基于梯形模糊数的模糊矩阵方程的解法
The Solution Method of Fuzzy Matrix Equation Based on Trapezoidal Fuzzy Numbers
DOI: 10.12677/PM.2026.161017, PDF,   
作者: 吴 俊：汉江师范学院数学与计算机科学学院，湖北 十堰；刘楷文：湖北大学人工智能学院，湖北 武汉
关键词: 模糊矩阵方程；模糊系统分析；模糊数；Fuzzy Matrix Equation； Fuzzy System Analysis； Fuzzy Numbers
摘要: 本文研究了求解对偶模糊矩阵方程的AX~+B~=CX~+D~方法. 利用模糊集的分解定理, 结合梯形模糊数水平截集的左右端点, 介绍了对偶模糊矩阵方程的广义解和代数解的计算方法, 研究了两种解之间的关系以及给出了唯一代数解存在的充分条件, 并以数值算例进行说明。
Abstract: This paper investigates the methods for solving the dual fuzzy matrix equation . By leveraging the decomposition theorem of fuzzy sets and combining the left and right endpoints of the level cuts of trapezoidal fuzzy numbers, the calculation methods for the generalized solution and algebraic solution of the dual fuzzy matrix equation are introduced. The relationship between the two types of solutions is stud- ied, sufficient conditions for the existence of a unique algebraic solution are provided, and numerical examples are presented for illustration.
文章引用：吴俊, 刘楷文. 基于梯形模糊数的模糊矩阵方程的解法[J]. 理论数学, 2026, 16(1): 137-145. https://doi.org/10.12677/PM.2026.161017

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