| In practical production and scientific experiments,problems related to uncertainties emerge and need to be solved urgently,so mathematical models of uncertainty based on fuzzy numbers are born.Linear systems are theoretically mature and computationally easy to implement,and often have parameter uncertainties.Given the wide range of applications of fuzzy linear systems in various fields,it is particularly important to discuss their numerical solutions.In this paper we study the inverse problem of fuzzy matrices based on LR trapezoidal fuzzy numbers and its simple applications based on fuzzy number multiplication operations with the help of matrix analysis and computational methods.Firstly,the multiplication operation of LR trapezoidal fuzzy numbers is derived from the operation rules of LR triangular fuzzy numbers,where the LR near-zero trapezoidal fuzzy numbers and their basic operations are proposed.Secondly,the concept and properties of the inverse of LR near-zero trapezoidal fuzzy number matrix are given,and the computational theory and method of the fuzzy inverse are analyzed.Finally,the application of fuzzy inverse in the approximate solution of completely fuzzy linear systems is discussed.The computation of a large number of examples in the paper clarifies the feasibility and effectiveness of the proposed algorithm.Since fuzzy matrix is a powerful tool for solving fuzzy linear systems,the study of fuzzy inverse in this paper enriches and develops the theory of fuzzy linear systems. |
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