Approximate Solution of Complex LR Fuzzy Linear Matrix Equation
محورهای موضوعی : 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.
کلید واژه: Complex fuzzy numbers, Matrix analysis, Fuzzy matrix equations, Approximate solutions.,
چکیده مقاله :
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.
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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