覆盖模糊S-粗集模型

Covering fuzzy S-rough sets model

建立了基于覆盖理论的模糊S-粗糙集模型,并讨论其性质。在覆盖单向S-粗集x的最小描述的基础上,给出了x的最大描述的定义。给出了覆盖模糊S-粗集上、下近似算子定义,讨论了算子的基本性质,证明了覆盖S-粗糙集模型下所有模糊集的下近似构成一个模糊拓扑,并得到模糊单向S-粗集X相对于覆盖单向S-粗集和覆盖约简单向S-粗集的上下近似分别相等。

This paper is devoted to the study of the covering fuzzy S-rough sets model.The maximal description of x of covering one direction singular rough sets is given based on the minimal description of x.The upper and lower approximation operations are defined with their basic properties being discussed.It is proved that the set of all lower approximations of fuzzy sets constitutes a fuzzy topology.The upper and lower approximations of fuzzy one direction singular rough sets are respectively equal after covering is reducted.