Pan-Pacific Management Review 2011, Vol.14, No.1: 1-27
1
A DISSONANCE REDUCTION METHOD FOR INTUITIONISTIC FUZZY MULTI-CRITERIA
DECISION-MAKING PROBLEMS
TING-YU CHEN Department of Industrial and Business Management College of Management,
Chang Gung University
YI-JEN LI Graduate Institute of Business Administration College of Management,
Chang Gung University
HSIAO-PIN WANG Graduate Institute of Industrial and Business Management College of Management,
Chang Gung University
ABSTRACT Considering that cognitive dissonance is regarded as a momentous psychological
factor in the decision making, this study proposes new techniques not only to tackle
multi-criteria decision making problems but also to reduce the cognitive dissonance
yielded by the decision maker under intuitionistic fuzzy environment. By applying the
intuitionistic fuzzy weighted averaging (IFWA) operator and the score function, the
proposed method derives the optimal weights of criteria and generates the priority of
alternatives from the mathematical programming. In order to diminish the dissonance,
the attractiveness of alternatives is magnified as large as possible in the programming
problem based on the Euclidean distance. A numerical example is given to demonstrate
the detailed calculating procedure; besides, an empirical case concerning a digital
camera selection problem is employed to ascertain the feasibility of the developed
method. According to the empirical results, the optimal alternative calculated by the
mathematical programming satisfies decision makers and indeed reduces the
dissonance. This study comes up with a successful manner to effectively reduce the
dissonance when decision makers face a multi-criteria decision making problem.
2 Pan-Pacific Management Review January
Keywords: cognitive dissonance, multi-criteria decision making, intuitionistic fuzzy set,
intuitionistic fuzzy weighted averaging (IFWA), score function
INTRODUCTION
Problems for multi-criteria decision-making (MCDM) are common cases, including
individual matter in real life. The decision-making problem has been a subject of an extensive
research effort that has resulted in a multitude of models and approaches with roots in
different kind of areas ranging from social science, mathematical science to cognitive science
(Szmidt & Kacprzyk, 2008). Although there has existed substantial MCDM methods,
including AHP (analytic hierarchy process), SMART (simple multi-attribute rating
technique), VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje), ANP
(analytic network process), and TOPSIS (technique for order preference by similarity to ideal
solution), most of them mainly consider the problem itself, focusing on the relative
importance between criteria and the priority of alternatives. Little research has been devoted
to exploration of the decision maker’s psychological factors such as the cognitive dissonance
in the decision-making methods. Without a better skeleton of psychological factors, MCDM
methods may remain incomplete in the explanations.
The theory of cognitive dissonance was pioneered by Festinger (1957) and offered
insights into persuasion (attitude change) resistance. According to this perspective, when
individuals are receiving new information which disagrees with existing cognitions, they
experience the dissonance. As cognitive dissonance is psychology uncomfortable, individuals
are motivated to reduce or eliminate it and restore cognitive consonance.
Once a decision is made, subsequent preferences are revealed along with an increase on
the attractiveness of the chosen alternative and a decrease on the attractiveness of the rejected
alternative. It is because the positive aspects of the rejected alternatives and the negative
aspects of the chosen alternative are dissonant with the post decision, and are changed to
reduce the unpleasant states associated with dissonance. A difficult decision signifies that the
alternatives are close to each other in attractiveness, and an easy decision signifies that the
alternatives are remote from each other in attractiveness (Liberman & Forster, 2006). The
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 3
more approaching the alternatives to be chosen are, the higher the level of dissonance occurs
(Mittelstaedt, 1969). When evaluating the non-inferior/non-dominated alternatives over the
given conflicting criteria, the decision makers will search the information about the
alternatives according to intrinsic and extrinsic cues, and establish a preference order. If the
decision is characterized by difficulty and importance, or the decision makers have doubts
and anxieties about the final decision, the level of post-decision dissonance will result easily
(Hawkins, Best, & Coney, 2001). In addition, dissonance will increase with the relative
attractiveness of the rejected alternatives (Greenwald, 1969). As there is a deficiency in
MCDM problems which involve cognitive dissonance, the presence, magnitude, and affects
of the dissonance need studying. The main purpose of this study is to propose a MCDM
method to reduce the dissonance, especially under intuitionistic fuzzy environment.
Owing to lacks of knowledge and information processing capabilities, decision makers
would be incapable of evaluating with crisp values. In order to properly tackle the vague
human judgments, a great number of studies have developed several MCDM approaches base
on various imprecise sets. Unlike a fuzzy set proposed by Zadeh (1965) and merely giving a
membership degree to which an element belongs to a set, an intuitionistic fuzzy set (IFS)
provides both a membership degree and a non-membership degree. The IFS, developed by
Atanassov (1986) is a useful tool to deal with the vagueness. In addition to the membership
and non-membership degrees, the IFS is characterized by a supplementary hesitancy degree
to capture the human indeterminacy in the decision-making process. The IFSs display a richer
apparatus to grasp imprecision than the conventional fuzzy sets. Due to the applicable nature
of IFSs, a great deal of research has extended IFSs to MCDM issues (Boran, Gene, Kurt, &
Akay, 2009; Miao & Wang, 2008; Li, Wang, Liu, & Shan, 2009).
Chen and Tan (1994) presented the evaluation function and score function for handling
multicriteria fuzzy decision-making problems. Based on Chen and Tan’s work, Liu and Wang
(2007) employed intuitionistic fuzzy point operators to reduce the degree of uncertainty
before implementing the evaluation function; besides, a series of new score functions for
tackling the MCDM problems were also proposed. Lin, Yuan, and Xia (2007) utilized a
linear programming model which permits the decision maker to alter the evaluating weights
during the decision-making process. Miao and Wang (2008) adopted a mathematical
4 Pan-Pacific Management Review January
programming model combining the extended TOPSIS skill to conduct multi-attribute and
multi-person decision-making problems. Boran et al. (2009) used the intuitionistic fuzzy
weighted averaging operator to aggregate individual opinions of decision makers.
Taking into account the human thoughts with uncertainty and the dissonance arousal
explicitly, this study proposes two mathematical programming models to solving MCDM
problems under the intuitionistic fuzzy decision situation. One is based on the intuitionistic
fuzzy weighted averaging operator and the score function to generate optimal weights of
criteria, and then to obtain preference order of alternatives. The other further adds the
maximal of alternative attractiveness to anticipate reducing the dissonance. Finally, an
empirical study was employed to support the feasibility and effectiveness of the proposed
methods.
DECISION ENVIRONMENT BASED ON IFSs
Atanassov (1986) generalized the concept of fuzzy set and defined the concept of IFSs.
Tizhoosh (2008) suggested that IFSs and interval-valued fuzzy sets (IVFSs), which were
presented by Gorzlczany (1987) and Turksen (1996), constitute a mathematical isomorphism,
but perform with different semantics. It is worthwhile to mention that IVFSs are mathematically equivalent to IFSs (Dubois, Gottwald, Hajek, Kacprzjk, & Prade, 2005).
