Relative Entropy Approach To Uncertain Linguistic Judgement Matrice In Group Decision Making

Judgment matrix, which is called preference relation, is a kind of common decision-making information form. Due to the complexity of decision-making problem, fuzziness and uncertainty of decision environment, experts can provide linguistic variable information, not the accurate number information when they have pair-wise comparison to the many alternatives. Thus, in terms of theoretical and practical value,there is a great significance as to the study of group decision-making method which base on linguistic information under uncertain environment; And it has become one of the hot subjects for researching.This thesis mainly deals with uncertain linguistic preference relation consistence, transformation with interval number judgment matrix and its ranking problems. its summary goes as followsFirstly, the conception of uncertain linguistic judgment matrix is proposed, based on the concept of linguistic judgment matrix. Mutual transformation formulas are given among the linguistic preference relation, reciprocal judgment matrix and fuzzy preference relation. The operational laws are discussed to the uncertain linguistic variables, and mutual transformation formulas are developed between uncertain linguistic judgment matrix and numerical judgment matrix.Secondly, based on OWA operator and COWA operator for aggregating the information, the interval fuzzy preference relation can be obtained by using the transformation formula between them. The condition of satisfying consistency of the interval fuzzy preference relation is also investigated. In the meantime, the experts' weighting method is constructed by using consistency index in the group decision-making.Under the criterion of relative entropy, the optimal model is established by the minimizing the difference between group priority vector and the individual priority vector with uncertain linguistic preference relation. The solution of the model is discussed. The numerical example is illustrated to show that this method has certain effectiveness.Finally, the dissertation is summarized, and uncertain linguistic preference relation research prospects in the future are also given.