)
Possible overkill: the performance of companies’ products and service quality attributes is high,
but the importance of customers’ awareness is low. According to the quadrants of quality
attributes, managers know clearly that the current delivering service quality attributes of their
company are their advantages or disadvantages, and then to make their strategies to each quality
attribute of every quadrant. Comparing to other management methods, IPA not only implement
surveys for the degree of acceptance about importance and performance of quality attributes, but

21
also provide statistical analysis of coefficient of practical to understand practical importance and
influence.
Although IPA method is easy to be applied and its results are obvious to be interpreted, there are
still hidden problems. Therefore, after Martilla and James’ [18] IPA method published, many
scholars have proposed modified models. For example: Deng et al. [2] believed that general
statistical methods to obtain importance needed many basic assumptions, so he managed to use
neural-liked method to obtain importance and to correct the IPA model. Matzler et al. [18]
thought that the organization's overall satisfaction with the performance of quality attributes is a
function of the degree. Matzler et al. [19] study suggests the importance of quality attributes is a
function of performance quality attributes. Matzler and Sauerwein [20] that the degree of
importance is the performance of a function to show the overall degree of satisfaction as
independent variables as dependent variables to do multiple regression analysis, the obtained
regression equation, the regression coefficient of the important quality attributes as the degree to
re-establishment of importance and performance analysis matrix. Lee et al. [13] also used
multiple regression analysis to establish the overall satisfaction with the quality characteristic of
the implicit importance to the quality attributes of the gap analysis and calculation performance
While the above research and discovery of the theory and application of IPA significant
contribution, only a few studies explore the causal relationship between the quality attributes and
influence each other. Therefore, in addition to the theories of Matzler and Sauerwein [20], which
is that the function of satisfaction quality attributes is implicit importance, and Lee, Li, Yen, and
Huang [14], which is employed multiple regression analysis to establish quality attributes and the
overall satisfaction of the implicit importance, this study also takes take the fuzziness of human
thinking into consideration to redesign questionnaires. In the redesigned questionnaires,
ambiguous words are used to understand the causal relationship and mutual influence of quality
attributes, and then to modify the importance of quality attributes and the priorities of
improvements, which can prevent companies from making wrong decisions.
2.2 Modified IPA Model
From IPA literatures, this study modifies the more relationable IPA model; as well as the causal
relationship and mutual influence of each quality attribute, which were not studied by previous
researches, this study employs the fuzzy DEMATEL to revalue the importance and to identify
core issues for making quality attributes of the improvement and the allocation of resources more
rational. In the study, proposed the modified IPA model and fuzzy DEMATEL, there are the
following topics to be discussed: (1) multiple regression analysis is used to establish the
performance of each quality attribute and the equation of function of overall satisfaction, which
the regression coefficients are viewed as the assessed values of each importance quality attribute;
(2) IPA matrix is based on the implicit importance and performance to establish the vertical axis
and horizontal axis; (3) fuzzy DEMATEL is employed to analyze the causal relationship and
mutual influence of each quality attribute; (4) integration of IPA and fuzzy DEMATEL is to
explain re-make relative strategies and improvements.
Matzler and Sauerwein [20] and Matzler et al. [19] explained two IPA model measurements of
importance quality attributes, one is called the explicit importance, which is customers’ self-
expressional importance toward quality attributes; another one is known as the implicit
importance, which is used coefficients of multiple regression equation to obtain customers’