More detailed information about the relationship between IFSs and other models of
imprecision was discussed by Deschrijver and Kerre (2007).
Definition 2.1. Atanassov (1986) let X be a finite universe of discourse. An IFS A in X
is an object having the following form:
XxxxxA AA )(),(, (1) where the function ]1,0[: XA and ]1,0[: XA define the degree of
membership and the degree of non-membership of the element Xx to the set XA ,
respectively, such that 1)()(0 xx AA . The value of
)()(1)( xxx AAA (2)
calls the intuitionistic index. It is the degree of uncertainty (or indeterminacy) (Atanassov,
1999) or the degree of hesitancy (Szmidt & Kacprzyk, 2000) associated with the membership
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 5
of element Xx in IFS A.
The presentation of a decision-making problem which contains multiple alternatives
and criteria under the intuitionistic fuzzy environment can be concisely expressed in a
decision matrix M. The values in the matrix are composed of the evaluations of the i-th
alternative, iA , with respect to the j-th criterion, jc . The evaluations of each alternative with
respect to each criterion are measured on a fuzzy concept of “excellence” based on similar
intuitionistic fuzzy definitions given by Li (2005) and Lin et al. (2007). Suppose that there
exists a non-inferior alternative set mAAAA ,...,, 21 . Each alternative is assessed on n
criteria, denoted by nCCCC ,...,, 21 . Assume that ij and ij are the degree of
membership and the degree of non-membership of the alternative AAi with respect to the
criterion CC j to the fuzzy concept “excellence”, respectively, where 10 ij ,
10 ij and 10 ijij . Denote that ijijijij xX ,, is one of IFSs in the finite
universe of discourse X. The intuitionistic index of the alternative iA in the set ijX is
defined by ijijij 1 . The intensity of the “excellence” of the alternative iA with
respect to the criterion xj is given by ij , but is affected by ij and ij . Especially, when
ij gets larger, a higher hesitation margin of the “excellence” occurs. The intuitionistic fuzzy
decision matrix M is defined as the following form:
. 1C 2C … nC
),(),(),(
),(),(),(),(),(),(
2211
2222222121
1112121111
2
1
mnmnmmmm
nn
nn
mA
AA
M
(3)
Further consider the relative importance of criteria, and let j and j be the degree
of membership and the degree of non-membership of the criterion CC j to the fuzzy
concept “importance”, respectively, where 10 j , 10 j and 10 jj . The
6 Pan-Pacific Management Review January
intuitionistic index jjj 1 . The intensity of the “importance” of the criterion
CC j is given by j , but is affected by j and j . Especially, when j gets larger, a
higher hesitation margin of the “importance” occurs. Since IFSs and IVFSs are
mathematically equivalent, the weights of criteria lie in the closed interval
],[],[ jjjjj ww ul , where jjw
l and jjjjw 1u . ljw and
ujw are the
lower bound and upper bound of the membership to the fuzzy concept “importance” in IVFSs,
respectively. The lower bound of membership in IVFSs is equal to the degree of membership
in IFSs. The length between lower bound and upper bound in IVFSs is equal to the degree of
uncertainty in IFSs. Obviously, 10 ul jj ww for each criterion Cc j . In addition,
11
n
jjwl and 1
1
n
jjwu are assumed in order to determine weights ]1,0[jw
) ,,2 ,1( nj satisfying ul jjj www and 11
n
jjw . An interval weight vector of all
criteria can be concisely expressed by W as follows:
],[,],,[],,[ 2211 unlnulul wwwwwwW ],[,],,[],,[ 222111 nnn . (4)
DECISION MAKING WITH DISSONANCE REDUCTION
Intuitionistic Fuzzy Aggregation Operator
Several approaches have been developed to aggregate sets under fuzzy environment.
Chen and Tan (1994) proposed new techniques in which the degrees that each alternative
satisfies and does not satisfy the decision-maker’s requirement can be assessed by the
evaluation function based on the maximum and minimum operators of the vague values.
Hong and Choi (2000) presented Max-min, Max-max, and Max-center methods to tackle
multicriteria fuzzy decision-making problems. Deschrijver and Kerre (2005) introduced
aggregation operators on the lattice L, which is the underlying lattice of both interval-valued
fuzzy sets and intuitionistic fuzzy sets, and considered some particular classes of binary
aggregation operators based on t-norms on the unit interval. Liu and Wang (2007) extended
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 7
the intuitionistic fuzzy point operators to the works proposed by Chen and Tan (1994) and
Hong and Choi (2000) in order to reduce the degree of uncertainty of the elements
corresponding to an IFS in advance. Xu (2007) developed a similarity measure based on the
set-theoretic approach, and defined the notions of positive and negative ideal set to further
calculate the scores of alternatives. In spite of the adequacy to compute the performance of
each alternative, these techniques are merely employed based on the maximum and minimum
operators. A simple boundary operation may lead to the loss of information and the
imprecision in the preference order of alternatives. To aggregate a collection of intuitionistic
fuzzy values without any loss of information, Xu (2007) developed the intuitionistic fuzzy
weighted averaging (IFWA) operator.
Definition 3.1. Harsanyi (1955) let WA: RR n , if WA
n
jjjnw awaaa
121 ) ,, ,(WA (5)
then WA is called a weighted averaging operator, where Tnwwww ),,,( 21 is the weight
vector of ), ,...,2 ,1( nja j with ]1,0[ jw and ,11
n
jjw R is the set of all real
numbers.
According to the basic operations given by Atanassov (1986), De, Biswas, and Roy
(2000) defined the concentration, dilation, and normalization of IFSs and presented some new
operations on IFSs. Several operations pertaining to the IFWA operator are presented as
follows:
Definition 3.2. Let ) ,(~ ~~ aaa and ) ,(~
~~ bbb be two intuitionistic fuzzy values;
then
) ,(~~ ~~~~~~ babababa ; (6)
) ,(~~ ~~~~~~ babababa ; (7)
0 ), ,)1(1(~ ~~ aaa ; (8)
0 ),)1(1 ,(~ ~~ aaa . (9)
8 Pan-Pacific Management Review January
Xu (2007) proposed the properties of intuitionistic fuzzy values, including the
Commutativity, Distributive laws, and Associativity, and completed the proof.
Definition 3.3. Let ) ,(~ ~~ aaa and ) ,(~
~~ bbb be two intuitionistic fuzzy values,
and , 1 , 2 >0
abba ~~~~ ; (10)
baba ~~)~~( ; (11)
aaa ~)(~~ 2121 . (12)
The IFWA operator extends the WA to accommodate the situations where the input
arguments are intuitionistic fuzzy values. For MCDM problems, the IFWA operator
aggregates each weighted evaluating values of criteria, and scores the performance of the
alternative.
