覆盖矩阵和max-min合成模糊关系方程的极小解  

Covering Matrices and Minimal Solutions of Fuzzy Relational Equations with max-min Composition

作　　者：何鹏[1] 王学平[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《模糊系统与数学》2015年第2期109-117,共9页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11171242)

摘　　要：讨论[0,1]格上max-min合成模糊关系方程R⊙x=b极小解的计算问题。首先定义方程R⊙x=b的极小覆盖子矩阵,用极小覆盖子矩阵给出了方程的解是极小解的充要条件。然后给出用方程R⊙x=b的极小覆盖子矩阵求解方程所有极小解的算法,并对算法计算复杂性进行了估计。This paper investigates how to calculate minimal solutions of fuzzy relational equations with max-min composition R （·）x = b in [0, 1 ] lattice. First, we introduce the notion of minimal covering submatrix of the equation, then give a necessary and sufficient condition that a solution of equations R（·）x = b is minimal using Minimal covering submatrix of the equation. Futhermor, we propose two algorithms for computing all minimal solutions of the equations. In the end, we discuss the computational complexity of our algorithms proposed.

关 键 词：[0 1]格 模糊关系方程 极小解 覆盖子矩阵 算法 

分 类 号：O153[理学—数学] O159[理学—基础数学]