覆盖广义粗糙集的模糊性

Fuzziness of Covering Generalized Rough Sets

在研究覆盖广义粗糙集的基础上,利用两个距离函数Hamming和Euclidean距离函数,结合模糊集的最近寻常集,引入了覆盖广义粗糙集模糊度的概念,给出了一种模糊度计算方法,并证明了该模糊度的一些重要性质。这些结果在覆盖广义粗糙集的理论研究和应用都发挥着一定作用。

Rough set theory has been considered as a useful mean to model the vagueness and has been applied successfully in many fields. And every rough set is associated with some amount of fuzziness. Some measure of fuzziness in rough sets has been provided. On the other hand, rough set theory has been generalized with coverings instead of classical partition. So it is necessary to consider the amount of fuzziness in covering generalized rough sets. The main aim of the paper is to study the problem. A measure of fuzziness in covering generalized rough sets is proposed in this paper. Moreover, some characterization and properties of this measure are achieved with examples, which is every useful for next research works in covering generalized rough sets.