期刊
MATHEMATICAL AND COMPUTER MODELLING
卷 53, 期 9-10, 页码 1788-1797出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.mcm.2010.12.057
关键词
Fuzzy sets; Type-2 fuzzy sets; Similarity measure; Inclusion measure; Entropy; Clustering
Similarity measures of type-2 fuzzy sets are used to indicate the similarity degree between type-2 fuzzy sets. Inclusion measures for type-2 fuzzy sets are the degrees to which a type-2 fuzzy set is a subset of another type-2 fuzzy set. The entropy of type-2 fuzzy sets is the measure of fuzziness between type-2 fuzzy sets. Although several similarity, inclusion and entropy measures for type-2 fuzzy sets have been proposed in the literatures, no one has considered the use of the Sugeno integral to define those for type-2 fuzzy sets. In this paper, new similarity, inclusion and entropy measure formulas between type-2 fuzzy sets based on the Sugeno integral are proposed. Several examples are used to present the calculation and to compare these proposed measures with several existing methods for type-2 fuzzy sets. Numerical results show that the proposed measures are more reasonable than existing measures. On the other hand, measuring the similarity between type-2 fuzzy sets is important in clustering for type-2 fuzzy data. We finally use the proposed similarity measure with a robust clustering method for clustering the patterns of type-2 fuzzy sets. (C) 2011 Elsevier Ltd. All rights reserved.
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