Research On Properties Of Fuzzy Matrix Recombination And Decomposition Under Max-? Operator

Fuzzy mathematics deals with fuzzy phenomena.When the factors are interlaced,complex,multivariable and nonlinear,the accuracy of the conclusion is different because of the different operators.When max min operator is used,the utilization of membership degree is less than other operators.When the total information is less,it is easy to cause distortion,which makes the meaningful description ability reduce correspondingly.In order to make up for the distortion,the max-·type operator is proposed,which has strong data utilization,distortion,adaptability and response ability in the fuzzy system with mutual influence of mutual conditions.This thesis is divided into five chapters,from the introduction of the type operator(max--)to the study of basic properties,and then to the changes in the properties of the fuzzy matrix when combining the composition and decomposition of the type operator(max--),and finally to analyze and demonstrate the advantages of the type operator(max--)in dealing with complex systems with mutual conditions and mutual influences.In chapter 2,the max-image operator is proposed,and the max-image operator is the continuous improvement of max-min operator.Secondly,some properties of fuzzy sets are discussed and summarized through some properties of classical sets,and the fuzzy sets are transformed into fuzzy matrices.It is proved that the compound operation of fuzzy matrices under max-si-operator satisfies the commutative property under certain conditions,which brings convenience to the compound operation of fuzzy operators.Furthermore,the fundamental properties of the compound operation are studied,and the sufficient conditions for satisfying the commutative property are obtained.In chapter 3,we prove the monotone identity and convergence principle of power sequence of fuzzy matrix under the compound operation of max-operator,and obtain the necessary and sufficient conditions for the convergence of fuzzy matrix a.some special fuzzy matrices are introduced to discuss the necessary conditions for the convergence.In chapter 4,the internal consistency between fuzzy matrix decomposition and fuzzy relation equation is discussed,and a simple discriminant method is put forward to determine whether there is a solution for fuzzy relation equation when max-operator is applied.The method of finding the maximum solution and its related properties are given.Finally,when the fuzzy matrices A and B have special properties,the corresponding special properties of their solutions are demonstrated.The fifth chapter,discuss the Max-min operator(also called Zadeh operator)and the contrast between the Max-·operator found Max-than Max min operator-·operator has the very good algebraic properties,operation process is simple,but the Max-·operator in compound operation data information utilization and adaptability to be better than the Max-min operator,shows that when choosing fuzzy operator is part of the objectivity.