Approximate Solution of Complex LR Fuzzy Linear Matrix Equation

Subject Areas : Transactions on Fuzzy Sets and Systems

Xiaobin Guo ¹ , Xiangyang Fan ² , Hangru Lin ³

1 - Department of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.
2 - Department of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.
3 - Department of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.

Received: 2024-07-31 Accepted : 2024-10-06 Published : 2024-11-05

Keywords: Complex fuzzy numbers, Matrix analysis, Fuzzy matrix equations, Approximate solutions.,

Abstract :

‎This paper aims at solving a class of linear LR complex fuzzy matrix equations $A\widetilde{X}B=\widetilde{C}$ using a matrix approach‎. ‎By using the basic operation of LR fuzzy number matrix‎, ‎the original complex fuzzy matrix equation is transformed into a clear matrix equation group‎. ‎Two new and simplified models for calculating fuzzy solutions are designed in detail‎, ‎and sufficient conditions for strong fuzzy solutions are analyzed‎. ‎Finally‎, ‎two examples are given to illustrate the feasibility and effectiveness of the proposed method‎. ‎Now that the complex fuzzy numbers can describe uncertain factors more vivid and reasonable than the real fuzzy numbers sometimes and the wide application of matrix equations under uncertain conditions‎, ‎our research work enriches the fuzzy linear systems theory‎.

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