22
importance quality attributes. Matzler and Sauerwein [20] proved that customers’ self-
expressional importance is not a function of satisfaction quality attributes, and the implicit
importance is a function of satisfaction quality attributes, which is obtained by using the multiple
regression equation, meanwhile, performance as independent variable and overall satisfaction as
dependent variable, so the coefficients obtained from the multiple regression equation are a better
measurement for customers’ importance toward quality attributes. Therefore, the multiple
regression equation as follows:
εββββ +++++= kk XXXY ...22110 (1)
and
Y = overall satisfaction；
iX = performance of item i‘s quality attribute (i = 1, 2,…, k)
This study turns the position axis of two-dimensional performance-importance matrix based on
the traditional IPA model into the scale of importance based on regression coefficients. The scale
of importance is the vertical axis based on the multiple regression coefficients (β), the scale of
performance is the horizontal axis, and the split values of the vertical and horizontal axis is used
for specifying four quadrants of quality attributes’ performance and importance two-dimensional
matrix. The definition of the four quadrants is remained the same as Martilla and James’ [18] IPA
model, so easy-explained and direct-interpreted traits are still remained in the modified IPA.
Usually, when undergoing improvements of quality attributes, quality attributes are assumed to be
independent, and each of those will be improved directly in accordance with the IPA matrix.
While quality attributes have a causal relationship, one quality attribute being improved will
affect other quality attributes at the same time; therefore, the highly-influenced quality attributes
should be improved first. As regards the causal relationship among the quality attributes and its
influence toward decision-making and improvements, the methodology of fuzzy DEMATEL and
the integration of IPA and the fuzzy DEMATEL are discussed in the following chapters in this
study.
3. THE FUZZY DEMATEL METHOD
3.1 Decision Making Trial and Evaluation Laboratory
DEMATEL was developed by Battelle memorial association of Geneva research prominence
(Gabus and Fontela, [4]; Fontela and Gabus, [3]), at that time, DEMATEL was used in studying
the world’s complicated problem, such as: race, hunger, environmental protection, and energy,
etc. problems (Fontela and Gabus, [3]). In recent years, Japan, Korea, and Taiwan have broadly
applied DEMATEL to solve problems in different fields, such as: Tamura et al. [25] adopted
DEMATEL to explore the customer’s insecure factor for food and improvement measures;
Hajime et al. [6] integrated QFD,TRIZ and DEMATEL to resolve the design conflict of
innovated product developing process; Nanayo and Toshiaki [27] adopted amended DEMATEL
to process integrated evaluation on medical system; Kenichi and Yoshihiro [11] adopted
DEMATEL to analyze the function and failure of snow melting equipment; Kim [12] integrated
PCA,AHP and DEMATEL to evaluate the impact in cattle industry and agricultural information;
Wu and Lee [29] adopted Fuzzy DEMATEL to develop the core ability of manager; Lin and Wu
[17] applied Fuzzy DEMATEL to the group decision problem. Therefore, DEMATEL has been
successfully adopted in many fields. The purpose of DEMATEL is to directly compare the

23
interaction relationship between variables and use matrix to calculate the directly and indirectly
causal relationships and influence level between variables, especially using the visual structural
matrix and causal diagram to express the causal relationships and influence level between
variables in the complicated system and assist making the decision. Therefore, DEMATEL can
turn complicated system into a causal relationship with a clear structure[32][33], and simplify the
relationships between variables in the complicated system to just cause and effect relation,
through the interaction influence level between quantified variables to find out the core problem
in the complicated system and the improvement direction. The study referred to the study of Lee
et al., ([14][15]), and briefly describe the structure of DEMATEL and the calculating steps.
3.1.1 Define the variables and establish the measurement scale
List and define a complicated system’s influence variables by using documentation exploration,
brain storming or professional opinions, now assuming there are n variables that impact the
complicated system. Establish the measurement scale of the pair-wise comparison of causal
relationships and level between variables, the measurement scale respectively are 0, 1, 2, and 3
level, which respectively represent “no impact”, “low impact”, “high impact” and “great impact”
(Lin and Wu [17]). In addition, the measurement scale is also divided into 0, 1, 2, 3, 4, and 5
level, which respectively represent “no impact”, “very low impact” “low impact”, “medium
impact” “high impact” and “great impact” (Kim [12]), and Huang et al. [10] adopted 11 levels, 0,
1,…, 10, from “no impact” to “great impact”.
3.1.2 Establish Direct-Relation Matrix
When the variable amount is n, through the survey questionnaire professional opinions to process
pair-wise comparison on the variables depending on their influence relationships and level, then
the direct-relation matrix, X, of n×n can be obtained. In direct-relation matrix, X, ijx represents
the variable, the level of i impact variable j, and the diagonal variable iix of direct-relation
matrix, X is set to 0.












