Group decision making with intuitionistic fuzzy preference relations

摘要

The capability of intuitionistic fuzzy preference relation in representing imprecise or not reliable judgments which exhibit affirmation, negation and hesitation characteristics make it an attractive research area in group decision making. As traditional fuzzy set theory cannot be used to express all the information in a situation as such, its applications are limited. In Zadeh’s fuzzy set, the membership degree of an element is defined by a real value, and nonmembership is expressed by a complement of membership. This membership definition actually ignores the decision maker’s hesitation in the decision making process. The advantage of Atanassov’s intuitionistic fuzzy sets is the capability of representing inevitably imprecise or not totally reliable judgments and the capability of expressing affirmation, negation and hesitation with the help of membership definitions. The consistency of intuitionistic fuzzy preference relations and the priority weights of experts gathered from these preference relations play an important role in group decision making problems in order to reach an accurate decision result. In this paper, we propose a group decision making process with the usage of intuitionistic fuzzy preference relations where we mainly focus our attention on the investigation of consistency of intuitionistic fuzzy preference relations. Initially, we present two different optimization models to minimize the deviations from additive and multiplicative consistency respectively. The optimal deviation values obtained from the model results enable us to improve the consistency of considered preference relations. Then, based on consistent collective preference relations, two mathematical programming models are established to obtain the priority weights, of which the first is a linear programming model considering additive and the second one is a nonlinear model considering multiplicative consistency. Furthermore, a number of numerical illustrations are presented to observe the validity and practicality of the models. Finally, comparative analyses were performed in order to examine the differences between fuzzy and intuitionistic fuzzy preference relations and the results of the analyses showed that the priority vectors and ranking of the alternatives maintained from fuzzy or intuitionistic fuzzy preference relations change significantly.