intuitionistic fuzzy decision analysis with dissonance...

Pan-Pacific Management Review

2012,Vol.15, No.2: 99-129

99

INTUITIONISTIC FUZZY DECISION ANALYSIS WITH DISSONANCE REDUCTION FOR

OPTIMISTIC/PESSIMISTIC DECISION MAKERS

TING-YU CHEN Graduate Institute of Business and Management

Department of Industrial and Business Management College of Management, Chang Gung University

JIH-CHANG WANG

Department of Information Management College of Management, Chang Gung University

ABSTRACT

The theory of Atanassov’s intuitionistic fuzzy sets has been developed and has been successfully applied in the field of multiple criteria analysis. However, there is a lack of information about the role of optimism and pessimism on subjective judgments and cognitive dissonance accompanying the decision process. This paper presents a new method of reducing cognitive dissonance and relating optimism and pessimism to multiple criteria decision analysis under Atanassov’s intuitionistic fuzzy decision environment. We utilize optimistic and pessimistic point operators to measure the effects of optimism and pessimism, respectively, and further determine the suitability function through weighted score functions. Considering two objectives of maximal suitability and dissonance reduction, several optimization models are constructed to obtain optimal weights for criteria and to acquire the corresponding suitability degree for alternative rankings. We anticipate that the proposed method will give insight into the influences of optimism, pessimism, and cognitive dissonance on decision analysis.

Keywords: Intuitionistic fuzzy set; multiple criteria analysis; optimism; pessimism; cognitive dissonance; optimization model; decision analysis.

(Received: October, 2010; 1st revised: March, 2011 accepted: November, 2011)

INTRODUCTION Atanassov’s intuitionistic fuzzy set (A-IFS) is characterized by three functions

expressing the degrees of belongingness, non-belongingness, and hesitation (Atanassov, 1986). A-IFSs have been found to be highly valuable in assessing uncertainty and vagueness (De, Biswas, & Roy, 2000; Xu & Yager, 2008) and have become a popular

100 Pan-Pacific Management Review July

topic of investigation in the fuzzy set community (Dubois, Gottwald, Hajek, Kacprzyk, & Prade, 2005). The decision information given by decision makers, especially in complex decision making problems is often imprecise or uncertain due to a lack of data, time pressure, or the decision makers’ limited attention and information processing capabilities (Xu & Yager, 2008). A-IFSs are very suitable for capturing imprecise or uncertain decision information. Given that decision makers can change their evaluating weights during the decision making process, Li (2005) constructed several linear programming models to generate optimal weights for attributes using A-IFSs. Similarly, Lin, Yuan, and Xia (2007) used intuitionistic indices to propose a linear programming model for decision making problems based on A-IFSs. Using intuitionistic fuzzy point operators, Liu and Wang (2007) presented new score functions to solve multi-criteria decision problems in the intuitionistic fuzzy environment. Ye (2009) proposed a decision making method based on a novel accuracy function in an interval-valued intuitionistic fuzzy environment to account for hesitation degree. Xu (2007a) applied his proposed similarity measure to multi-attribute decision making based on A-IFSs. Park, Kwun, Park, and Park (2009) investigated group decision making problems based on the correlation coefficients of interval-valued A-IFSs. Ye (2010) proposed a fuzzy decision-making method using the weighted correlation coefficients of A-IFSs. Xu (2007b) defined the concepts of intuitionistic preference relation, consistent intuitionistic preference relation, incomplete intuitionistic preference relation and acceptable intuitionistic preference relation and used these concepts to develop an approach to group decision making. Atanassov, Pasi, and Yager (2005) also applied A-IFSs to group decision making; they discussed the intuitionistic fuzzy interpretations of the processes of multi-person and multi-measurement tools multi-criteria decision-making. Pankowska and Wygralak (2006) introduced the concept of general A-IFSs with triangular norm-based hesitation degrees. They combined the general concept of A-IFSs, hesitation degrees and relative scalar cardinalities involving generalized sigma counts of fuzzy sets to construct very flexible algorithms for group decision making with individual and social fuzzy preference relations. Tan and Chen (2009) proposed an intuitionistic fuzzy Choquet integral operator for multi-attribute decision making, in which they considered interaction phenomena among the decision criteria. Xu (2010) developed Choquet integrals of weighted intuitionistic fuzzy information and applied them to multi-criteria decision making. Wei (2010) developed group decision making methods based on induced intuitionistic fuzzy ordered weighted geometric operators.

There are many useful methods for multiple criteria decision analysis on the basis of A-IFSs; however, there is little research on the effect of dispositional optimism and pessimism. Optimism and pessimism, concepts that were pioneered by Scheier and Carver (1985), are fundamental constructs that reflect how people respond to their

2012 Ting-Yu Chen & Jih-Chang Wang 101

perceived environment and how to construe and affect subjective judgments. Although the theories differ in specifics, the idea that optimists and pessimists diverge in the ways in which they explain and predict future events is commonly agreed upon (Fischer & Chalmers, 2008). Optimists view their lives positively and anticipate desirable outcomes, whereas pessimists construe their lives negatively and expect unfavorable outcomes (Sanna & Chang, 2003). Hey (1979) indicated that the Hurwicz procedure can solve the decision problem considering optimistic or pessimistic viewpoints. Using a pessimism-optimism index, the Hurwicz procedure is an amalgamation of the maximin and maximax methods, in that it accounts for both the worst and the best outcomes. Similarly, Dubois and Prade (1995) proposed optimistic and pessimistic qualitative criteria based on the max-min and min-max rules, respectively.

Furthermore, Yager (1992) suggested that a decision maker’s attitude could be modeled with a pseudo-probability distribution by applying ordered weighted averaging (OWA) operators, and he demonstrated that the Hurwicz approach is a special case of his method. Yager (1993) proposed that the orness measure with an OWA operator can be interpreted as a measure of optimism in decision making, whereas the andness is a measure of pessimism. Furthermore, Yager (2002) developed an attitudinal fuzzy measure generated from the cardinality index for attitudinal characterization, including optimistic, neutral, and pessimistic characteristics. The risk attitude of a decision maker, as defined by Yager, is defined in one dimension in which optimism and pessimism are two relative extremes. In other words, a person who does not have an optimistic inclination is regarded as a neutralist or pessimist. However, most psychological studies indicate that optimism and pessimism belong to two divergent dimensions (Dember Martin, Hummer, Howe, & Melton, 1989; Chang, 1998; Chang, D’Zurilla, & Maydeu-Olivares, 1994). Some research findings have shown that expressions of pessimism were not equal to expressions of lack of optimism and further demonstrated that optimism and pessimism merged as two distinct factors (Chang Maydeu-Olivares, & D’Zurilla, 1997; Marshall, Wortman, Kusulas, Hervig, & Vickers, 1992; Scheier, Carver, & Bridges, 1994).