=
0
0
0
21
221
112
L
MOMM
L
L
nn
n
n
xx
xx
xx
X (1)
At the same time, establish symbol matrix, S, to indicate the positive (+) or negative (-).
3.1.3 Calculate normalized direct-relation matrix
There are two calculation methods of normalized direct-relation matrix, such as: Wu and Lee
[29], Lin and Wu [17], Kim [12], and Seyed-Hosseini et al. [24] all used the biggest sum of

24
column vector as the normalized base; and Tzeng et al. [28] also used the biggest sum of column
vector as the normalized base.
Set








≤≤
=
∑=
n
j
ijx
ni
Max
11
1
λ or




















≤≤







≤≤
=
∑∑ ==
n
i
ij
n
j
ij
x
nj
Max
x
ni
Max
Min
11
1
1
,
1
1
λ (2)
From the calculation of equation (2) and (3), times direct-relation matrix, X, by λ to receive
normalized direct-relation matrix, N.
XN λ= (3)
Therefore, using normalized direct-relation matrix, N to go through the Markov Chain Matrix in
the absorbing state to obtain the similar sub-stochastic matrix, according to the study of Goodman
[6].
Ο=
∞→
k
k
Nlim 且 ( ) ( ) 12
lim
−
∞→
−Ι=++++Ι NNNN k
k
L (4)
O is null matrix, and I is identity matrix.
3.1.4 Direct / Indirect Relation Matrix:
Due to the normalized direct-relation matrix, N has the characteristic of equation (4), therefore,
direct/ indirect relation matrix, T or total-relation matrix can be obtained from equation (5)
(Huang et al., [10]). In addition, indirect relation matrix, H or total-indirect relation matrix can be
obtained from equation (6) (Lin and Wu [17]).
( ) ( ) 12
lim
−
∞→
−=+++= NINNNNT k
k
L (5)
( ) ( ) 1232
lim
−
∞→
−=+++= NINNNNH k
k
L (6)
Set tij as the variable of direct/ indirect relation matrix, T, and i, j = 1, 2,…, n. The columns’ sum
of direct/ indirect relation matrix, T can be calculated from equation (7) and (8), and set Di as the
sum of column i, which represents variable, i is the cause that impact the sum of other variables;
Rj is the sum of column j, which represents variable, i is the result and the sum impacted by other
variables. Di and Rj are obtained from direct/ indirect relation matrix, T, which include direct and
indirect impact.
( )∑=
==
n
j
iji nitD
1
,,2,1 L (7)

25
( )∑=
==
n
i
ijj njtR
1
,,2,1 L (8)
3.1.5 Draw out causal diagram :
Define (Dk + Rk) as the prominence, and k = i = j = 1, 2,…, n, which means the overall level of
this variable being impacted and the impact to others, according to this value it can show the core
level of variable k in all the problems; and (Dk - Rk) is defined as the relation, which means the
difference level of the variable being impacted and the impact to others, according to this value, it
can show the attributed casual level of variable k in other problems, if it is a positive value, then
the variable is the relation type, if it is a negative value, then the variable is the cause type. Causal
diagram uses (D + R) as the transverse, and (D - R) as the longitudinal axis, and combine 2-D
graphics constructed the symbol matrix, S, use the diagram to express the purpose of going
through diagram to simplify the complicated casual relationship to the visual structure that is easy
to understand, the decision maker can base on the variable located position to judge whether the
variable shall be attributed to cause or effect type, and the level of variable being impacted and
the impact to others, and plan suitable decision to solve the problem in accordance with the
attributed type and impact level.
Respectively calculate the coordinate values (Dk + Rk, Dk - Rk) of various variables, and draw
them out in the causal diagram. When Dk - Rk are positive values, the variable k is attributed to
cause; if Dk - Rk are negative values, then variable k shall be attributed to effect type. When Dk +
Rk are bigger, that means the bigger level of the variable impacted other variables is than other
variables impacted the variable. It can be known from the causal diagram: if Dk - Rk are negative
value and the values of Dk + Rk are very small, that means variable k is more independent, and
there are less factors which will impact the variable; and when Dk - Rk is positive value and the
values of Dk + Rk are very small, that means variable k also is independent, and can impact a few
other variables; if Dk - Rk are negative values and the values of Dk + Rk are very big, that means
variable k is the core problem required to be solved, however, it is not to directly improve the
variable; when Dk - Rk are positive values and the values of Dk + Rk are big, which means variable
k is the driving factor of solving the core problem, it shall be listed as the priority handling
subject. Therefore, if the decision maker can base on the causal relationship of variable, and the
interaction influence level between variables to find out the driving variable of the core problem
in the complicated system, and plan the suitable decision to solve the problem in accordance with
the attributed type and influence level.
3.2 Fuzzy Theory
3.2.1 The fuzzy logic
The Fuzzy Theory, introduced by Zadeh [31], is a mathematical way to describe the classes of
materials in real life in order to make up the traditional shortcoming of binary logic. The theory is
very useful for tackling ambiguities of human thought because it can convert ambiguities of
human thought to specific values. In the fuzzy logic, each number between 0 and 1 indicates a
partial truth, on the contrary, crisp set correspond to binary logic: 0 or 1; thus, fuzzy logic can
handle ambiguities and imprecise judgments mathematically (Al-Najjar & Alsyouf [1]; Wu &
Lee [29]). The essential definitions of the fuzzy logic are as the following (Wu & Lee [29])