Definition 3.4. Let )(XIFSX ij , AAi , CC j . The ),( ijijijX is a
collection of intuitionistic fuzzy values given by j=1, 2,…, n, and the IFWA: n , if
inniiijw xwxwxwX 2211)(IFWA , (13)
then IFWA is called an intuitionistic fuzzy weighted averaging operator of dimension n,
where Tnwwww ),,,( 21 is the weight vector of ijx (j = 1, 2,…, n), with ]1,0[jw ,
11
n
jjw , and is the set of all intuitionistic fuzzy values. More specifically, based on
Definition 3.3, if Tnnnw )/1 ,...,/1 ,/1( , the IFWA operator degenerates into an
intuitionistic fuzzy averaging operator of dimension n, which is defined as follows:
)(1)(IFA 21 iniiijw xxxnX . (14)
According to Definition 3.2 and 3.4, the IFWA operator can be rewritten and defined as
follows:
Definition 3.5. Let )(XIFSX ij , AAi , CC j . The )1,( ijijijX is a
collection of intuitionistic fuzzy values given by j = 1, 2,…, n, and
inniiijw xwxwxwX 2211)(IFWA
n
j
wij
n
j
wij
jj
11
,)1(1 (15)
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 9
where Tnwwww ),,,( 21 is the weight vector of ijx (j = 1, 2,…, n), with ]1,0[jw ,
11
n
jjw . The aggregated value by the IFWA operator is also an intuitionistic fuzzy value.
A MCDM Method Based on IFWA and Score Function
By applying the IFWA operator, each alternative can gain a score which consists of the
membership degree and non-membership degree. Nevertheless, it is difficult to immediately
compare the priority of alternatives in terms of three elements of , , and . To
facilitate the comparison, Chen and Tan (1994) presented a score function S to evaluate the
degree of suitability that an alternative satisfies a decision maker’s requirement. Let
),( ijijijX be an intuitionistic fuzzy value; based on the score function S, the suitability
of an intuitionistic fuzzy value for the alternative can be measured by
ijijijXS )( , (16) where ]1,0[ij , ]1,0[ij , 1 ijij , ]1,1[)( ijXS . The definition of the score
function equals the membership degree minus the non-membership degree. Incorporating the
IFWA operator, the score function is redefined in Definition 3.6.
Definition 3.6. Let )(XIFSX ij , AAi , CC j . The ),( ijijijX is a
collection of intuitionistic fuzzy values given by j=1, 2,…, n. The score function of each
alternative based on the IFWA operator is defined as follows:
n
j
wij
n
j
wiji
jjAS11
)1(1)( (17)
where ]1,1[)( iAS , for each i = 1, 2,…, m.
Under the intuitionistic fuzzy environment, the weights of criteria are characterized by
interval values. The length of an interval accounts for the degree of uncertainty. That is, the
possible weight of criterion can be any value within an interval. The decision maker can
change the evaluating weights of criteria between the lower bound and upper bound of an
interval. In this condition of adjustable weights, the degree to which the alternative iA
satisfies the decision maker’s requirement can be measured by an optimal programming with
the weighted score function and the IFWA operator. Besides, since there are m alternatives in
the decision-making problem, m programming models have to be solved. In this way, each
10 Pan-Pacific Management Review January
alternative can individually obtain the optimal weight vector. However, the optimal solutions
would be different in general so that the corresponding optimal values of the degree of
suitability for m alternatives cannot be compared. As the decision maker cannot evidently
judge the preference relations among all non-inferior alternatives, assigning an equal weight
1/m is plausible to aggregate m mathematical programming problems. The aggregated
mathematical programming problem is presented as follows:
n
jj
ujj
lj
m
ii
w
njwww
m
ASZ
1
1
.1
), ,,2 ,1( s.t.
)(max
(18)
A MCDM Method with Dissonance Reduction
There have existed some effective manners to reduce the dissonance, including attitude
change, opinion change, seeking and recall of consonant information, avoidance of dissonant
information, perceptual distortion, and behavioral change (Harmon-Jones & Harmon-Jones,
2007; Soutar & Sweeney, 2003; Sweeney, Hausknecht, & Soutar, 2000). Facing multiple
non-inferior alternatives to be evaluated, a decision maker will yield more post-decision
dissonance as this decision reaches a certain level of difficulty (Festinger, 1964; Menasco &
Hawkins, 1978). The number and the attractiveness of alternatives determine the level of
difficulty. Specifically, the more approaching the alternatives perform, the more difficult the
decision is. Hence, the dissonance generates in accordance with the attractiveness of
alternatives. To reduce the relative attractiveness of alternatives, an approach is offered to
magnify the difference between alternatives. For the score function of each alternative, the
sum of the Euclidean distance between alternative iA and other alternatives kA is equal to
2)()( ki ASAS . Due to the purpose of reducing decisional dissonance, the total distance
between each two of m alternatives must be maximized. That is, )!2)!2(
!(2
mmC m different
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 11
combinations of distance between each two alternatives need accumulating. The larger
distance between alternatives results in less dissonance. Thus, based on Eq. (18), the
maximization of
m
i
m
kki ASAS
1 1
2)()(21 is added to the original objective.
Since there are two objective functions, we transform the two-objective problem into a
single optimization problem according to the decision maker’s preference structure. Let
be a parameter which reflects the decision maker’s preference pertaining to the importance of
dissonance reduction when compared to the objective of maximal suitability degree, where
]1,0[ . To reduce dissonance, the following mathematical programming problem with an
adjustable parameter is considered.
n
jj
ujj
lj
m
i
m
kki
m
ii
w
njwww
ASAS
m
AS
1
1 1
2
1
.1
), ,,2 ,1( .t.s
2
)()()()1(max
(19)
In Eq. (19), the parameter α can be regarded as a function of involvement due to the fact
that the decision-making process is affected by the level of involvement (Rothschild, 1979).
More specifically, Brehm and Cohen (1962) indicated that involvement is a prerequisite for
the extent of dissonance. The dissonance would get large when decision makers are under
high-involvement decision-making environment (Anderson, 1973). Thus, it is necessary to
magnify the attractiveness of alternatives for reducing dissonance as the degree of
involvement is high. The parameter α determines the relative importance between the degree
of suitability and dissonance reduction. A large α will increase the salience of reducing
dissonance but impair the reachable levels of suitability. A small α causes the opposite effect.
Moreover, it is worthwhile to mention that the constraints of criterion weights in (18) and (19)
are equivalent, but the solutions of criterion weights may be unequal because of different
objectives in which the former is a straightforward model and the later further considers the
viewpoint of involvement to enlarge the distance among alternative and to reduce the
dissonance.
