区间二型模糊相似度与包含度

Similarity and inclusion measures between IT2 FSs

相似度与包含度是模糊集合理论中的两个重要概念,但对于二型模糊集合的研究还较为少见.鉴于此,提出了新的区间二型模糊相似度与包含度,首先选择了二者的公理化定义;然后基于公理化定义提出了新的计算公式,并讨论了二者的相互转换关系;最后通过实例来验证二者的性能,并将区间二型模糊相似度与Yang-Shih聚类方法相结合,用于高斯区间二型模糊集合的聚类分析,得到了合理的层次聚类树.仿真实例表明新测度具有一定的实用价值.

The similarity and inclusion measures between fuzzy sets are two important concepts in fuzzy set theory, but little effort as to them has been made on type-2 fuzzy sets. Therefore, a similarity measure and an inclusion measure between interval type-2 fuzzy sets （IT2 FSs） are proposed. Firstly, the axiomatic definitions of two measures are selected. Then, based on the selected definitions, the computation formulas are proposed, and four theorems that two measures can be transformed by each other are demonstrated. Finally, examples are presented to validate their performance and combine the proposed similarity measure with Yang and Shih＇s clustering method for an application to clustering analysis of Gaussian IT2 FSs, and a reasonably hierarchical clustering tree in different α-levels is obtained. Simulation results show the practicability of the proposed measures.