26
In order to obtain the correct answer, after dealing problems with the fuzzy logic, an appropriate
defuzzification method is still needed. The CFCS method (Converting Fuzzy data into Crisp
Scores) proposed by Opricovic and Tzeng [28] is a defuzzification method, which takes into
account not only each fuzzy number but also the overall factors under multi-criteria decision-
making, to solve each fuzzy number. This method is based on the output of fuzzy set, which may
convert fuzzy number into crisp scores. Comparing with other defuzzification methods, Wu and
Lee [29] indicated that CFCS method can give a better crisp value.。The CFCS method is based
on the procedure of determining the left and right scores by fuzzy min and fuzzy max, and the
total score is determined as a weighted average according to the membership function. The
procedure includes four-step algorithms described as follows:
(1) Normalization:
i
ji rr maxmax
= ,
i
ji ll minmin
= , ijlminmax
min =∆
Compute every aj, j = 1, …, J。
max
min
min
/)( ∆−= iijlj llx
max
min
min
/)( ∆−= iijmj lmx
max
min
min
/)( ∆−= iijrj lrx ( 1 )
(2) Compute left (ls) and right (rs) normalized value，j = 1, …, J
ljmjmj
ls
j xxxX −+= 1/
mjrjrj
rs
j xxxX −+= 1/ (2)
(3) Compute total normalized crisp value，j = 1, …, J
[ ] [ ]rs
j
ls
j
rs
j
rs
j
ls
j
ls
j
crisp
j xxxxxxx +−+−= 1/)1( ( 3 )
(4) Compute crisp values，j = 1, …, J
max
min
min
∆+= crisp
jiij xlf (4)
3.2.2 The procedure of fuzzy DEMATEL method
The fuzzy DEMATEL combines Fuzzy Theory and Decision Making Trial and Evaluation
Laboratory, which means that DEMATEL method is employed in a fuzzy environment. This
method is practical for analyzing the causal relationship among variables and the influence degree

27
of each variable. The analytical procedure of the fuzzy DEMATEL method is described as
follows (Lin & Wu [17])：
Step 1: Set the decision goal and set up a committee.
Decision-making is the process of defining the decision goals, gathering relevant
information, generating the broadest possible range of alternatives, evaluating the
alternatives for advantages, selecting the optimal alternatives, and monitoring the results
to ensure that the decision goals are achieved(Hess [7]). Thus, a decision goal is set
up first. Subsequently, a committee is set up for gathering group knowledge for problem
solving.
Step 2: Develop the evaluation criteria and design the fuzzy linguistic scale.
Evaluation criteria are developed based on expert opinions. However, the Evaluation criteria
have nature of causal relationships and usually comprise several complicated aspects, so the
DEMATAL method is employed to obtain variables from the complicated structure of causal
relationships. This study adopts a fuzzy wording scale instead of traditional measuring scale to
manage the variability of human thinking. The different influences are expressed by five degrees
{Very high, High, Low, Very low and No Influence}. Please see Table 1 for equilateral triangle
fuzzy functions.
Step 3: Acquire the assessments of decision-makers
To measure the relationship among criteria { }niCC i ,...,2,1== , a decision group of p experts
was asked to make sets of pair wise comparisons in terms of linguistic terms. Hence, p fuzzy
matrices ( )1(~
Z , )2(~
Z , …, )(~ p
Z ), each corresponding to an expert and with triangular fuzzy
numbers as its elements, were obtained. Denote )(~ K
Z as：
)(~ K
Z ＝














