On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering

  • Authors:

  • Miin-Shen Yang;Der-Chen Lin

  • Affiliations:

  • Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, Taiwan;Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, Taiwan and Department of Applied Mathematics, Chinese Culture University, Yangminshan, Taipei 11114, Taiwan

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2009

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Abstract

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 for type-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 @a-level, these clustering results consist of a better hierarchical tree.