12 Pan-Pacific Management Review January
Numerical Example
In this section, a multi-criteria decision-making problem is used to illustrate our
proposed methods. Suppose that there are five alternatives 54321 ,,,, AAAAAA , which is
assessed by four criteria 4321 ,,, ccccC . Assume that the degrees ij of membership
and the degrees ij of non-membership for the alternative AAi with respect to the
criterion CCi to the fuzzy concept “excellence” are represented by an intuitionistic fuzzy
decision matrix as follows:
1C 2C 3C 4C
)30.0 ,28.0()45.0 ,17.0()18.0 ,13.0()26.0 ,65.0()04.0 ,51.0()38.0 ,11.0()27.0 ,28.0()20.0 ,32.0()20.0 ,19.0()32.0 ,08.0()37.0 ,58.0()09.0 ,55.0()28.0 ,13.0()16.0 ,71.0()81.0 ,01.0()39.0 ,58.0()04.0 ,44.0()25.0 ,41.0()06.0 ,36.0()52.0 ,30.0(
5
4
3
2
1
AAAAA
D
The degrees j of membership and the degrees j of non-membership for the four
criteria CCi to the fuzzy concept “importance” are assumed below:
1C 2C 3C 4C
)88.0 ,03.0(),38.0 ,16.0(),36.0 ,49.0(),63.0 ,18.0()),(( 41 jj . The criteria weights also lie in the closed intervals and are expressed by W as follows:
1C 2C 3C 4C
]12.0 ,03.0[],62.0 ,16.0[],64.0 ,49.0[],37.0 ,18.0[W .
It should be noted that
4
1186.0
j
ljw and
4
1175.1
j
ujw .
By applying (18), we can obtain the following mathematical programming:
530.045.018.026.072.083.087.035.01(
)04.038.027.020.049.089.072.068.01()20.032.037.009.081.092.042.045.01()28.016.081.039.087.029.099.042.01()04.025.006.052.056.059.064.070.01(
max
43214321
43214321
43214321
43214321
43214321
wwwwwwww
wwwwwwww
wwwwwwww
wwwwwwww
wwwwwwww
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 13
.1,12.003.0,62.016.0,64.049.0,37.018.0
s.t.
4321
4
3
2
1
wwwwwwww
The optimal solution of the above programming is Tw )03.0 ,16.0 ,49.0 ,32.0( . The
optimal objective value of Z reaches 0.11. Taking the optimal weights to calculate the degrees
of the suitability for each alternative by (17), we can obtain
)( 1AS =0.20, )( 2AS =-0.09, )( 3AS =0.27, )( 4AS =0.03, )( 5AS =0.12.
According to the degrees of suitability, the priority of the five alternatives is given by
24513 AAAAA . Based on the decision matrix and our proposed method, the
alternative 3A is the best choice for the decision maker.
In order to expand the attractiveness of alternatives and reduce the dissonance, the
second proposed method in (19) is used to help the decision maker determine the best
alternative. Assume that the degree of involvement is 0.5. By applying (19), the optimal
solution of the programming is Tw )03.0 ,16.0 ,63.0 ,18.0( . The optimal objective value of
is 1.19. In the same way, the degrees of the suitability for each alternative can be
calculated by using (17). The results which take into account the distance between
alternatives are )( 1AS =0.25, )( 2AS =-0.22, )( 3AS =0.23, )( 4AS =0.01, )( 5AS =0.05. The
priority of the alternatives is ordered by 24531 AAAAA . Instead of 3A , 1A
becomes the best choice for the decision maker. The outcome explains that the latter method
which magnifies the distance between alternatives may help the decision maker obtain better
choice satisfying the intrinsic requirement; meanwhile, due to the explicit judgment on the
difficult option of approaching alternatives, it is likely to reduce the decisional dissonance. In
order to manifest that the proposed method is capable of diminishing the dissonance, an
empirical study was employed to support the effectiveness, and presented in the following.
14 Pan-Pacific Management Review January
AN EMPIRICAL STUDY
There are two method proposed in this study to tackle MCDM problems. One is derived
from an optimization model with weighted score functions and IFWA; the other further
deliberate the idea of involvement and the distance between alternatives. The former can be
regarded as an applicable approach to the MCDM analysis; the latter is developed to
anticipate diminishing the decision maker’s cognitive dissonance, and properly calculate the
best alternative corresponding to decision maker’s choice. For simplicity, the two methods
are labeled as non-dissonance method and dissonance method, respectively. In order to
ascertain that the method was competent to reduce the cognitive dissonance, an empirical
study was employed to observe the variation of cognitive dissonance and to manifest the
effectiveness and feasibility of the method.
Procedure and Measures
Measures for the empirical study were divided into five parts, including the
demographics, weights of criteria, decision matrix for a MCDM problem, involvement, and
cognition dissonance. The investigation adopted a two-step design to collect data. In the first
step, subjects were asked to respond all questions except the cognitive dissonance. When
obtaining the preliminary data, we calculated the scores of each alternative and determined
the best alternative according to the two proposed methods simultaneously. The subjects were
unqualified if the preliminary data they provided generated the equivalent top rank of
alternatives by applying different methods. The eligible subjects proceeded to answer the
questions pertaining to the cognitive dissonance in the second step. The extent of cognitive
dissonance was measured with the specific condition in which subjects needed to react the
attitude toward the case that they purchased or selected the alternative we gave by two
mathematical outcomes, respectively.
Since MCDM problems often involve imprecise, uncertain and subjective elements, it is
very appropriate to assess decisional process under fuzzy environment. Considering the
decision making is complex and vague, we utilized IFSs to capture the degrees of alternative
with respect to each criterion which were yielded by subjects. Due to the fact that
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 15
interval-valued fuzzy sets are mathematically equivalent to IFSs (Dubois et al., 2005),
subjects can give an interval score to represent the evaluating performance. The lower bound
of interval equals the membership degree in the IFS. The length of interval accounts for the
hesitancy degree. Obviously, the non-membership degree is calculated by one minus the sum
of the membership degree and hesitancy degree. The following is an instance to illustrate
how to construct a decision matrix in IFSs. Suppose that there are three alternatives
321 ,, AAAA which are evaluated by means of three criteria 321 ,, CCCC in the
fuzzy concept “excellence”. Assume that one decision maker conceives that the performance
on the 1A with respect to 1x is 89~99. It implies that he/she is sure that the extent in which
1A has excellent performance on 1x is 89. The extent in which he/she is not sure is
represented by the length of interval. The hesitancy degree amounts to 10. In order to achieve
the definition of IFSs, the interval score can be expressed by 1A = ( 1x , 0.89, 0.01, 0.10). The
rest evaluating performance of other alternatives with respect to criteria use the same way to
form the decision matrix.
Involvement is defined as the decision maker’s perceived relevance of the decision
based on inherent needs, values, and interests. The scale for involvement was developed
based on the RPII (Revised Personal Involvement Inventory) proposed by Zaichkowsky
(1994). Ten items were measured on 5-point Likert scales anchored by “strongly disagree
(0)” and “strongly agree (4)”.
The operational definition of cognitive dissonance is given by a psychologically
uncomfortable state derived from the discrepancy between the previous expectation and final
consequences after purchase. The scale for cognitive dissonance was developed based on
Sweeney et al. (2000). Twenty-two items were measured on 5-point Likert scales anchored
by “strongly disagree (0)” and “strongly agree (4)”.
Subjects and Stimulus
The research subjects employed in this study focuses on the homogeneity. Calder et al.