0
~
~
~
0
~
~
~
0
)(
2
)(
1
)(
2
)(
12
)(
1
)(
21
M
L
O
L
L
MM
k
n
k
n
k
n
k
k
n
k
z
z
z
z
z
z
； ,,,2,1 pk L= ( 5 )
Where ( ))()()()(
,, k
ij
K
ij
k
ij
k
ij umlz =
, and without loss of generality, elements
),...,2,1(~ )(
niz k
ii = will be
regarded as a triangular fuzzy number (0, 0, 0) whenever it is necessary. Fuzzy matrix )(~ K
Z is
called the initial direct-relation fuzzy matrix of expert K.
Step 4: Acquire the normalized direct-relation fuzzy matrix.
Let
)(~ k
ia be the triangular fuzzy numbers,

28








== ∑ ∑ ∑∑ = = ==
n
j
n
j
n
j
k
ij
k
ij
k
ij
n
j
k
ij
k
i umlza
1 1 1
)()()(
1
)()(
,,~~
and






∑=
=≤≤
n
j
k
ij
ni
k
ur
1
)(
1
)(
max
The linear scale transformation is then used as a normalization formula to transform the criteria
scales into comparable scales. The normalized direct-relation fuzzy matrix of expert k, denoted as
X(k), is given by














=
)(
)(
2
)(
1
)(
22
)(
22
)(
21
)(
1
)(
21
)(
11
)(
~
~
~
~
~
~
~
~
~
k
nn
k
n
k
n
k
k
k
k
n
k
k
k
x
x
x
x
x
x
x
x
x
X
M
L
O
L
L
MM ； ,,,2,1 pk L= (6)
Where






== )(
)(
)(
)(
)(
)(
)(
)(
)(
,,
~
~
k
k
ij
k
k
ij
k
k
ij
k
k
ijK
ij
r
u
r
m
r
l
r
z
x
As that in crisp DEMATEL method, we assume at least one I such that ∑=
n
j
k
iju
1
)(
< )(k
r . This
assumption is well satisfied in practical cases. Through basic calculation of the matrix, the
average matrix X
~
is obtained.
Step 5: Establish and analyze the structural model.
To compute the total-relation fuzzy matrix T
~
, we have to ensure the convergence of
0
~
lim =
∞→
w
w
X in advance. The elements of
w
X
~
are also triangular fuzzy matrix, as follows：














=
)(
)(
2
)(
1
)(
22
)(
22
)(
21
)(
1
)(
21
)(
11
)(
~
~
~
~
~
~
~
~
~
w
nn
w
n
w
n
w
w
w
w
n
w
w
w
x
x
x
x
x
x
x
x
x
X
M
L
O
L
L
MM ，其中， ( ))()()()(
,,~ w
ij
w
ij
w
ij
w
ij umlx =
Theorem 3.1. :
We further define three matrices,

29
[ ]














=
)(
)(
2
)(
1
)(
22
)(
22
)(
12
)(
1
)(
21
)(
11
)(
w
nn
w
n
w
n
w
w
w
w
n
w
w
w
ij
l
l
l
l
l
l
l
l
l
l
M
L
O
L
L
MM
[ ]














=
)(
)(
2
)(
1
)(
22
)(
22
)(
12
)(
1
)(
21
)(
11
)(
w
nn
w
n
w
n
w
w
w
w
n
w
w
w
ij
m
m
m
m
m
m
m
m
m
m
M
L
O
L
L
MM
and
[ ]














