| In the process of engineering calculation and system modeling,many uncertain parameters exist,how to describe and represent these uncertain parameters mathematically,it is more sophisticated and easier to define if it can be expressed as fuzzy numbers in a certain way.Therefore,fuzzy number analysis theory,fuzzy information system modelling,and fuzzy matrix systems have been the subject of intensive research.In fact,in system modelling and engineering process computation,for the description and computation of many nonlinear problems,the most considered and more desirable is whether it can be transformed into a linear system or matrix equation in some sense.Thus,the theoretical research and numerical computation of fuzzy matrix equations(including fuzzy linear systems)are receiving more and more attention.This thesis discusses the methods of computing dual fuzzy matrix equations based on the theory of fuzzy linear systems and computing matrix equations,including direct solutions and numerical computations.First,the generalized and algebraic solutions of the dual fuzzy matrix equation are defined,the relationship between the two types of solutions is investigated,the algebraic solutions are discussed,and the sufficient conditions for the existence of the unique algebraic solution of the dual fuzzy matrix equation are given.The solution formula and calculation method of the dual fuzzy matrix equation with triangular fuzzy number matrix are given.Secondly,the general dual fuzzy matrix equations and dual fuzzy linear systems are investigated based on the generalised inverse of the matrix.As a generalisation,a class of dual fuzzy matrix equations involving LR fuzzy numbers and the numerical computation of these equations are discussed.Using the iterative method,the solution matrices of the two transformed fuzzy matrix equations are combined to obtain the solution computation of the generalised dual fuzzy matrix equations,and an example is given. |
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