(1981) suggested that research subjects had better possess high homogeneity due to the fact
that high homogeneity can obtain more correct inference and reduce the covariance problem
16 Pan-Pacific Management Review January
yielded from heterogeneous subjects. The homogeneous subjects were very crucial to a
fundamental research on testing the reliability of proposed approaches. Pinto (2001) indicated
that compared with women, men had larger cognitive dissonance while making a decision
because men were more prone to dichotomous thinking and cognitive distortions than women.
The age can also lead to different level of cognitive dissonance; specifically, younger
decision makers are believed to be more sophisticated and yield higher expectations
(Thompson, Pitts, & Schwankovsky, 1993). That is, they have a higher desire for the
involvement and higher associated dissonance (Anderson, 1973). Taking the above factors
into consideration, we enrolled 220 male college students by the convenience sampling in our
investigation. On one hand, college students have many aspects in common to maintain the
homogeneity we request in this study. On the other hand, the target of younger men who may
generate lager dissonance helps us examine the variation of cognitive dissonance easily.
Of the 220 subjects, 10 responses were eliminated owing to incomplete data. This
resulted in a usable sample of 210 responses and a valid rate of 95.45%. Of the 210 subjects,
145 sets of data calculated equal top rank of alternatives by the two proposed methods. Thus,
there were only 65 subjects qualified for the second step to further respond the questionnaire
of cognitive dissonance.
A digital camera selection was designed as a MCDM problem. Digital cameras are one
of favorable and prevalent products that a majority of college students have an experience of
usage. As s stimulus, the digital camera itself has various criteria to be evaluated by decision
makers. Moreover, the digital camera is categorized as durable goods that people always
possess higher involvement when making a decision. Since high involvement is related to
high dissonance cognitive, the digital camera is an appropriate stimulus to inspect the
dissonance cognitive for a decision. Because Hunt (1970) indicated that the dissonance was
greater for high priced than for the low priced purchases, the price of stimulus products was
set up from NT$15,000 to NT$20,000. There were four evaluating criteria, including the
appearance, pixels, screen size, and optical zoom. The detailed information for the designed
MCDM problem is presented in Table 1.
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 17
TABLE 1 The evaluated alternatives and criteria Alternatives Criteria
A B C D E Appearance
Pixels 10 million 7.2 million 9 million 15 million 8 million Screen size 2.5” 3.5” 2.7” 2.5” 2.8” Optical zoom 12x 18x 7x 10x 20x
Empirical Results
Of the 210 subjects, there are 65 male students accomplishing the two-step investigation.
Table 2 shows that the percentage of major in social science (58.5%) is more than in natural
science (41.5%). The subjects enrolled in this study live in North Taiwan mostly, and the
percentage occupies 81.5%. As to the monthly income, most of subjects have
NT$12,501-17,500 to dominate in a month, followed by “NT$7,501-12,500”, “NT$17,501+”,
and “Less than NT$7,500”.
TABLE 2 Respondent demographics
Demographic Profile Category Frequency Percentage
Major Social science 38 58.5%
Natural science 27 41.5%
Permanent address North 51 81.5%
Others (Middle, South,
and East) 12 18.5%
Monthly income Less than NT$7,500 4 6.2%
NT$7,501-12,500 26 40.0%
NT$12,501-17,500 30 46.2%
NT$17,501+ 5 7.6%
18 Pan-Pacific Management Review January
The magnitude of post-decision dissonance has been viewed as an increasing function
in important (high involvement) decisions. The involvement is a parameter in the dissonance
method to adjust the priority of the best alternative. We expect that the adjusted method is
capable of assisting decision makers to select an ideal alternative and reduce the cognition
dissonance. A paired-sample T Test was implemented to examine the extent of cognitive
dissonance between the non-dissonance method and the dissonance method. Table 3 indicates
that there is indeed a salient difference in cognitive dissonance by the two methods. The
dissonance method succeeds in reducing the cognitive dissonance. When a decision maker
faces a MCDM problem, the dissonance method can calculate the best alternative which
meets the decision maker’s requirements, and effectively prevents the cognitive dissonance
from expanding. It is worthwhile to notice that although involvement and cognitive
dissonance were measured by the Likert scales anchored by 0 to 4, the scores were
aggregated and normalized within 0 and 1 in order to fit the axiom of IFSs.
TABLE 3 Paired-sample t test of cognitive dissonance Methods Mean SD t-value p-value
Non-dissonance method 0.630 0.128 10.3 0.00 Dissonance method 0.390 0.156
Table 4 demonstrates the detailed alternation of optimal alternatives by the two methods.
According to the mathematical calculation, the highest scores account for the best alternative
for the decision maker. The values of cognitive dissonance occur when the decision makers
select and purchase the specific alternative. The numerical results shows if choosing the
alternative which is given by the non-dissonance method, the decision maker yields relatively
high cognitive dissonance due to the inconsistency between the calculating alternative and the
real alternative in the decision maker’s mind. Nevertheless, the alternative calculated by the
dissonance method is close to the decision maker’s need. There is a prominent reduction in
the cognitive dissonance. Table 4 also reveals that the Alternative A is the optimal selection
by applying non-dissonance method. Of 65 decision matrices, the number of Alternative A
which is viewed as the best choice by mathematically calculating amounts to 38. But, only 2
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 19
Alternative A maintain the best choice by applying the dissonance method. By contrast,
Alternative E becomes the optimal choice for the decision makers. Getting a further look in
each cells of the table, we can observe the scores of 1st and 2nd place alternatives are so
approaching by the non-dissonance method that the 2nd place alternative improves the
position to the top by the dissonance method. It implies that our proposed dissonance method
is appropriate to deal with hardly discriminative alternatives and efficiently reduce the
dissonance when decision maker are tackling a MCDM problem.
TABLE 4 The optimal results by two methods Non-dissonance Method Dissonance Method
Alternatives Alternatives Subject No.
