基于粗隶属函数的粗糙集模型的推广

Generalization of Rough Set Model Based on Rough Membership Function

通过粗隶属函数,将粗糙集理论与模糊集理论联系起来,建立一种粗糙集理论与模糊集理论间的关系。把粗隶属函数视为论域上的一个特殊模糊集,用它的!-截集和强"-截集的概念,将经典粗糙集模型进行推广,提出基于等价关系的隶属度粗糙集模型,验证一些有用的性质,并证明该模型比Pawlak粗糙集模型具有更好的精度。最后将基于等价关系的隶属度粗糙集模型拓展到基于一般二元关系的广义隶属度粗糙集模型,并给出其相应的性质。

We combine the fuzzy set theory with rough set theory by rough membership function and establish a relation between them.We regard rough membership function as a special fuzzy set of the universe,and the classical rough set model is generalized by using the concepts of its -cut and strong-cut.Meanwhile,membership degree rough set model based on equivalence relation is proposed.We prove some useful properties and also testify that this model has higher precision than Pawlak rough set model.Finally,membership degree rough set model based on equivalence relation is extended to generalized membership degree rough set model based on general binary relation,and the relevant properties are also given.