多粒度覆盖粗糙模糊集模型不确定性研究

针对覆盖粗糙模糊集中存在的上下近似不一致问题.引入一种更为合理的覆盖粗糙模糊集模型,讨论了该模型的结构与相关性质,定义了基于此模型的粗糙度度量方法.基于覆盖粗糙模糊集中粗糙度相等的情形,提出模糊集中极大模糊集的概念,并利用模糊集与极大模糊集的距离问题定义了模糊集的优劣次序,从而有效解决了模糊集在覆盖粗糙模糊集中粗糙度的度量问题.通过引入粗糙熵等相关概念,证明了此模型中仍然存在随最简覆盖变细,两种度量单调减少的规律,并通过实例进行了验证.从而为进一步揭示粗糙集、粗糙模糊集及覆盖粗糙模糊集之间的不确定性度量规律提供了理论依据.

Uncertainty of Multiple Granularity Rough Fuzzy Set Model

Aiming at the disaccord of the lower and upper approximations for covering rough set,a reasonable covering model is introduced.The structure and correlative property of this model is discussed and proved.The method of roughness measuring over the covering rough fuzzy set is defined.The maximum fuzzy set is presented and problem of equal roughness is solved by defining distance between fuzzy set and the maximum fuzzy set.Then the correlate notion of rough entropy is constructed and an example is given to show the validity of the method of this model.By proving theorem,the conclusion that measuring of rough degree and rough entropy are monotonously decreasing with the subdivision of covering sets is obtained.The theoretical evidence of measuring of uncertainty among rough sets,rough fuzzy set and coving rough set is provided.