A B C D E Disa
A B C D E Disa
1 0.170* 0.139 0.128 0.135 0.143 0.57 0.231 0.705 0.705 0.705 0.706* 0.382 0.143* 0.134 0.137 0.140 0.134 0.69 0.126 0.186 0.187 0.188* 0.185 0.283 0.141* 0.097 0.103 0.076 0.102 0.36 0.222 1.144 1.142 1.141 1.145* 0.334 0.135* 0.102 0.106 0.095 0.109 0.70 0.181 0.694 0.695 0.693 0.696* 0.265 0.123* 0.097 0.064 0.109 0.120 0.76 0.412 0.790 0.774 0.796 0.801* 0.346 0.135 0.153 0.144 0.157* 0.114 0.85 0.152 0.905* 0.904 0.902 0.900 0.477 0.135* 0.108 0.118 0.129 0.124 0.58 0.072 0.598 0.599 0.599 0.600* 0.258 0.161* 0.151 0.134 0.160 0.147 0.78 0.218 0.476 0.470 0.479* 0.474 0.369 0.160* 0.154 0.140 0.144 0.154 0.66 0.201 0.332 0.330 0.332 0.337* 0.2310 0.124* 0.123 0.113 0.116 0.118 0.73 0.116 0.217* 0.213 0.214 0.215 0.2611 0.139* 0.129 0.132 0.118 0.090 0.65 0.365 0.531 0.532* 0.521 0.515 0.2712 0.085* 0.072 0.083 0.071 0.064 0.50 0.175 0.376 0.381* 0.376 0.375 0.3213 0.162* 0.140 0.135 0.138 0.131 0.74 0.229 0.462 0.464 0.466* 0.459 0.3314 0.172* 0.137 0.128 0.136 0.132 0.67 0.300 0.335* 0.327 0.331 0.322 0.2615 0.160 0.161 0.172* 0.171 0.171 0.64 0.185 0.215 0.221 0.222* 0.221 0.6816 0.121* 0.056 0.060 0.107 0.085 0.95 0.410 1.262 1.263 1.277* 1.270 0.3417 0.117 0.112 0.123* 0.121 0.118 0.72 0.111 0.222 0.225 0.226* 0.224 0.7218 0.167* 0.146 0.138 0.137 0.141 0.65 0.097 0.626 0.626 0.626 0.627* 0.1819 0.134* 0.100 0.105 0.097 0.111 0.68 0.278 0.498 0.501 0.497 0.503* 0.2420 0.083* 0.080 0.077 0.078 0.086 0.58 0.086 0.165 0.164 0.165 0.168* 0.2621 0.143* 0.115 0.115 0.115 0.124 0.63 0.197 0.459 0.459 0.459 0.462* 0.3122 0.125 0.125* 0.119 0.119 0.124 0.75 0.109 0.155 0.153 0.153 0.156* 0.8023 0.114 0.114 0.116* 0.115 0.114 0.60 0.093 0.097 0.097 0.098* 0.097 0.5724 0.121 0.121 0.129 0.130* 0.121 0.59 0.133 0.196 0.201* 0.200 0.196 0.2725 0.161* 0.146 0.138 0.137 0.141 0.83 0.233 0.327* 0.322 0.322 0.324 0.3326 0.165* 0.151 0.136 0.158 0.141 0.50 0.137 0.649 0.646 0.650* 0.648 0.3327 0.159* 0.152 0.138 0.142 0.153 0.70 0.199 0.374 0.368 0.370 0.375* 0.3128 0.137* 0.117 0.127 0.132 0.122 0.68 0.188 0.315 0.319 0.322* 0.317 0.2829 0.132* 0.100 0.104 0.097 0.112 0.50 0.142 0.698 0.699 0.698 0.700* 0.5030 0.147* 0.120 0.087 0.072 0.085 0.88 0.386 1.428* 1.420 1.416 1.419 0.6831 0.112 0.124* 0.103 0.101 0.119 0.61 0.035 0.600 0.600 0.600 0.601* 0.2332 0.118 0.117 0.112 0.122* 0.123 0.53 0.116 0.219 0.217 0.222 0.222* 0.3533 0.131* 0.117 0.129 0.118 0.117 0.51 0.140 0.266 0.271* 0.267 0.265 0.5134 0.140* 0.125 0.115 0.125 0.089 0.65 0.355 0.527* 0.521 0.526 0.506 0.3535 0.173* 0.140 0.148 0.162 0.138 0.60 0.326 0.475 0.480 0.488* 0.474 0.3636 0.125* 0.125 0.071 0.071 0.115 0.64 0.456 0.682* 0.649 0.649 0.677 0.19
20 Pan-Pacific Management Review January
Non-dissonance Method Dissonance Method Alternatives Alternatives Subject No. A B C D E Dis
a
A B C D E Disa
37 0.114* 0.096 0.087 0.093 0.101 0.70 0.200 0.397 0.394 0.396 0.400* 0.2538 0.133* 0.130 0.108 0.100 0.100 0.49 0.306 0.519* 0.507 0.503 0.503 0.0339 0.057 0.071 0.123* 0.123 0.121 0.74 0.489 0.871 0.900 0.899* 0.899 0.4540 0.170* 0.116 0.130 0.135 0.143 0.52 0.335 0.827 0.832 0.834 0.837* 0.3141 0.170* 0.159 0.159 0.160 0.162 0.25 0.129 0.217 0.216 0.217 0.218* 0.0142 0.071 0.061 0.106* 0.062 0.104 0.76 0.364 0.688 0.700 0.689 0.710* 0.2743 0.141 0.105 0.076 0.143 0.153* 0.49 0.191* 0.139 0.136 0.187 0.190 0.0344 0.158* 0.039 0.101 0.114 0.112 0.35 0.577 1.778 1.797 1.801* 1.800 0.0145 0.053* 0.075 0.090 0.090 0.101 0.56 0.302 0.652 0.659 0.659 0.664* 0.0046 0.023 0.017 0.079 0.082* 0.082 0.78 0.464 1.143 1.168 1.169 0.160* 0.0747 0.096 0.117* 0.099 0.094 0.116 0.57 0.209 0.421 0.413 0.411 0.422* 0.3348 0.070 0.098 0.138 0.142 0.143* 0.56 0.487 0.770 0.796 0.798* 0.797 0.0249 0.074 0.095 0.134 0.142* 0.140 0.73 0.480 1.036 1.054 1.057 1.056* 0.1550 0.067 0.113 0.124 0.136 0.138* 0.53 0.221 1.423 1.424 1.426* 1.425 0.1951 0.047 0.080 0.135 0.137* 0.137 0.56 0.351 1.971 1.980 1.980 1.981* 0.2352 0.170* 0.116 0.128 0.135 0.143 0.45 0.373 0.756 0.761 0.764 0.768* 0.1953 0.047 0.125 0.138 0.139 0.140* 0.64 0.530 1.076 1.082 1.083* 1.082 0.0254 0.049 0.117 0.144 0.157 0.158* 0.75 0.381 2.148 2.152 2.155* 2.154 0.0755 0.063 0.101 0.139 0.140* 0.130 0.64 0.441 1.328 1.340* 1.338 1.337 0.3356 0.027 0.068 0.123 0.111 0.126* 0.57 0.653 1.379 1.407* 1.399 1.405 -0.0557 0.068 0.074 0.092 0.083 0.093* 0.45 0.174 0.486 0.499* 0.495 0.495 0.0058 0.065 0.086 0.098 0.122 0.124* 0.61 0.361 1.073 1.077 1.085* 1.081 0.0559 0.007 0.120 0.160 0.127 0.161* 0.74 0.700 2.573 2.584* 2.575 2.584 0.2460 0.015 0.057 0.085* 0.079 0.084 0.63 0.420 0.943 0.955 0.953 0.956* 0.0061 0.016 0.020 0.068 0.075 0.076* 0.53 0.394 0.581 0.613 0.618* 0.617 0.0962 0.170* 0.116 0.130 0.135 0.143 0.72 0.393 0.581 0.589 0.592 0.596* 0.4463 0.170* 0.159 0.159 0.160 0.162 0.67 0.144 0.209 0.209 0.210 0.211* 0.5564 0.071 0.069 0.104* 0.069 0.099 0.64 0.618* 0.543 0.615 0.565 0.616 0.2765 0.148* 0.093 0.090 0.143 0.146 0.80 0.453 0.356 0.632 0.365 0.765* 0.52
Note: “a” denote the extent of cognitive dissonance. “*” denotes the optimal alternatives.