=
)(
)(
2
)(
1
)(
22
)(
22
)(
12
)(
1
)(
21
)(
11
)(
w
nn
w
n
w
n
w
w
w
w
n
w
w
w
ij
u
u
u
u
u
u
u
u
u
u
M
L
O
L
L
MM
then [ ] [ ] [ ] w
u
w
ij
w
m
w
ij
w
l
w
ij XuXmXl === )()()(
,,
Theorem 3.2. : It holds that Ο=
∞→
w
w
Xlim
, and
( ) ( ) 12
lim
−
∞→
−Ι=++++Ι XXXX k
w
L
; where
O is null matrix and I is identity Matrix.
Theorem 3.3. : According to the crisp case, we define the total-relation fuzzy matrix T
~
as
( ) ( ) 12 ~~~~~
lim
~ −
∞→
−=+++= XIXXXXT k
w
L (7)
令














=
nn
n
n
nn t
t
t
t
t
t
t
t
t
T
~
~
~~
~
~
~ 2
1
2
22
12
1
21
11
M
L
O
L
L
MM
Where ( )''''''
,,
~
ijijijij umlt =
, then
[ ] ( ) 1'' −
−×= llij XIXlMatrix
[ ] ( ) 1'' −
−×= mmij XIXmMatrix

30
[ ] ( ) 1'' −
−×= uuij XIXuMatrix
According to the above theorems, the matrices[ ] [ ] [ ])()()(
,, w
ij
w
ij
w
ij uml are obtained. These matrices
are able to construct to be the total-relation fuzzy matrix, and then the matrix can be
defuzzificated by applying the CFCS method and computing four-step algorithms to obtain crisp
value, which is converted from fuzzy numbers, determining the left and right scores by fuzzy
min and fuzzy max, and the total score is determined as a weighted average.
4. INTEGRATION OF IPA AND FUZZY DEMATEL
When undergoing improvements of quality attributes, quality attributes are assumed to be
independent, and each of those will be improved directly in accordance with the IPA matrix.
While quality attributes have causal relationships, one quality attribute being improved will affect
other quality attributes at the same time; therefore, the highly-influenced quality attributes should
be improved first. To understand the causal relationship among the quality attribute, the two-
dimension causal diagram based on the analytical results of the fuzzy DEMATEL can be a
reference. The average value of each axis can be divided into four quadrants: Quadrant I
represents an area in which listed quality attributes are with high prominence and relation, and it
means the quality attributes are the core issues and will affect other quality attributes, which
should be listed as first improvements; Quadrant II represents an area in which listed quality
attributes are with low prominence but high relation, and it means the quality attributes are highly
independent and will affect less quality attributes; Quadrant III represents an area in which listed
quality attributes are with low prominence and relation, and it means the quality attributes are
highly independent and will be affected by less quality attributes; Quadrant IV represents an area
in which listed quality attributes are with high prominence but low relation, and it means the
quality attributes are the core issues and will be affected by other quality attributes. The quality
attributes in Quadrant III、IV can be neglected and viewed as independent quality attributes
because of those prominence lower than the average and with little influence. Therefore, the
integration of IPA and fuzzy DEMATEL can be divided into two parts and each with four
strategies, as in Table2：
4. CASE STUDY AND DISCUSSION
This study uses a Taiwanese bank as a case study, and employs IPA and the fuzzy DEMATEL
model to improve customer satisfaction. The bank in the case study is one of the first leading
banks in Taiwan, it has been operating 65 years, its total capital is NTD 500 billion, and its
performance is growing steadily. In this research, there are eight questions about service
satisfaction shown in the questionnaire which is mainly designed for the customers traded with
the bank in 2010. They include: employees can provide timely services (Q1), service facilities
attractive (Q2), banks provide the service to meet all the needs of customers (Q3), banks are
reliable (Q4), employees are polite (Q5), employees can be expected to understand customers’
needs (Q6), employees can provide customers with individual care and service without limitation
of service time (Q7), employees have a neat appearance and service (Q8). The questionnaire is
combined with IPA and the fuzzy DEMATEL mode to analyze, which could provide the

