On The Theories And Methods Of Uncertainty Fuzzy Judgment Matrix

The fundamental theories and method problems of uncertainty fuzzy judgment matrix are studied.The consistent theories of uncertainty fuzzy number judgment matrix are discussed. The concepts such as general transitivity, satisfied consistency, restricted max-max transitivity, restricted max-min transitivity, restricted weak monotonicity and weak monotonicity are given, in which the relationships between them are studied. It is also demonstrated that the consistent concept given is sound. The method to judge whether an uncertainty fuzzy number judgment matrix is satisfied consistent is proposed, which is illustrated by numerical examples that these methods are effective. Based on the consistent theories, the research on priority method of the uncertainty fuzzy number judgment is given. The eigenvector model of complementary judgment matrix, the least square modal of interval fuzzy number judgment matrix and the least square triangular fuzzy number judgment model are proposed, respectively. It is also given numerical examples to show these methods are feasible and effective.The research on the collective uncertainty fuzzy judgment matrices with incomplete information is given. The priority modals of uncertainty fuzzy judgment matrix with incomplete information are proposed, of which the existence condition of the solution is studied. The relationships between the collective uncertainty fuzzy judgment matrices with incomplete information and the individual judgment matrix with incomplete information are discussed. The relationships between the collective uncertainty fuzzy judgment matrices with incomplete information and the collective judgment matrices with complete information are also discussed.The research on the fundamental theories of two tuple linguistic judgment matrix is given. The consistent theories of two tuple linguistic judgment matrix are discussed. The concepts such as general transitivity, satisfied consistency, restricted max-max transitivity, restricted max-min transitivity, restricted weak monotonicity and weak monotonicity of two tuple linguistic judgment matrix are given, in which the relationships between them are studied. It is also demonstrated that the consistent concept given is sound. The method to judge whether a two tuple linguistic judgment matrix is satisfied consistent is proposed, which is illustrated by numerical example that this method is effective. The relationship between two tuple linguistic judgment matrix and uncertainty fuzzy number judgment matrix is investigated. Using the transformation relations between the two tuple linguistic and uncertainty fuzzy number, it is also demonstrated that the two tuple linguistic judgment matrix which is transformed by the uncertainty fuzzy number judgment matrix is still has the completely consistent property, which ensures the transformed judgment information is intact and genuine.The research on collective decision making problem based on different fuzzy preference information is given. With regard to the different fuzzy preferences judgment information given by different experts, based on the relationships between fuzzy number and two-tuple linguistic, using max-min operator and LOWA operator, two kinds of group decision making methods for judgment matrices with different fuzzy preferences respectively are proposed. It is also illustrated by a numerical example that the proposed method is effective.The problem of group decision making based on intuitionistic fuzzy judgment matrix is investigated. Approaches to intuitionistic fuzzy group decision making are proposed from three different preference views. Using the operations of intuitionistic fuzzy numbers, the priority method of intuitionistic fuzzy judgment matrix is given. It is illustrated by a numerical example that the approaches proposed are in accord with the rules of group decision making.