Although the dissonance method can reduce the cognitive dissonance, it is impossible to
make the extent of dissonance approach none. There are only five alternatives and four
criteria for the decision makers to evaluate. The experimental alternatives and criteria may
not satisfy all subjects’ anticipation. The optimal alternative appearing in this study is merely
a relative selection rather than an absolute one. Therefore, a little bit dissonance in the
decision is acceptable.
CONCLUSIONS
Discussions
The MCDM approaches have been developed for a long while without any suspension
because of the importance of decision making in various fields. Dissimilar to the well-known
skills such as the AHP, SMART, VIKOR, ANP, and TOPSIS which cope with multiple
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 21
criteria, this study formulated the MCDM problem as two types of mathematical
programming structures based on the intuitionistic fuzzy concept. Since the indeterminate
factor always emerges when the decision maker is evaluating criteria and making a decision,
it is very proper to quantify human thoughts by applying IFSs in which in addition to the pros
and cons, the uncertain opinions are also well-expressed. In virtue of the uncertainty, the
weights of each criterion can be constructed within an interval and solved by the
mathematical programming.
Assumed all non-inferior alternatives to be of equal importance, the first programming
model was proposed based the IFWA operator and the score function to add another
technique for the MCDM analyses under intuitionistic fuzzy environment. The second
proposed model further considered the extent of involvement and the distance between
alternatives to effectively reduce the cognitive dissonance during the decision. An empirical
study was employed to manifest the effort of dissonance reduction. The consequent results
indicate that our proposed method is competent to diminish the cognitive dissonance as the
decision maker select or purchase the specific alternative. It is because the specific alternative
calculated by the dissonance method is in accordance with what the decision maker demands.
Superior to the non-dissonance method, the method further considering the dissonance tries
to enlarge the distance between alternatives so that it can assist in distinguishing the
difference among alternatives and reducing dissonance after a post-purchase decision.
However, involvement is a moderator between the two proposed methods. More specifically,
the two methods are equal when involvement approaches none. Dealing with
low-involvement decisions such as the routine decision, users may obtain similar outcomes
based on the non-dissonance or dissonance method. Relatively, the dissonance method is
suitable for the extensive decision and the limited decision due to higher involvement
demand in the process of decision making.
Managerial Implications
After the transactions are accomplished, what the enterprises are concerned is to look
forward to an increase on consumer satisfaction and consumer loyalty. Controlling the
magnitude of post-decision dissonance is a plausible manner to decrease the consumers’
22 Pan-Pacific Management Review January
negative opinions and to increase the positive preference for products or services. Facing a
difficult, important, and inalterable decision, consumers would experience the post-decision
dissonance easily. In this study , the proposed method helps consumers make a relatively
proper decision and effectively diminish the dissonance. As long as the post-decision
dissonance can be reduced, the brand loyalty and the possibility of repurchase will enhance
(Mittelstaedt, 1969).
In order to confront the tough competition, enterprises keeps on developing new
products, especially in the high-tech industry. The product line becomes various through the
line stretching and extension. Although the alternatives are abundant, it is so hard for
consumers to choose an appropriate product without any efforts that the dissonance occurs
after the decision is made. The marketers can utilize the presented method to magnify the
attractiveness of alternatives and assist consumers in selecting the best alternative and in
reducing the dissonance. In practice, the telecom companies in Taiwan have designed a web
page in which the users need to evaluate several criteria. Based on the evaluating values, the
web page will execute mathematical calculation and advise the users of a suitable phone rate.
We suggest that companies, which sell high-tech merchandise such as digital cameras, mobile
phones, notebooks, etc., can make use of our proposed method to create an auxiliary web
page for consumers to choose the best alternative.
Limitations
In order to examine a significant decrease on the cognitive dissonance, this study
mainly focused on the male and younger subjects who easily possess larger dissonance.
Hence, we do not ascertain whether the proposed method has the same effect on female and
elder decision makers. The future work can investigate a cross of different gender or age.
Moreover, the future stimulus can be employed more extensively to achieve the completeness
of the dissonance method for various products. The selection of experimental stimulus may
be picked up dependence on the decision category such as the extend problem solving,
limited problem solving, and routinized problem solving.
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 23
REFERENCES
Anderson, R. E. 1973. Consumer dissatisfaction: The effect of disconfirmed expectancy on perceived product performance. Journal of Marketing Research, 10(1): 38-44.
Atanassov, K. T. 1986. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1): 87-96. Atanassov, K. T. 1999. Intuitionistic Fuzzy Sets: Theory and Applications. New York:
Physica, Heidelberg. Boran, F. E., Genc, S., Kurt, M., & Akay, D. 2009. A multi-criteria fuzzy group decision
making for supplier selection with TOPSIS method. Expert Systems with Applications, 36(8): 11363-11368.
Brehm, J. W. & Cohen, A. R. 1962. Exploration in Cognitive Dissonance. New York: Wiley. Calder, B. J., Philillips, L. W., & Tybout, A. M. 1981. Design research for application.
Journal of Consumer Research, 8(3): 197-207. Chen, S. M. & Tan, J. M. 1994. Handling multicriteria fuzzy decision making problems
based on vague set theory. Fuzzy Sets and Systems, 67(2): 163-172. De, S. K., Biswas, R., & Roy, A. R. 2000. Some operations on intuitionistic fuzzy sets. Fuzzy
Sets and Systems, 114(3): 477-484. Deschrijver, G. & Kerre, E. E. 2005. Implicators based on binary aggregation operators in
interval-valued fuzzy set theory. Fuzzy Sets and Systems, 153(2): 229-248. Deschrijver, G., & Kerre, E. E. 2007. On the position of intuitionistic fuzzy set theory in the
framework of theories modeling imprecision. Information Sciences, 177(8): 1860-1866. Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., & Prade, H. 2005. Terminological
difficulties in fuzzy set theory-the case of “intuitionistic fuzzy sets”. Fuzzy Sets and Systems, 156(3): 485-491.
Festinger, L. 1957. A Theory of Cognitive Dissonance. New York: Harper and Row Publishers, Inc.
Festinger, L. 1964. Conflict, Decision and Dissonance. Stanford, California: Stanford University Press.
Gorzlczany, M. B. 1987. A method for inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems, 21(1): 149-160.
Greenwald, H. J. 1969. Dissonance and relative versus absolute attractiveness of decision alternatives. Journal of Personality and Social Psychology, 11(4): 328-333.
Harmon-Jones, E. & Harmon-Jones, C. 2007. Cognitive dissonance theory: After 50 years of development. Zeitschrift fürSozialpsycjologie, 38(1): 7-16.