Following the psychological studies above, more elegant methods to account for optimism and pessimism in decision making are needed. The proposed methods in this study address the effects of optimism and pessimism separately; moreover, the degree of determinacy associated with the membership of the element is considered to capture the hesitation influenced by optimism and pessimism. The proposed methods are adaptable to specific situations by adjusting the parameter values within the point operators depending on the nature of the optimism and pessimism. The employment of a point operator for each alternative and each criterion requires the introduction of information on alternatives into the model. Through point operators, the proposed


methods can adjust the parameter values, and thus, they are more adaptable to real problems.

Little attention has been given to the concept of dissonance in decision analysis based on A-IFSs. The concept of dissonance has been discussed widely in the social psychology field (Harmon-Jones & Harmon-Jones, 2007). Festinger (1957) described cognitive dissonance as a psychologically uncomfortable state that motivates an individual to reduce that dissonance. Festinger (1957) and Straits (1964) have shown that whenever an individual makes a decision, he/she often has some degree of cognitive dissonance. Faced with the necessity of choosing among non-inferior alternatives, the decision maker collects and evaluates information about the alternatives, eventually establishing a preference order. When a person makes a decision from among alternatives, each of which has certain advantages and disadvantages over the others, varying levels of post-decision dissonance will result (Bell, 1967; Milliman & Decker, 1990). More specifically, the decision maker will have doubts and anxieties about the choice he/she has made because the foregone alternatives had certain desirable traits, and the option selected has undesirable characteristics that he/she must now accept or tolerate. The magnitude of post-decision dissonance has been viewed as an increasing function in important (high involvement) decisions (Menasco & Hawkins, 1978; Milliman & Decker, 1990). On the other hand, Festinger (1964) and Mittelstaedt (1969) have suggested that dissonance increases with the number of rejected alternatives.

If the post-decision dissonance experienced by the decision maker is great enough, it can cause that individual to withdraw the choice or exchange one alternative for another. In other words, a high level of dissonance may cause the decision maker to reduce dissonance by changing his/her decision (Mittelstaedt, 1969) or justifying decisions post hoc (Kopalle & Lehmann, 2001). The preference order does not stabilize due to the existence of dissonance. The decision maker must adjust the decision situation and make a new choice; this may increase decision efforts and overall costs. Therefore, from the standpoint of decision effectiveness, it is crucial that post-decision dissonance should be minimized to the fullest extent possible.

An appropriate method is necessary to cope with decisional dissonance and to ascertain the influences of optimism and pessimism on the decision making process. The proposed method is a new idea to study cognitive dissonance and dispositional optimism and pessimism under an intuitionistic fuzzy environment in which we can obtain more reasonable decisional results corresponding to the real world. Under the intuitionistic fuzzy decision situation, we develop several score functions based on optimistic and pessimistic point operators for the sake of quantifying optimism and pessimism. Furthermore, the suitability function to determine the degree to which an alternative satisfies the decision maker’s requirement is assessed according to weighted


score functions. Next, we construct optimization models to generate optimal weights for criteria to solve a multi-criteria decision making problem with two objectives, one for the maximal overall performance of alternatives and the other for the maximal discrimination of alternative attractiveness. Finally, the feasibility and effectiveness of the proposed method are illustrated by using a numerical example followed by a discussion.

DECISION ENVIRONMENT BASED ON A-IFSs

Preliminaries The concept of A-IFS is a generalization of ordinary fuzzy sets. In the following

section, we briefly review some relevant definitions, relations, and operations of A-IFSs (Atanassov, 1986, 1989, 1995, 1999). It is worthwhile to mention that interval-valued fuzzy set (IVFS) theory is mathematically equivalent to A-IFS theory (Deschrijver & Kerre, 2003; Dubois et al., 2005). Although A-IFS and IVFS are based on different semantics (Dubois et al., 2005; Grzegorzewski & Mrówka, 2005), they constitute an isomorphism (Tizhoosh, 2008). Because IVFS and A-IFS are equipollent generalizations of ordinary fuzzy sets (Burillo & Bustince, 1996), the contents in this paper can be immediately expressed in terms of IVFS notation.

Definition 2.1. Let X be an ordinary finite non-empty set. An A-IFS A in X is an expression given by:

XxxxxA AA )(),(, , (1) where )(xA : X[0,1], )(xA : X[0,1] with the condition 1)()(0 xx AA

for all x in X. The numbers )(xA and )(xA denote the membership degree and the non-membership degree of the element x in A, respectively.

Definition 2.2. For each A-IFS A in X, the value of

)()(1)( xxx AAA (2)

represents the degree of uncertainty (or indeterminacy) (Atanassov, 1999), or the degree of hesitancy (Szmidt & Kacprzyk, 2000) associated with the membership of element

xX in A-IFS A. We call )(xA the intuitionistic index of x in A.

Definition 2.3. For AIFS(X) (the class of A-IFSs in the universe X) and for

every ]1,0[, : XxxxxxAJ AAA )(),()(, )(, ; (3) XxxxxxxAJ AAAA )()),()(1()(, )(*, ; (4)


XxxxxxAH AAA )()(),(, )(, ; (5) XxxxxxxAH AAAA ))()(1()(),(, )(* , ; (6) XxxxxAP AA )),(min(),),(max(, )(, for 1 ; (7) XxxxxAQ AA )),(max(),),(min(, )(, for 1 . (8)

Intuitionistic fuzzy decision environment A multi-criteria decision making problem can be concisely expressed in a decision

matrix whose elements indicate the evaluation or value of the i-th alternative, Ai, with respect to the j-th criterion, xj. In this paper, we extend the canonical matrix format to the intuitionistic fuzzy decision matrix D. Using the similar definitions of Li (2005) and Lin et al. (2007), the evaluations of each alternative with respect to each criterion on the fuzzy concept of “excellence” are given using A-IFSs. We suppose that there exists a

non-inferior alternative set mAAAA ,...,, 21 . Each alternative is assessed on n criteria, which are denoted by nxxxX ,...,, 21 . We 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 Xxj to the fuzzy concept “excellence”, respectively, where

10 ij , 10 ij and 10 ijij . We also denote that ijijjij xX ,, . The intuitionistic index of the alternative iA in the set ijX is defined by

ijijij 1 . When ij is larger, the hesitation margin of the decision maker as to the “excellence” of the alternative Ai with respect to the criterion xj, whose intensity is

given by ij , is higher. The intuitionistic fuzzy decision matrix D is defined as the following form:

),(),(),(

),(),(),(),(),(),(

2211

2222222121

1112121111

2

1

21

mnmnmmmm

nn

nn

m

n

A

AA

D

xxx

. (9)

Similarly, let j and j be the degree of membership and the degree of

non-membership of the criterion Xxj to the fuzzy concept “importance”,

respectively, where 10 j , 10 j and 10 jj . The intuitionistic

index jjj 1 . When j is larger, the hesitation margin of the decision maker as

to the “importance” of the criterion Xxj , whose intensity is given by j, is higher.

