On Similarity And Inclusion Measures Between Type-2 Fuzzy Sets With An Application To Clustering

摘要

In this paper we define similarity and inclusion measures between type-2 fuzzy sets. We then discuss their properties and also consider the relationships between them. Several examples are used to present the calculation of these similarity and inclusion measures between type-2 fuzzy sets. We finally combine the proposed similarity measures with Yang and Shih's (M.S. Yang, H.M. Shih, Cluster analysis based on fuzzy relations, Fuzzy Sets and Systems 120(2001) 197-212] algorithm as a clustering method fortype-2 fuzzy data. These clustering results are compared with Hung and Yang's [W.L. Hung, M.S. Yang, Similarity measures between type-2 fuzzy sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12 (2004) 827-841] results. According to different α-level, these clustering results consist of a better hierarchical tree.