About The Vague Relationship And Vague Study Some Properties Of The Matrix

Fuzzy mathematic is an important branch of mathematic. Because vague set is a generalization and promotion of fuzzy set, vague set can express and deal with fuzzy information more reasonably and more accurately. Vague set have became a powerful tool to process fuzzy information. On the basic of describing vague theory, this paper use methods of the classical theory and fuzzy theory to vague set. We research vague relation and vague matrix deeply, and obtain some important results.The main works are as follows:1The operational natures of the vague relation are studied. We obtain the method of calculating about transitive closure of vague relation.2The algebraic properties of the vague matrix are discussed, we prove that the algebraic structure of all m x n vague matrixes is a quasi-Boolean algebra. Based on the transitive closure calculation of vague matrix, we further study of the transitive closure matrix problem. And we find that the transitive closure matrix of vague matrix have relations with it’s order n and give the conclusion.3We give several new calculating methods about the problem of transitive closure of vague relation by analyzing the connection between the vague matrix and the vague relation. Comparing with some of the existing calculating methods of transitive closure of vague relation, pointing out their shortcomings,, we find the new method is more practical through a example.