Because A-IFSs and IVFSs are mathematically equivalent, the decision maker’s weight


lies in the closed interval ],[],[ ul jjjjj ww , where jjw l and

jjjjw 1u . Obviously, 10 ul jj ww for each criterion Xxj . In

addition, 11

l

n

jjw and 1

1

u

n

jjw are assumed in order to determine the weights

]1,0[jw (j=1,2,,n) that satisfy uljjj www and 1

1

n

jjw .

Atanassov et al. (2005) discussed the possibility of using measurement tool estimations, which are accounting experts’ opinions about the separate tools. Based on the measurement tool estimations and the measurement tool scores, Atanassov et al. deformed the measurement tool estimations, including optimistic estimation, optimistic estimation with restrictions, pessimistic estimation, pessimistic estimation with restrictions, estimation with a decrease in uncertainty, and estimation with an increase in uncertainty. In this paper, we extend the concept of measurement tool estimations to develop optimistic and pessimistic point operators for the purpose of obtaining optimistic and pessimistic score functions.

OPTIMISTIC AND PESSIMISTIC POINT OPERATORS ON A-IFSs Here, we relate optimism and pessimism to multi-criteria decision making

behavior and establish appropriate assessment tools for measuring them in a decision analysis. Optimists construe their lives and future states of the world positively, whereas pessimists construe their lives and future states of the world negatively. In addition, optimists expect greater overall utility or favorable outcomes, but pessimists expect less overall utility or unfavorable outcomes. The above rationale coincides with several of Atanassov’s operators, as shown in (3)-(8). By extension we develop new point operators denoted by

ijijJ , ,

*, ijij

J , ijijH , , *

, ijijH , ijijP , and ijijQ , for

each AAi , Xxj and ]1,0[, ijij . These estimations of A-IFSs are known as

optimistic or pessimistic point operators. Optimistic point operators

Definition 3.1. For each AAi and Xxj , taking ]1,0[, ijij , we define

optimistic point operators ijij

J , , *

, ijijJ , ijijP , : IFS(X)IFS(X) as follows for

ijX IFS(X):

XxxXJ jijijijijijjijijij ,, )(, ; (10) XxxXJ jijijijijijijijjijijij ),1(, )(* , ; (11)


XxxXP jijijijijjijijij ),min(),,max(, )(, for 1 ijij . (12)

Using ijij

J , , *

, ijijJ and ijijP , on ijX separately enhances the evaluation of

the alternative Ai with respect to criterion xj on the fuzzy concept “excellence” because of the increasing degree of membership. Therefore,

ijijJ , ,

*, ijij

J and ijijP , can

reflect the fact that optimistic decision makers construe the decision situation positively and assume favorable outcomes. From Definition 3.1, we know that the membership degree of )(, ijXJ ijij is the sum of the membership part of ijX and a part of the

intuitionistic index. Later, we will prove that the repeated usage of ijij

J , will lead to

the highest membership degree of one (ultra-optimistic) if the time period of redistributing the intuitionistic index is sufficiently large. The operator * , ijijJ also

demonstrates a similar phenomenon. In contrast, the deformation of optimistic estimation by

ijijP , has the limitation of ),max( ijij . Namely, the operator ijijP ,

represents an optimistic estimation with restrictions. The proofs of Theorems 3.1 and 3.2 were given in the author’s previous research (Chen, 2010).

The optimistic point operator ijij

J , transforms the A-IFS ijX into another

A-IFS )(, ijXJ ijij with intuitionistic index:

ijijijijjXJ xijijij )1()1()()(, . (13)

Theorem 3.1. Let ijX IFS(X), AAi , Xx j , and ]1,0[, ijij . Let be a

positive integer, and let )(, ijXJ ijij

= ))((1,, ijXJJ ijijijij , where ijij XXJ ijij )(

0, .

(i) ; )1(])1(1[)1()(1

0

1)(,

k

kij

kijijijijijijjXJ

xijijij

(14)

(ii)

1

0

1)(

)1(])1(1[)1()1()(,

k

kij

kijijijijijijijijjXJ

xijijij

. (15)

For the optimistic point operator * , ijijJ defined in (11), the intuitionistic index of

)(* , ijXJ ijij is:

).1()1()()(* , ijijijijjXJ

xijijij

(16)


positive integer, and let )(*, , ijXJ ijij = ))((

1*,,

*, ijXJJ ijijijij

, where ijij XXJ ijij )(

0*,, .


(i) ; )1(])1(1[)1()(1

0

1)(*, ,

k

kij

kijijijijijijijjXJ xijijij

(17)

(ii)

. )1( ])1(1[)1()1()(1

0

1)(*, ,

k

kij

kijijijijijijijijijjXJ xijijij (18)

For the optimistic point operator ijij

P , defined in (12), the intuitionistic index of

)(, ijXP ijij is:

),min(),max(1)()(, ijijijijjXP xijijij . (19)

Theorem 3.3. Let ijX IFS(X), AAi , Xx j , ]1,0[, ijij and

1 ijij . Let be a positive integer, and let )(, ijXP ijij

= ))((1

,, ijXPP ijijijij , where

ijij XXP ijij )(0

, .

(i) ),max()()(, ijijjXP

xijijij

; (20)

(ii) ),min()()(, ijijjXP xijijij

; (21)

Pessimistic point operators Definition 3.2. For each AAi and Xx j , taking ]1,0[, ijij , we define

the pessimistic point operators ijij

H , , *

, ijijH , ijijQ , : IFS(X)IFS(X) as follows for

ijX IFS(X):

XxxXH jijijijijijjijijij ,, )(, ; (22) XxxXH jijijijijijijijjijijij )1(,, )(* , ; (23) XxxXQ jijijijijjijijij ),max(),,min(, )(, for 1 ijij . (24)

Applying ijij

H , , *

, ijijH and ijijQ , lowers the intensity of the fuzzy concept

“excellence” by virtue of the decreasing degree of membership, which fulfills the condition that pessimistic decision makers construe the decision situation negatively and expect unfavorable outcomes. Because the separate membership degrees of

)(, ijXH ijij and )(*

, ijXH ijij equal a part of the membership degree of ijX from

Definition 3.2, we obtain the lowest membership degree of zero (ultra-pessimistic) by using a sufficient amount of the two operators. The point of emphasis is that the operator

ijijQ , represents pessimistic estimations with restrictions, and it has limited

optimism on ),min( ijij .


