The Theory And Application Of Intuitionistic Fuzzy Homomorphism

In the paper, the theory of intuitionistic fuzzy homomorphism is studied deeply, by which the problems of clustering analysis and multiple attribute decision-making are discussed. The main contents may be summarized as follows:1.The isomorphism and homomorphism of intuitionistic fuzzy sets are defined, and the sufficient and necessary conditions and other properties about isomorphism and homomorphism of intuitionistic fuzzy sets are discussed. And then the essence of intuitionistic fuzzy sets is characterized.2.The isomorphism and homomorphism of intuitionistic fuzzy relations are defined, and the sufficient and necessary conditions about isomorphism and homomorphism of intuitionistic fuzzy relations are given. At last, the operation properties between intuitionistic fuzzy sets are discussed on the conditions of isomorphism and homomorphism.3.The concepts of classified isomorphism about the intuitionistic fuzzy equivalent relation and the intuitionistic fuzzy similarity relation are given, and the conditions of which different intuitionistc fuzzy relations determine the same classification are studied. And then, we prove that an intuitionistic fuzzy similarity relation is classified isomorphic to its transitive closure. Finally, we propose a fuzzy clustering algorithm based on intuitionistic fuzzy similarity relations and an example is illustrated to the consistency of clustering analysis.4. For the situations that attribute values are expressed by intuitionistic fuzzy values and the information on attribute weight is known, the problem of the multiple decision-making is studied: Firstly, the traditional TOPSIS is analyzed, and then a new solution of intuitionistic fuzzy positive-ideal alternatives and negative-ideal alternatives is given by which the uncertainty information is processeddeal by orientation entropy. Finally, the process of intuitionistc fuzzy multiple attribute decision-making is given, and a practical example is illustrated to verify the effectiveness of this method.5.For the situations that attribute values and attribute preference values are expressed by intuitionistic fuzzy values and the information on attribute weight is unknown, the problem of the multiple decision-making is studied: Firstly, the solution of the attribute weight vector in [7] is analyzed, and then we modify it based on the homomorphism of intuitionistic fuzzy sets and give a math model for solving the optimization attribute weight vector. Finally, the process of intuitionistc fuzzy multiple attribute decision-making is introduced, and a practical example is illustrated to verify the effectiveness of this method. 6. For the situations that attribute values and alternatives preference values are expressed by intuitionistic fuzzy values and the information on attribute weight is unknown, the problem of the multiple decision-making is studied: Based on the above two situations, a math model for solving the optimization attribute weight vector is built, and the process of intuitionistc fuzzy multiple attribute decision-making is introduced. At last, a practical example is illustrated to verify the effectiveness of this method.