The Study Of The Consistence Of The Fuzzy Matrices

Fuzzifying is one of the most important problems in fuzzy mathematics, which contains two processes named fuzzifying and defuzzifying in the fuzzy sets theory and its applications. The connection between these two processes has always been the most important to study, especially the study of the consistence.This thesis is the continued study of unified fuzzifying method, and the purpose of this paper is to study the consistence of some fuzzy matrices. The followings are our main results:·We present the definition of generalized product of fuzzy matrices and discuss the operational preservation of fuzzy matrices and Boolean matrices in an extensive range. We obtain a consistent principle of fuzzy matrices and Boolean matrices. This provides a novel viewpoint and methodology for the research into fuzzy matrices.·We give the thoery of consistence of classical matrices, which sovles the problem of the consistence of the classical matrices, Which gives us a more complete viewpoint of the consistence og the matrices.·We give the definition of finite production, and discuss the consistance of the fuzzy sets and the membership function of their coorespoding cut matrices in general cases, and obtain a general fuzzy method, which enrichs the fuzzifying theory and makes the study of fuzzifying more wide, also we found its application in the mine problem and fuzzy programming.·Furthermore, We introduce a new kind of transitive matrix--main diagonal transitive matrix, and we discuss equivalent characterization, its graphic properties and consistent properties of its cut matrices.