The pessimistic point operator ijij

H , , defined in (22), transforms the A-IFS ijX

into another A-IFS )(, ijXH ijij with the intuitionistic index:

.)1()1()()(, ijijijijjXH xijijij (25)


positive integer, and let )(, ijXH ijij

= ))((1,, ijXHH ijijijij , where ijij XXH ijij )(

0, .

(i) ; )1(])1(1[)1()(1

0

1)(,

k

kij

kijijijijijijjXH xijijij

(26)

(ii)

1

0

1)(

)1(])1(1[)1()1()(,

k

kij

kijijijijijijijijjXH

xijijij

. (27)

For the pessimistic point operator * , ijijH defined in (23), the intuitionistic index

of )(* , ijXH ijij is:

).1()1()()(* , ijijijijjXH

xijijij

(28)


positive integer, and let )(*, , ijXH ijij = ))((

1*,,

*, ijXHH ijijijij

, where ijij XXH ijij )(

0*,, .

(i) ; )1(])1(1[)1()(1

0

1)(*, ,

k

kij

kijijijijijijijjXH xijijij

(29)

(ii)

. )1( ])1(1[)1()1()(1

0

1)(*, ,

k

kij

kijijijijijijijijijjXH xijijij (30)

For the pessimistic point operator ijij

Q , defined in (24), the intuitionistic index

of )(, ijXQ ijij is:

),max(),min(1)()(, ijijijijjXQ xijijij . (31)

Theorem 3.6. Let ijX IFS(X), AAi , Xx j , ]1,0[, ijij and

1 ijij . Let be a positive integer, and let )(, ijXQ ijij

= ))((1,, ijXQQ ijijijij , where

ijij XXQ ijij )(0

, .

(i) ),min()()(, ijijjXQ

xijijij

; (32)

(ii) ),max()()(, ijijjXQ

xijijij

; (33)


OPTIMISTIC-PESSIMISTIC DECISIONS WITH DISSONANCE REDUCTION

Optimistic and pessimistic score functions The evaluation value of alternative Ai with respect to criterion xj can be

determined by the score function S, which has been conceptualized and applied to multi-criteria decision making problems by Chen and Tan (1994), Hong and Choi (2000), and Liu and Wang (2007). The definition of the score function equals the membership degree minus the non-membership degree, which is also called the core or degree of support (Li, Olson, & Qin, 2007). By applying

ijijJ , ,

*, ijij

J and ijijP , ,

Definitions 4.1-4.3 present optimistic score functions. Definitions 4.4-4.6 are suitable for pessimistic cases on the basis of

ijijH , ,

*, ijij

H and ijijQ , .

Definition 4.1. Let ijX IFS(X) and ]1,0[, ijij for each AAi and

Xx j . Let be a positive integer. The optimistic score function )(, ijJ XS ijij

based

on the ijij

J , point operator is defined as the degree of support of )(, ijXJ ijij

:

ijijk

kij

kijijijijijijijJ XS ijij

1

0

1)1(])1(1[)1()(,

, (34)

where ]1 ,1[)(,

ijJ XS ijij

and 1)(

, ijJ XS ijij .


Xx j . Let be a positive integer. The optimistic score function )(*,

ijJ XS ijij

based

on the * , ijijJ point operator is measured as follows:

ijijk

kij

kijijijijijijijijJ XS ijij

1

0

1)1(])1(1[)1()(*,

, (35)

where ]1 ,1[)(*,

ijJ XS ijij

and 1)(*

, ijJ XS ijij

.

Definition 4.3. Let ijX IFS(X), ]1,0[, ijij and 1 ijij for each

AAi and Xx j . Let be a positive integer. The optimistic score function

)(, ijP

XSijij

based on the ijij

P , point operator is measured as follows:

},3,2,1{for ),min(),max()(,

ijijijijijP

XSijij

, (36)

where ]1 ,1[)(,

ijP XS ijij

.



Xx j . Let be a positive integer. The pessimistic score function )(, ijH XS ijij

based

on the ijij

H , point operator is measured as follows:

1

0

1)1(])1(1[)1()(,

k

kij

kijijijijijijijijijH XS ijij , (37)

where ]1 ,1[)(,

ijH XS ijij

and 1)(

, ijH XS ijij

.


Xx j . Let be a positive integer. The pessimistic score function )(*,

ijH XS ijij

based

on the * , ijijH point operator is measured as follows:

1

0

1)1(])1(1[)1()(*,

k

kij

kijijijijijijijijijijH XS ijij

, (38)

where ]1 ,1[)(*,

ijH XS ijij

and 1)(*

, ijH XS ijij

.

Definition 4.6. Let ijX IFS(X), ]1,0[, ijij and 1 ijij for each

AAi and Xx j . Let be a positive integer. The pessimistic score function

)(, ijQ

XSijij

based on the ijij

Q , point operator is measured as follows:

},3,2,1{for ),max(),min()(,

ijijijijijQ

XSijij

, (39)

where ]1 ,1[)(,

ijQ XS ijij

.

Recall that nwww ,,, 21 are the weights of the criteria nxxx ,,, 21 , respectively,

where ]1,0[,,, 21 nwww and 121 nwww . Based on the simple additive

weighted method, we can obtain a total score for each alternative simply by multiplying the optimistic or pessimistic score function for each criterion by the importance weight that is assigned to the criterion and then summing these products over all of the criteria.