Harsanyi, J. C. 1955. Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. Journal of Political Economy, 63(4): 309-321.
Hawkins, D. I., Best, R. J., & Coney, K. A. 2001. Consumer Behavior: Building Marketing Strategy (8th ed.). New York: McGraw-Hill.
24 Pan-Pacific Management Review January
Hong, D. H. & Choi, C. H. 2000. Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 114(1): 103-111.
Hunt, S. D. 1970. Post-transaction communications and dissonance reduction. Journal of Marketing, 34(3): 46-51.
Menasco, M. B. & Hawkins, D. I. 1978. A field test of the relationship between cognitive dissonance and state anxiety. Journal of Marketing Research, 15(4): 650-655.
Miao, X. & Wang, Y. 2008. Intuitionistic fuzzy multiattribute group decision making models using mathematical programming approach. Journal of Computational Information Systems, 4(6): 2793-2801.
Mittelstaedt, R. 1969. A dissonance approach to repeat purchasing behavior. Journal of Marketing Research, 6(4): 444-446.
Li, D. F. 2005. Multiattribute decision making models and methods using intuitionistic fuzzy sets. Journal of Computer and System Sciences, 70(1): 73-85.
Li, D. F., Wang, Y. C., Liu, S., & Shan, F. 2009. Fractional programming methodology for multi-attribute group decision-making using A-IFS. Applied Soft Computing, 9(1): 219-225.
Liberman, N. & Forster, J. 2006. Inferences from decision difficulty. Journal of Experimental Social Psychology, 42(3): 290-301.
Lin, L., Yuan, X. H., & Xia, Z. Q. 2007. Multicriteria fuzzy decision-making based on intuitionistic fuzzy sets. Journal of Computer and System Sciences, 73(1): 84-88.
Liu, H. W. & Wang, G. J. 2007. Multi-criteria decision-making methods based on intuitionistic fuzzy sets. European Journal of Operational Research, 179(1): 220-233.
Pinto, J. C. 2001. On the costs of parameter uncertainties part 2: Impact of EVOP procedures on the optimization and design of experiments. Canadian Journal of Chemical Engineering, 79(3): 412-421.
Rothschild, M. L. 1979. Advertising strategies for high and low involvement situation. In Maloney, J. C. & Silverman, B. (Eds.), Attitude Research Plays for High Stakes: 74-93. Chicago: American Marketing Association.
Soutar, G. N. & Sweeney, J. C. 2003. Are there cognitive dissonance segments? Australian Journal of Management, 28(3): 227-249.
Sweeney, J. C., Hausknecht, D., & Soutar, G. N. 2000. Cognitive dissonance after purchase: A multidimensional scale. Psychology and Marketing, 17(5): 369-385.
Szmidt, E. & Kacprzyk, J. 2000. Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems,114(3): 505-518.
Szmidt, E. & Kacprzyk, J. 2008. Atanassov’s intuitionistic fuzzy sets as a promising tool for extended fuzzy decision making models. In Bustince, H. (Ed.), Studies in Fuzziness and Soft Computing: 335-355. Berlin: Springer.
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 25
Thompson, S. C., Pitts, J. S., & Schwankovsky, L. 1993. Preferences for involvement in medical decision-making: Situational and demographic influences. Patient Education and Counseling, 22(3): 133-140.
Tizhoosh, H. R. 2008. Interval-valued versus intuitionistic fuzzy sets: Isomorphism versus semantics. Pattern Recognition, 41(5): 1812-1813.
Turksen, I. B. 1996. Interval-valued strict preference with Zadeh triples. Fuzzy Sets and Systems, 78(2): 183-195.
Xu, Z. S. 2007. Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optimization and Decision Making, 6(2): 109-121.
Zadeh, L. A. 1965. Fuzzy sets. Information and Control, 8(3): 338-353. Zaichkowsky, J. L. 1994. Research notes: The personal involvement inventory: Reduction,
revision, and application to advertising. Journal of Advertising, 23(4): 59-70.
26 Pan-Pacific Management Review January
Biographical Sketch
Ting-Yu Chen is currently an Associate Professor of the Department of Industrial and
Business Management at Chang Gung University in Taiwan. She received her B.S. degree in
Transportation Engineering and Management, M.S. degree in Civil Engineering, and Ph.D.
degree in Traffic and Transportation from National Chiao Tung University in Taiwan. Her
current research interests include multiple criteria decision making, fuzzy set theory, and
consumer decision analysis. She has published over 190 papers in peer-reviewed journals and
conference proceedings. She has received several awards, including the Distinguished
Research Award from the Chinese Institute of Transportation, the Outstanding Faculty Award
of Academic Research from Chang Gung University, the Distinguished Research Award
from the Chinese Management Association, Research Award from Chung Yuan Management
Review, and the Distinguished Young Scholar Award from Academia Sinica.
Yi-Jen Li received her M.S. degree in Business Administration in 2009 from Chang
Gung University in Taiwan. She was a part-time research assistant in the Graduate Institute
of Business Administration at Chang Gung University from September 2008 to July 2009.
Her research interests include fuzzy multiple criteria decision making and marketing
research.
Hsiao-Pin Wang received the B.S. degree in Statistics and Information Science in 2005
from Fu Jen University in Taiwan. He received his M.S. degree in Business Administration in
2007 from Chang Gung University in Taiwan. He was a full-time research assistant in the
Graduate Institute of Business Administration at Chang Gung University from November
2008 to February 2010. His research interests include fuzzy systems and marketing research.
2011 Ting-Yu Chen, Yi-Jen Li, & Hsiao-Pin Wang 27
直覺模糊多準則決策問題之降低失調方法
陳亭羽
長庚大學工商管理學系
李宜珍
長庚大學企業管理研究所
王曉斌
長庚大學工商管理研究所
中文摘要
考量認知失調於決策中為一項重要的心理變數,本研究藉由直覺模糊集合發展一套新的
多準則決策方法,設法降低決策者的認知失調情況。本方法利用直覺模糊加權平均運算
子與計分函數建構數學規劃模型,以規劃求解計算方式取得準則的權重,並排列方案優
劣順序。為了降低決策者期望與實際方案的失調程度,額外使用歐幾里得距離測度擴大
決策方案間的距離,以幫助決策者找出最佳方案。本研究提供一個數值例以便解釋詳細
的計算過程,此外經由一個實證研究以驗證研究方法的可行性。根據實證結果顯示,以
本研究方法為基礎所計算出的最佳方案,確實能夠滿足決策者同時亦能降低決策者的失
調程度。本研究成功發展一套有效降低認知失調的技術,幫助決策者解決多準則決策的
問題。
關鍵詞:認知失調、多準則決策、直覺模糊集合、直覺模糊加權平均運算、計分函數
通訊地址:陳亭羽,長庚大學工商管理學系副教授,333 桃園縣龜山鄉文化一路 259 號。 聯絡電話:886-3-2118800 分機 5678 E-mail address: [email protected]