模糊粗糙集的模糊邻域算子刻画

Characterizations of Fuzzy Rough Sets by Means of Fuzzy Neighborhood Operators

在模糊集合的公理化定义及其直积的基础上 ,提出基本模糊点的模糊邻域算子概念。用模糊邻域算子来定义模糊集的上近似和下近似 ,可以用模糊集的上、下近似来刻画模糊关系的自反性、对称性和传递性等性质。在模糊粗糙集的模糊邻域算子定义下 ,模糊粗糙集与粗糙模糊集可以统一起来。

In this paper, we present the concept of fuzzy neighborhood operators based on axiomatic definition of fuzzy sets and direct product of fuzzy sets.Using fuzzy neighborhood operators,we define the concept of fuzzy rogh sets. We give the characterizations of properties of fuzzy relation by means of the upper approximation and the lower approximation of fuzzy sets. We discuss the properties of fuzzy rough sets.