Let QiHi

Hi

Pi

Ji

Ji zzzzzz ,,,,,

** be the total scores of alternative Ai using the point operators

ijijJ , ,

*, ijij

J , ijijP , , ijijH , , *

, ijijH and ijijQ , , respectively. These are defined as

follows:

)()()(,2,21,1 2211 inJniJiJ

Ji XSwXSwXSwz ininiiii

; (40)

)()()( *,

*2,2

*1,1

2211*

inJniJiJJi XSwXSwXSwz

ininiiii

; (41)

)()()(,2,21,1 2211 inPniPiP

Pi XSwXSwXSwz ininiiii

; (42)


)()()(,2,21,1 2211 inHniHiH

Hi XSwXSwXSwz ininiiii

; (43)

)()()( *,

*2,2

*1,1

2211*

inHniHiHHi XSwXSwXSwz

ininiiii

; (44)

)()()(,2,21,1 2211 inQniQiQ

Qi XSwXSwXSwz ininiiii

. (45)

We denote these total scores as the suitability functions to determine the degrees to which an alternative satisfies the decision maker’s requirements. After comparing the total scores for all alternatives, the alternative with the highest score is the one prescribed to the decision maker. However, information regarding multiple criteria corresponding to decision importance may be incomplete in real applications, and, thus, we develop an optimization model for multi-criteria decision making in an intuitionistic fuzzy environment with criteria being explicitly taken into account.

Optimization model with weighted score functions

Based on the simple additive weighted method, the suitability function zi that determines the degree to which the alternative Ai satisfies the decision maker’s requirements can be measured by an optimization model with weighted score functions. For each alternative AAi , we compute the optimal value of the suitability function zi

using the following programming models:

1

),,,2,1( s.t.

)(max

1

ul

1,

n

jj

jjj

n

jjijJ

Ji

w

njwww

wXSzijij

or

1

),,,2,1( s.t.

)(max

1

ul

1

**

,

n

jj

jjj

n

jjijJ

Ji

w

njwww

wXSzijij

(46)

for each i=1,2,…,m. (ii) For the optimistic condition with restrictions:

1

),,,2,1( s.t.

)(max

1

ul

1,

n

jj

jjj

n

jjijP

Pi

w

njwww

wXSzijij

(47)

for each i=1,2,…,m.


(iii) For the pessimistic condition:

1

),,,2,1( s.t.

)(max

1

ul

1,

n

jj

jjj

n

jjijH

Hi

w

njwww

wXSzijij

or

1

),,,2,1( s.t.

)(max

1

ul

1

**

,

n

jj

jjj

n

jjijH

Hi

w

njwww

wXSzijij

(48)

for each i=1,2,…,m. (iv) For the pessimistic condition with restrictions:

1

),,,2,1( s.t.

)(max

1

ul

1,

n

jj

jjj

n

jjijQ

Qi

w

njwww

wXSzijij

(49)

for each i=1,2,…,m.

Take ijij

J , as an example to explain the solving process of the programming

model. Because there are m alternatives in set A, we must solve a total of m linear programming models using the Simplex method. Although we can obtain the optimal weight vector for each alternative, the optimal solutions may be generally different, and, thus, the corresponding optimal values of the suitability functions for all m alternatives cannot be compared. Given that the decision maker cannot easily or obviously judge the preference relations among all non-inferior alternatives, it is reasonable to assume that all non-inferior alternatives have equal importance. Therefore, by assigning an equal weight 1/ m, we aggregate m linear programming models into the following model:

.1

),,,2,1( s.t.

)(max

1

ul

1 1,

n

jj

jjj

m

i

n

jjijJ

J

w

njwww

m

wXSz

ijij

(50)

In a similar manner, we can combine m linear programming models into a single programming model with regard to * , ijijJ , ijijP , , ijijH , ,

*, ijij

H and ijijQ , ,

respectively.


Optimization model with dissonance reduction Under the dissonance theory, the existence of dissonance gives rise to pressures to

reduce dissonance and to avoid any increase in dissonance. When dissonance exists, an individual will attempt to reduce it by such methods as playing down or avoiding the importance of the negative aspects of the decision and enhancing the positive elements (Bell, 1967; Kimura & HShinoki,H 2007; Maertz, HHassan, & HMagnusson, 2008). This behavior is called dissonance reduction (Harmon- Jones et al., 2008). There are several possible ways to reduce dissonance, such as attitude change, opinion change, a recall of consonant information, the avoidance of dissonant information, perceptual distortion, and behavioral change (Sweeney, Hausknecht, & Soutar, 2000; Soutar and Sweeney, 2003; Harmon-Jones, Gerdjikov, & Harmon-Jones, 2008).

Within decisional contexts, dissonance theory predicts that when the level of difficulty of a decision is greater, the post-decision dissonance is also greater (Festinger, 1964; Menasco & Hawkins, 1978). Aroused dissonance is presumed to be a function of predecision conflict, which is in turn a result of the difficulty of the decision. Level of difficulty is a positive function of the number of alternatives that are considered and of the attractiveness of the various alternatives. Therefore, conflict is the result of a mutually exclusive choice process. Festinger (1964) considered the magnitude of post-decision dissonance as a positive function of the importance of the decision and of the relative attractiveness of the non-chosen alternatives and as a negative function of the number of the common characteristics among the alternatives.

All these findings make it clear that an effective decision making method must solve the problem of decisional dissonance. In this study, we construct an optimization model with the two objectives being maximal suitability degree and dissonance reduction. The latter objective is to magnify the difference between alternatives to reduce the relative attractiveness of the unselected alternatives. In addition, the importance of this objective increases with the number of alternatives and the importance (or degree of involvement) of the decisions. Conversely, dissonance may be aroused after being exposed to incomplete or unknown information. In the present paper, the usage of optimistic or pessimistic point operators will lower the degree of hesitation (or uncertainty) and reduce decisional dissonance.

For the suitability function defined by ijij

J , , the sum of the Hamming distances

between alternative Ai and the other ( 1m ) alternatives is equal to

m

i

n

j jijJwXS

ijij1 11 ,)(

n

j jjiJwXS

jiji1)(

11,1

. To reduce decisional dissonance,

we must maximize the total distances for m alternatives, that is,


m

i

m

i

n

j

n

j jjiJjijJwXSwXS

jijiijij1 1 1 11 11,1,)()(

. Let QHHPJJ yyyyyy ,,,,, **

be the sums of pairwise differences between suitability functions by using the point operators

ijijJ , ,

*, ijij

J , ijijP , , ijijH , , *

, ijijH and ijijQ , , respectively. These are

defined as follows:

m

i

m

i

n

jjjiJijJ

J wXSXSyjijiijij

1 1 1111,1,

)()(

; (51)

m

i

m

i

n

jjjiJijJ

J wXSXSyjijiijij1 1 11

1*1,1

*,

*

)()(

; (52)

m

i

m

i

n

jjjiPijP

P wXSXSyjijiijij

1 1 1111,1,

)()(

; (53)

m

i

m

i

n

jjjiHijH

H wXSXSyjijiijij

1 1 1111,1,

)()(

; (54)

m

i

m

i

n

jjjiHijH

H wXSXSyjijiijij1 1 11

1*1,1

*,

*

)()(

; (55)

m

i

m

i

n

jjjiQijQ

Q wXSXSyjijiijij

1 1 1111,1,

)()(

. (56)

By assigning weights to the two objective functions of z and y, we combine them

into a single-objective function; that is, we transform the two-objective problem into a single optimization problem according to the decision maker’s preference structure. Let be a coefficient reflecting the decision maker’s preference concerning the importance of dissonance reduction when compared to the objective of maximal suitability degree where ]1,0[ . Considering the relative weight or worth of each objective, we modify

the programming models as follows: (i) For the optimistic condition:

;1

),,,2,1( s.t.

