Consistency And Related Issues On Uncertain Information

For the decision making problem that a group of experts will choose the best alternative from a set of alternatives. During the process of decision making, experts usually use the preference relations to describe their preference degree over alternatives. Since irrational decision may be made if the degree of consistency is poorer, the researh on the consistency of preference relations in group decision making is of great importance. This paper mainly studies the consistency of reciprocal preference relations, fuzzy preference relations, intuitionistic fuzzy preference relations and linguistic preference relatios, and presents methods to group decision making with intuitionistic fuzzy preference relations and linguistic preference relatios based on the consistency.This thesis first introduces the background and current status of group decision making problems, uncertain information and the consistency of uncertain judgment matrices. Then, reciprocal preference relations, fuzzy preference preference relations and their consistency are introduced, and some common operators to gather information are given. For group decision making under intuitionistic fuzzy information, on the basis of the definition of multiplicative consistency on intuitionistic fuzzy judgment matrices, several equivalent forms of multiplicative consistency are presented. To find a simple way to test the consistency of the intuitionistic fuzzy judgment matrix, its shadow matrix is introduced, by which an intuitionistic fuzzy judgment matrix can be transformed into a reciprocal judgment matrix. Meanwhile, a novel ranking method of the intuitionistic fuzzy judgment matrix is presented via this transformation. For group decision making with linguistic information, the educed matrix of a linguistic judgment matrix is introduced to quantify the linguistic preference relation, and it has shown that the linguistic judgment matrix and its educed matrix are with the same consistency. Therefore, the ranking problem of linguistic preference relations can be dealt with fuzzy preference relations. Since the fact that the best alternative obtained may be different based on additive consistency or multiplicative consistency, the tendency of additive consistency and multiplicative consistency of experts are defined, an optimization model is constructed to solve group decision making problem, and an approach to group decision making based on the two kinds of consistency is developed under the environment of linguistic information. Finally, conclusions and remarks about the current work and the further research are given.