31
direction for managers to identify improvements and then to enhance the competitiveness of the
company.
4.1 Constructing Questionnaire and Survey of IPA and fuzzy DEMATEL
IPA questionnaire of this study is designed to understand customers’ actual perception toward
quality attributes in order to examine the actual performance of companies. In the questionnaire,
there are check boxes for each question about satisfaction, and satisfaction are classified as "1"
meant "very dissatisfied "and “7" meant “very satisfied. " In addition, there are also questions
about importance of product and service quality toward customers in order to understand
customers’ priority and their value, and importance is classified as "1" meant "very unimportant"
and "7" meant "very important." Moreover, the customers are asked to evaluate for the overall
performance of the company at the end of the questionnaire, and the scale of scores is from 1 to 7
points, which is as the assessment of the overall satisfaction.
The design of Fuzzy DEMATEL questionnaire adopts experts’ opinions, and 15 bank executives
answer the eight questions (Q1 ~ Q8) to develop the direct relation matrix. The direct relation
measurement scale is the fuzzy linguistic scale, not the traditional measurement scale. There are
five different linguistic expressions representing five different degree of influence in this direct
relation measurement scale, namely, {Very high, High, Low, Very low, No}. This study not only
uses customer satisfaction information and the modified IPA model to establish the matrix of
importance and satisfaction, but also employs Fuzzy DEMATEL to analyze direct and indirect
relations, and then to point out key issues and improvements.
4.2 Analyzed Results
Multiple regression analysis is used to obtain importance of each question and is used as a
standard to judge the level of the overall satisfaction. Referring to Table 3, the significant factors
(P value <0.05) affecting the overall satisfaction are: banks are reliable (Q4), employees can
provide customers with individual care and service without limitation of service time (Q7). The
regression coefficient can represent the relative importance. According to the modified IPA
model, the horizontal axis is performance and the vertical axis is implicit importance, the value of
regression coefficient, and then the two-dimensional matrix of importance - performance is
obtained. This matrix is divided into four groups of the eight questions, which are the references
for the bank to make strategies of developments. Table 4 is the data obtained through using the
modified IPA model. In addition to the modified importance of the regression coefficients and the
performance for each question, there are also included the priority of improvements. The quality
attributes falling into "Concentrate here" quadrant means these quality attributes must be
improved immediately, and the order of quality attributes to be improved are: employees can
provide timely services (Q1) and employees can provide customers with individual care and
service without limitation of service time (Q7); the quality attribute falling into "Keep up the
good work" quadrant is banks are reliable (Q4) ; the quality attributes falling into "Possible
overkill" quadrant are service facilities attractive (Q2), banks provide the service to meet all the
needs of customers (Q3), employees are polite (Q5), and employees can be expected to
understand customers’ needs (Q6). The quality attributes in the "Low priority" quadrant is
employees have a neat appearance and service (Q8).

32
The design of Fuzzy DEMATEL questionnaire adopts experts’ opinions, and 15 bank executives
answer the eight questions (Q1 ~ Q8) to analyze eight variables and the causal relationship
between the degree of mutual influence. There are five different linguistic expressions
representing five different degree of influence in this direct relation measurement scale, from No
Influence to Very High Influence, which let those experts express their opinion about the degree
of influence, shown as in Table 5.
According to Table 1，The fuzzy scale of Table 5 can be turned into the direct-relation matrix
with fuzzy value. In accordance with the suggestion of Lin and Wu [18], after using formula (2)
to establish the direct-relation matrices lX , mX and uX , these three matrices can be computed
individually by using DEMATEL.
Based on Formula (3), Lin and Wu’s [18] method is adopted to standardize the direct-relation
fuzzy matrices. l m u≤ ≤ , the linguistic value and the max value of u is the standardized basis,
and the value of r is 1/6.75; meanwhile,
( ) ( ) ( ) ( )
( )
( ) ( ) ( ) ( ), ,
k k k k
K ij ij ij ij
k k k kij
z l m u
x
r r r r
 