)()()(

)1(max

1

ul

1 1 1

1 1

1

11,1,

,

n

jj

jjj

m

i

m

i

n

jjjiJijJ

m

i

n

jjijJ

w

njwww

wXSXSm

wXS

jijiijij

ijij

(57)

or


.1

),,,2,1( s.t.

)()()(

)1(max

1

ul

1 1 1

1 1

1

1*1,1

*,

*,

n

jj

jjj

m

i

m

i

n

jjjiJijJ

m

i

n

jjijJ

w

njwww

wXSXSm

wXS

jijiijij

ijij

(58)

(ii) For the optimistic condition with restrictions:

.1

),,,2,1( s.t.

)()()(

)1(max

1

ul

1 1 1

1 1

1

11,1,

,

n

jj

jjj

m

i

m

i

n

jjjiPijP

m

i

n

jjijP

w

njwww

wXSXSm

wXS

jijiijij

ijij

(59)

(iii) For the pessimistic condition:

;1

),,,2,1( s.t.

)()()(

)1(max

1

ul

1 1 1

1 1

1

11,1,

,

n

jj

jjj

m

i

m

i

n

jjjiHijH

m

i

n

jjijH

w

njwww

wXSXSm

wXS

jijiijij

ijij

(60)

or

.1

),,,2,1( s.t.

)()()(

)1(max

1

ul

1 1 1

1 1

1

1*

1,1*

,

*,

n

jj

jjj

m

i

m

i

n

jjjiHijH

m

i

n

jjijH

w

njwww

wXSXSm

wXS

jijiijij

ijij

(61)


(iv) For the pessimistic condition with restrictions:

.1

),,,2,1( s.t.

)()()(

)1(max

1

ul

1 1 1

1 1

1

11,1,

,

n

jj

jjj

m

i

m

i

n

jjjiQijQ

m

i

n

jjijQ

w

njwww

wXSXSm

wXS

jijiijij

ijij

(62)

The parameter essentially controls the relative importance of the two objectives of dissonance reduction and aggregated suitability functions. For example, a large -value increases the importance of reducing dissonance but impairs the reachable levels of the suitability functions. A small -value has the opposite effect. It is noteworthy that can be a function of the number of alternatives and the degree of involvement. Decisional dissonance increases with the number of rejected alternatives (Festinger, 1964; Mittelstaedt, 1969) and with the relevance of the decisions (Menasco & Hawkins, 1978; Milliman & Decker, 1990). Therefore, the parameter relates to the number of alternatives and decision relevance, and the latter can be defined by the degree of involvement. The definition of involvement used for the purpose of decision relevance is the decision maker’s perceived relevance of the decision based on his/her inherent needs, values, and interests.

If a dynamic specification of the parameter is not desired, the present method also allows for a static parameter specification for simplicity. However, we suggest that different -values should be chosen separately for optimistic and pessimistic conditions. That is, the proposed programming model must be performed by assigning a fixed -value under optimistic and pessimistic conditions, respectively. The specification of the parameter can mostly allow decision makers to reflect their optimistic or pessimistic attitudes. Optimism and self-enhancing deception are often positively correlated, and the latter can help to maintain the former (Norem, 2002). For instance, optimists often use retroactive pessimism to diminish the sting of failure (Sanna and Chang, 2003). Because optimists always adopt active coping strategies (Iwanaga, Yokoyama, & Seiwa, 2004), and post hoc restructuring of the situation is done when the decision outcome is known, they experience less cognitive dissonance than pessimists do. Therefore, a reasonable specification mechanism of the parameter is suggested: ]5.0,0[ under optimistic conditions and ]1,5.0[ under pessimistic

conditions. The optimal solution Tnwww ),,,( 21 w can be obtained by solving one of

(57)-(62). We emphasize that the suitability functions of each alternative serve as the


basis for implementing the ranking procedure. Using ijij

J , as an example, the

optimal value of the suitability functions for the alternative AAi can be computed

as follows:

n

jjijJ

Ji wXSz

ijij1

)(,

(63)

for each i=1,2,…,m. When Jiz is higher, the alternative Ai is better. Therefore,

the best alternative AAi * can be generated such that:

. max* Jiiii zAAA (64) Moreover, the m alternatives can be ranked according to the decreasing order of

Jiz 's for all AAi .

ILLUSTRATION AND DISCUSSIONS

Illustrative example

For an optimistic decision maker, suppose there are five alternatives },,,{ 521 AAAA , which are evaluated using three criteria },,{ 321 xxxX . Assume

that the degrees ij of membership and the degrees ij of non-membership for the alternative AAi with respect to the criterion Xxj to the fuzzy concept

“excellence” are given below:

)37.0 ,14.0()36.0 ,31.0()13.0 ,59.0()03.0 ,36.0()66.0 ,15.0()32.0 ,32.0()42.0 ,33.0()24.0 ,01.0()08.0 ,81.0()29.0 ,48.0()22.0 ,33.0()16.0 ,03.0()24.0 ,51.0()40.0 ,43.0()64.0 ,21.0(

5

4

3

2

1

321

AAAAA

D

xxx

.

The degrees j of membership and the degrees j of non-membership for the three criteria Xx j to the fuzzy concept “importance” are assumed below:

)79.0,01.0()43.0,57.0()23.0,07.0()),((

31

321

jj

xxx

.

The criterion weights also lie in the closed intervals, respectively. Namely,

]21.0,01.0[]57.0,57.0[]77.0,07.0[]),([

31ul

321

jj wwxxx

.


It should be noted that 165.03

1

l j

jw and 155.13

1

u j

jw .

