Abstract
In the paper, a class of fuzzy matrix equations AX=B where A is an m × n crisp matrix and is an m × p arbitrary LR fuzzy numbers matrix, is investigated. We convert the fuzzy matrix equation into two crisp matrix equations. Then the fuzzy approximate solution of the fuzzy matrix equation is obtained by solving two crisp matrix equations. The existence condition of the strong LR fuzzy solution to the fuzzy matrix equation is also discussed. Some examples are given to illustrate the proposed method. Our results enrich the fuzzy linear systems theory.
Highlights
Systems of simultaneous matrix equations are essential mathematical tools in science and technology
We propose a practical method for solving a class of fuzzy matrix system AX B in which A is an m × n crisp matrix and B is an m × p arbitrary LR fuzzy numbers matrix
We propose a model for solving the LR fuzzy matrix system, i.e., convert it into two crisp systems of matrix equations
Summary
Systems of simultaneous matrix equations are essential mathematical tools in science and technology. At least some of the parameters of the system are represented by fuzzy rather than crisp numbers. It is very important to develop a numerical procedure that would appropriately handle and solve fuzzy matrix systems. The concept of fuzzy numbers and arithmetic operations were first introduced and investigated by Zadeh [1] and Dubois [2]
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