粗糙support-intuitionistic模糊集及其聚类分析应用

摘要

Theories of rough sets and fuzzy sets have been used for modeling various types of uncertainty. Dubois and Prade investigate the problem of combining fuzzy sets with rough sets. In this paper, the notion of Rough Support-Intuitionistic Fuzzy(RSIF)sets is introduced. The concepts of rough sets, rough intuitionistic fuzzy sets and support-intuitionistic fuzzy sets are introduced. The lower and upper approximations of support-intuitionistic fuzzy sets with respect to Pawlak's approximation space are defined and the properties of Rough Support-Intuitionistic Fuzzy(RSIF)approximation operators are discussed. Their expression of similarity degree is proposed. This idea is applied into clustering analysis, and an exam-ple is given to verify its reasonableness.%粗糙集和模糊集理论已经被用于各种类型的不确定性建模中.Dubois和Prade研究了将模糊集和粗糙集结合的问题.提出了粗糙support-intuitionistic模糊集.介绍了粗糙集、粗糙直觉模糊集和support-intuitionistic模糊集等的概念;定义了在Pawlak近似空间中的support-intuitionistic模糊集的上下近似,讨论了一些粗糙support-intuitionistic模糊集近似算子的性质,给出了其相似度表达式;将其应用到聚类分析问题中,并通过一个实例验证其合理性.