Consider the optimistic point operator ijij

J , and let ijij and ijij in

(34) for each AAi and Xx j . We obtain the optimistic score functions of ijX

(i=1,2,,5; j=1,2,3) as shown in Table 1 where =1,2,,7. TABLE 1 The results of the optimistic score function )(

, ijJXS

ijij

in the numerical example

X11 X12 X13 X21 X22 X23 X31 X32 X33 X41 X42 X43 X51 X52 X53=1 -0.1681 0.3431 0.5799 0.0287 0.4301 0.5063 0.8927 -0.0401 0.2361 0.3328 -0.2571 0.5787 0.7383 0.2827 0.0717=2 0.0526 0.5840 0.7792 0.0778 0.6240 0.7223 0.9751 0.0129 0.4741 0.5504 -0.0511 0.7306 0.8875 0.5077 0.2496=3 0.2358 0.7462 0.8882 0.1087 0.7493 0.8495 0.9949 0.0330 0.6417 0.6956 0.1181 0.8276 0.9532 0.6612 0.3724=4 0.3863 0.8487 0.9444 0.1359 0.8323 0.9200 0.9990 0.0452 0.7575 0.7934 0.2579 0.8897 0.9807 0.7666 0.4668=5 0.5087 0.9111 0.9725 0.1619 0.8877 0.9579 0.9998 0.0553 0.8364 0.8597 0.3743 0.9294 0.9921 0.8391 0.5439=6 0.6077 0.9483 0.9865 0.1871 0.9248 0.9779 1.0000 0.0649 0.8900 0.9046 0.4714 0.9548 0.9968 0.8890 0.6086=7 0.6875 0.9701 0.9934 0.2115 0.9496 0.9885 1.0000 0.0743 0.9261 0.9351 0.5529 0.9711 0.9987 0.9234 0.6638

From Table 1, we have the suitability functions Jiz of each alternative by using

(48), and we obtain the objective Jz in (50) as follows:

=1: 5)9727.17587.08244.1( 321 wwwzJ ;

=2: 5)9558.26775.15434.2( 321 wwwzJ ;

=3: 5)5794.33078.29882.2( 321 wwwzJ ;

=4: 5)9784.37507.22953.3( 321 wwwzJ ;

=5: 5)2401.40675.35222.3( 321 wwwzJ ;

=6: 5)4178.42984.36962.3( 321 wwwzJ ;

=7: 5)5429.44703.38328.3( 321 wwwzJ .

Let =0.3. Given =4, we obtain the following linear programming model:


321

321321

321321

321321

321321

321321

0.42290.50870.1873

0.29070.72140.01830.13220.21270.2056

0.45320.06570.84480.03030.57440.6575

0.16250.78710.86310.47760.08210.5944

0.05470.59080.40710.18690.80350.6127

0.02440.01640.25043.05

9784.37507.22953.37.0

max

www

wwwwww

wwwwww

wwwwww

wwwwww

wwwwww

.1,21.001.0,57.057.0,77.007.0

s.t.

321

3

2

1

wwwwww

The optimal solution of the above linear programming is T)21.0,57.0,22.0(w .

The optimal objective value can then be computed, and J

=1.0183. In addition, by applying (63), we can then obtain

Jz1 =0.7671,

Jz 2 =0.6975,

Jz3 =0.4046,

Jz 4 =0.5084,

Jz 5 =0.7507.

The optimal ranking order of the five alternatives is given by

1 5 2 4 3A A A A A , and A1 is the best choice. The detailed results for =1,2,,7

are presented in Table 2. TABLE 2 The results by solving programming models in the numerical example

1w 2w 3w J J

z1 J

z 2 J

z3 J

z 4 J

z 5 Ranking order

=1 0.42 0.57 0.01 0.8723 0.1308 0.2623 0.3544 -0.0010 0.4719 A5 A3 A2 A1 A4=2 0.42 0.57 0.01 0.8692 0.3628 0.3956 0.4216 0.2093 0.6646 A5 A3 A2 A1 A4=3 0.42 0.57 0.01 0.9148 0.5333 0.4812 0.4431 0.3677 0.7810 A5 A1 A2 A3 A4=4 0.22 0.57 0.21 1.0183 0.7671 0.6975 0.4046 0.5084 0.7507 A1 A5 A2 A4 A3=5 0.22 0.57 0.21 1.0958 0.8355 0.7428 0.4271 0.5977 0.8108 A1 A5 A2 A4 A3=6 0.42 0.57 0.01 1.1595 0.8056 0.6155 0.4659 0.6582 0.9315 A5 A1 A4 A2 A3=7 0.42 0.57 0.01 1.2126 0.8516 0.6400 0.4716 0.7176 0.9524 A5 A1 A4 A2 A3

Selecting the best alternative obtained by Jiz 's may be risky because this

conclusion is partly based on uncertain or indeterminate information. In the same way


as Liu and Wang (2007), we denote the best alternative yielded by optimization models

with )(, ijJ

XSijij

as the grade- risky choice, and so do )(*, ijJ

XSijij

, )(

, ijPXS

ijij

,

)(, ijH

XSijij

, )(*, ijH

XSijij

and )(

, ijQXS

ijij

, respectively. From Table 2 we know that A5

is the grade-1, grade-2, grade-3, grade-6 and grade-7 risky choice. A1 is the grade-4 and grade-5 risky choice.

Discussions

The specification of parameters ij and ij depend on the optimistic or pessimistic nature of the decision maker. The optimism or pessimism the decision maker can be assessed using the Life Orientation Test (LOT) by Scheier and Carver (1985), the Revised Life Orientation Test (LOT-R) by Scheier et al. (1994), or the Extended Life Orientation Test (ELOT) by Chang et al. (1997). The three scales have strong predictive and discriminative validity (Conway, Magai, Springer, & Jones, 2008; Nicholls, Polman, Levy, & Backhouse, 2008). LOT-R is a 10-item scale that includes three positive items and three negative items. Four filler items are not used in the scoring. Negative items are reverse scored and summed with positive items. We can administer the LOT-R to decision makers at the beginning of the decision making processes and differentiate them into different types, i.e., optimists, neutralists and pessimists, on the basis of their LOT-R scores. The values of parameters ij and ij can then be set according to the normalized LOT-R score.

The parameter can reform the degree of hesitancy and a new A-IFS will be generated in terms of times reformation. When a larger positive is used, the choice made produces a higher risk. The grade- risky choice implies that some type of dissonance will arise to some degree. Therefore, a small value is more appropriate for employing point operators. Because the appropriateness of intuitionistic fuzzy optimistic/pessimistic point operators is generally context-dependent, we suggest that the empirical studies should be conducted for parameter settings in the context of various applications.

Faced with the necessity of choosing among non-inferior alternatives, the decision-maker evaluates and provides available information on the alternatives and eventually establishes a preference order. When a person makes a decision based on available alternatives, each of which had certain advantages and disadvantages over the others, varying levels of post-decision dissonance result (Milliman & Decker, 1990). Because the decision-maker might have doubts and anxieties about the choices, the proposed method can be used to differentiate the relative attractiveness of the alternatives and to reduce post-decision dissonance further.


