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多粒度粗糙集和覆盖粗糙直觉模糊集是处理不确定性、不精确性问题的重要理论,为了更有效地处理该问题,本文将多粒度粗糙集与覆盖粗糙直觉模糊集结合起来进行研究.首先,在多粒度粗糙集理论、覆盖理论和直觉模糊集理论的基础上,给出了新的基于最小描述的模糊覆盖粗糙隶属度和非隶属度概念.用模糊覆盖粗糙隶属度和非隶属度,反映各个元素从属于直觉模糊集A的程度.最大描述与最小描述都是用来描述覆盖粗糙直觉模糊集的基本特征,因此又从最大描述概念出发,给出了基于最大描述的模糊覆盖粗糙隶属度和非隶属度概念;其次,分别基于最小描述和最大描述,给出了乐观和悲观多粒度覆盖粗糙直觉模糊集的下近似(上近似)算子的定义,并对各个算子的性质进行了讨论;最后,用例子进行了验证.该研究为多粒度覆盖粗糙集和直觉模糊集的融合提供了一种新方法.
Multi-granularity rough sets and rough set intuitionistic fuzzy sets are important theories to deal with uncertainty and inaccuracy. In order to deal with this problem more effectively, we combine multi-granularity rough sets and rough set fuzzy intuitionistic fuzzy sets to study them.Firstly, Based on the theory of multi-granularity rough set theory, covering theory and intuitionistic fuzzy set theory, a new concept of fuzzy sub-degree and non-sub-degree of fuzzy coverage based on minimum description is given.With fuzzy membership, Reflects the extent to which each element is subordinate to intuitionistic fuzzy set A. The maximum description and the minimum description are both used to describe the basic characteristics of covering rough intuitionistic fuzzy sets and therefore the maximum description is given based on the maximum description of fuzzy coverage, Degree and non-membership degree. Secondly, the definitions of lower approximation (up approximation) operators of optimistic and pessimistic multi-granularity covering rough intuitionistic fuzzy sets are given respectively based on the minimum description and the maximum description. The properties of each operator Finally, an example is given to verify the new algorithm.It provides a new method for the fusion of multi-granularity covering rough sets and intuitionistic fuzzy sets Law.