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On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering. (English) Zbl 1186.62091

Summary: 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 M.S. Yang’s and H.M. Shih’s [Fuzzy Sets Syst. 120, No. 2, 197–212 (2001; Zbl 1013.68187)] algorithm as a clustering method for type-2 fuzzy data. These clustering results are compared with W.L. Hung’s and M.S. Yang’s [Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 12, No. 6, 827–841 (2004; Zbl 1059.03058)] results. According to different \(\alpha \)-level, these clustering results consist of a better hierarchical tree.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H86 Multivariate analysis and fuzziness
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