However, exact data may be difficult to determine precisely because human judgment is often vague. Sometimes, the available information is not sufficient for an exact definition of a degree of membership for certain elements. There may be some degree of hesitation between membership and non-membership. For example, many economic phenomena display complex characteristics, such as financial intermediations, security prices in the presence of short-sale constraints, and reactions to stock returns. Consider the decision of a firm to designate a leader with the goal being to maximize the firm’s value. The performance of the firm depends on the decisions of its leader, which in turn depends on that leader’s evaluations and subjective judgments of the industry and the competitive environment. Corporate managers must be able to perceptively diagnose a company’s external and internal environments to succeed in crafting a strategy that is an excellent fit with the company’s situation, builds a competitive advantage, and boosts company performance. Corporate financial and accounting decisions require the use of more precise and accurate judgment data instead of crisp data or ordinary fuzzy data. The analytical approach described in this study can not only deal with complicated evaluative data, but it can also assess the hesitation degrees on outcome expectancies under optimistic/pessimistic viewpoints to aid in corporate financial and accounting decision-making.

Additionally, in the field of socio-psychology, consumer behavior has become an integral part of strategic market planning. The belief that ethics and social responsibility should also be integral components of every marketing decision is embodied in contemporary marketing concepts. The societal marketing concept calls on marketers to fulfill the needs of their target markets in ways that improve society as a whole. Thus, analytical data must synthesize all of the variables involved in the consumer decision-making process and include the important topics of social responsibility and marketing ethics because they impact consumer behavior. In the process of making strategic marketing decisions, marketers must be able to handle the complicated nature of the analytical data, which is subject to varying psychological and sociocultural influences on a consumer’s buying behavior and the underlying interrelated influences of social responsibility and marketing ethics. The proposed method can be used in this real-world case that displays complex decision-making scenarios.

CONCLUSIONS

A large amount effort has been focused on Atanassov’s intuitionistic fuzzy multi-criteria decision making analysis, but little attention had been given to the influence of dispositional optimism and pessimism on subjective evaluations. In general, optimists are often confident that their decision goal is attainable and anticipate


desirable evaluation values; therefore, they may overestimate the decision outcomes. In contrast, pessimists are often skeptical of the level of attainment, and they are more likely to underestimate the decision outcomes. Viewed in this light, this study incorporated the influences of optimism and pessimism into decision analysis. This paper presented an approach for including optimism and pessimism in decision making problems under an intuitionistic fuzzy environment. We utilized optimistic and pessimistic point operators to capture the effects caused by optimism and pessimism. In addition, the suitability function that measures the overall evaluations of alternatives is composed of weighted score functions.

According to Festinger’s theoretical foundation, the existence of dissonance, which is psychologically uncomfortable, motivates the decision maker to try to reduce decisional dissonance and achieve consonance. Given that decision making almost always provokes dissonance, we provided an efficient way to handle multi-criteria decision making problems with dissonance reduction. Considering two objectives of maximal suitability function and maximal discrimination of alternative attractiveness, we constructed optimization models for coping with poorly known membership grades to determine optimal criterion weights and the corresponding degree of suitability. The use of our proposed method can reduce the relative attractiveness of unselected alternatives and lessen the degree of dissonance experienced by the decision maker. Because of their equivalent mathematical structure, the results proposed in this paper can be used analogously for IVFSs.


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11B


Biographical Sketch

Ting-Yu Chen is currently a Professor of the Graduate Institute of Business and Management and the Department of Industrial and Business Management (joint appointment) 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 analysis, fuzzy set theory and fuzzy decision analysis, consumer decision making, and consumer marketing applications. She has published over 100 papers in peer-reviewed journals and 100 papers in conference proceedings. She has received several awards, including the Distinguished Research Award from the Chinese Institute of Transportation, the Distinguished Research Award from the Chinese Management Association, the Distinguished Young Scholar Award from Academia Sinica, the Faculty Outstanding Research Performance Award from Chang Gung University (twice), the Distinguished Research Award from Chung Yuan Management Review, the Outstanding Rewards of Specialized Research Grants from the National Science Council of Taiwan, the Outstanding Faculty Award of Student Counseling from Chang Gung University (twice), and the Rewards of Developing Innovative Courses from Chang Gung University. Dr. Chen is an Honorary Member of the Phi Tau Phi Scholastic Honor Society of Taiwan.

Jih-Chang Wang received the B.S. degree in Computer Engineering, the(Color or M.S. degree in Management Science, and the Ph.D. degree in Traffic and gray) Transportation from National Chiao Tung University in Taiwan. He was a research fellow in the Energy and Environmental Research Group at National Chiao Tung University from 1997 to 1998, an Assistant Professor of the Department of Information Management at I-Shou University in Taiwan from 1998 to 1999, and an Assistant Professor of the Department of Information Management at Chang Gung University in Taiwan from 1999 to the present. His current research interests include soft computing, network modeling and analysis, multiple criteria decision making, and electronic commerce.


降低樂/悲觀決策者認知失調之直覺模糊決策分析

陳亭羽長庚大學企業管理研究所暨工商管理學系

王日昌長庚大學資訊管理學系

中文摘要

Atanassov 所發展之直覺模糊集合理論，已成功地應用在多準則分析的領域。然而，

樂觀與悲觀在直覺模糊決策中所扮演的角色鮮少探討，特別是對伴隨決策過程中

之主觀判斷與認知失調的影響。在 Atanassov 直覺模糊決策環境之下，本研究提出

減少認知失調與考量樂觀和悲觀之多準則決策分析方法。我們利用樂觀及悲觀運

算子，分別來衡量樂觀主義與悲觀主義的影響，並進一步透過加權計分函數來構

建適合度模型。考慮到二個目標：最大化適合度及認知失調降低程度，本研究建

構出幾個最佳化模型，以求得評估準則之最佳權重，並獲取與適合度相對應的方

案排序。我們期望此方法能有效處理決策者樂觀、悲觀特質在認知失調與決策分

析的影響。

關鍵詞：直覺模糊集合、多準則分析、樂觀、悲觀、認知失調、最佳化模型、決

策分析

通訊地址：陳亭羽，長庚大學企業管理研究所暨工商管理學系教授，桃園縣龜山

鄉 333 文化一路 259 號。聯絡電話：886-3-2118800 分機 5678。

E-mail address: [email protected]

intuitionistic fuzzy decision analysis with dissonance...

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