基于最小/最大描述的多粒度覆盖粗糙直觉模糊集模型

摘要

Covering rough sets and intuitionistic fuzzy sets,which have strong complementary,are the basic theories of dealing with uncertainty.It is a hot research topic to combine covering rough sets and intuitionistic fuzzy sets.In this paper,the combination of multigranularity covering rough sets and intuitionistic fuzzy sets was studied.Firstly,minimal and maximal descriptions,which are extended from single granulation to multigranulation,were proposed based on multigranulation,and the fusion of multigranularity was discussed.Secondly,the concept of fuzzy covering rough membership and non-membership was defined on minimal and maximal descriptions respectively.Then,two new models were structured,which are multigranulation covering rough intuitionistic fuzzy sets based on minimal description and multigranulation covering rough intuitionistic fuzzy sets based on maximal description,and their properties were discussed and illustrated with examples.Finally,the relationships of the two models were researched.This study provides a new method for the combination of multigranulation covering rough sets and intuitionistic fuzzy sets.%覆盖粗糙集和直觉模糊集都是处理不确定性问题的基础理论,它们有着很强的互补性,且覆盖粗糙集和直觉模糊集的融合研究是一个新的热点.对多粒度覆盖粗糙集和直觉模糊集的融合进行深入研究.首先将最小描述、最大描述从单一粒度推广到多个粒度,提出了多粒度的最小描述和最大描述,讨论了多粒度的融合;其次,分别给出了基于最小描述和最大描述的模糊覆盖粗糙隶属度、非隶属度的概念,构建了两种新的模型即基于最小描述的多粒度覆盖粗糙直觉模糊集和基于最大描述的多粒度覆盖粗糙直觉模糊集,并讨论了它们的性质,同时举例说明;最后,分析和研究了两种模型的关系.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方法.