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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.
Aiming at the problem of inconsistent top-bottom approximation in the coverage of rough fuzzy sets, a more reasonable model of covering rough fuzzy sets is introduced, the structure and related properties of the model are discussed, and the roughness measurement method based on this model is defined. The concept of fuzzy maximal fuzzy sets is proposed in the case of equal concentration of rough surfaces and the order of the advantages and disadvantages of fuzzy sets is defined by using the distance between fuzzy sets and maximal fuzzy sets so that the rough set of fuzzy sets We introduce the concepts of rough entropy and other related concepts and prove that there are still some rules of monotonically decreasing with the simplest cover in the model and the examples are validated by the examples.Thus, The fuzzy set and the coverage of rough fuzzy sets of uncertainty between the law of measurement provides a theoretical basis.