= =  
 
%
% is
employed to obtained the direct-relation fuzzy matrices of lX 、 mX and uX . According to
Theorem 3.1., the fuzzy matrix X is destructed into lX 、 mX 、 uX . When the convergence of
the standardized direct-relation fuzzy matrices is close to infinity, the matrices also are close to a
zero matrix. Therefore, the total-relation matrix of lX 、 mX 、 uX can be obtained from formula
(7). The total-relation matrix of lX 、 mX 、 uX is be integrated and then the total-relation fuzzy
matrix T . Following formula (1) to (4) to defuzzifize, the linguistic value of the total-relation
fuzzy matrix T turns into the crisp case. Because of the complication of causal relationships
among quality attributes, the influential degree of causal relationships lower than 0.25 can be
viewed as no causal relationships, shown as Table 7.
The causal relationship of each quality attributes is clear after using Fuzzy DEMATEL method.
Take employees can provide timely services (Q1) as an example. From Table７, it shows that
employees can provide timely services (Q1) affects banks are reliable (Q4) directly, and the
influential degree is 0.28; the influential degree of employees can provide customers with
individual care and service without limitation of service time (Q7) is 0.28.
Next, follow formula (8) and (9) to compute Di of every row and Ri of every column to obtain
prominence (Di + Ri) and relation (Di - Ri), shown as Table 8.
The average value is obtained by adding prominence (Di + Ri) and relation (Di - Ri) and
subtracting with 8, and this average value is viewed as the estimated value of centered causal
matrix, and the value can divide the matrix into four quadrants, shown as Figure 3. According to
Figure 3, the quality attributes with high prominence and high relation are employees are polite
(Q5), employees can be expected to understand customers’ needs (Q6), and employees can
provide customers with individual care and service without limitation of service time (Q7), which
means these three quality attributes are the core quality attributes affecting others; the quality

33
attributes with high prominence but low relation are banks provide the service to meet all the
needs of customers (Q3) and banks are reliable (Q4), which means these two are the core quality
attributes affected by others. As for the rest of quality attributes, they can be neglected and
viewed as independent attributes because their prominence are lower than the average 3.390.
5. CONCLUSION
Since Martilla and James [19] first used IPA method in the marketing strategy on development
companies, many scholars have researched relative field and modify their original model to help
managers to solve practical problems. However, there are still hidden problems with these models
needed to be discussed, including: (1) the positive importance quality attributes does not take the
impact of performance quality attributes and the overall satisfaction into account; (2) when there
are causal relationships among quality attributes, the quality attributes assumed independent in
the traditional IPA model will lead to wrong decision-making; (3) Respondents are forced to
choose the only answer which represents specific value in the traditional questionnaires, and the
results of such questionnaire cannot truly reflect how the respondents feel. In this study, multiple
regression analysis is employed to establish the performance quality attributes and implicit
importance of the overall satisfaction, and then to find the factors affecting the overall
satisfaction. Moreover, regression coefficients are viewed as importance, and higher value of
coefficients, higher importance quality attributes to establish the modified IPA model. In
addition, considering fuzziness of human thinking, fuzzy DEMATEL is used to map out causal
relationships among quality attributes, and then to identify core issues and improvements.
The integration of the modified IPA model combined with fuzzy DEMATEL method in this study
not only diminishes the hidden problems of the traditional model, modified the causal
relationships and the degree of mutual influence of quality attributes in IPA model, but also
identifies directions and focuses of quality attributes to helping managers to solve problems with
minimal resources. This study uses a first leading Taiwanese bank as a case study, and employs
the IPA which is modified by multiple regression analysis and the fuzzy DEMATEL model. The
methodology is provided managers with a more reasonable assessment of importance and
performance.
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Table 1 The correspondence of linguistic terms and values
Table 3：Multi regression coefficients of performance and the overall satisfaction

36
Table 2: The integration of IPA and fuzzy DEMATEL

37
Table 4：the results of the modified IPA model
Table 5: the results of experts’ opinion
Table 6: Total-relation matrix

38
Table 7: direct/indirect –relation matrix (Tcut=0.25)
Table 8：Coefficients of prominence and relation
Figure 1: Causal Matrix of Order-winner Criteria

INTEGRATION OF IMPORTANCEPERFORMANCE ANALYSIS AND FUZZY DEMATEL

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