基于布尔矩阵的模糊粗糙集代数运算与表示定理

Algebraic Operations and Representing Theorems of Fuzzy Rough Sets Based on Boolean Matrix

主要研究模糊粗糙集理论基本概念与基本运算的矩阵表示,用布尔矩阵对模糊粗糙集理论中的基本概念进行描述,并通过布尔矩阵运算性质研究、揭示和刻画模糊粗糙集知识空间的基本代数性质。文中定义了布尔矩阵"与积"和"或积"两种逻辑运算,分别对模糊粗糙集理论中的模糊可能(fuzzy diamond)算子和模糊必然(fuzzy box)算子计算过程进行描述,对模糊粗糙集理论的基本概念和基本代数性质给出了基于布尔矩阵的表示定理,为基于模糊粗糙集理论的知识表示与知识获取提供了一种能行与可计算的思路与方法。

This paper studies the matrix representations of the basic notations and operations in the Fuzzy Rough Sets. In order to give out a complete matrix description of the fuzzy rough set, two kind of operations called ＂and-product＂ and ＂or-product＂ between the Boolean matrixes are introduced, which corresponds separately to the notation of the fuzzy diamond and that of the fuzzy box. Based on the Boolean matrix operations, the representation theorems about the basic notations and algebraic properties of the fuzzy rough sets are proved.