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    Please use this identifier to cite or link to this item: https://irlib.pccu.edu.tw/handle/987654321/24053


    Title: Similarity, inclusion and entropy measures between type-2 fuzzy sets based on the Sugeno integral
    Authors: Hwang, CM (Hwang, Chao-Ming)
    Yang, MS (Yang, Miin-Shen)
    Hung, WL (Hung, Wen-Liang)
    Lee, ES (Lee, E.Stanley)
    Contributors: Dept Appl Math
    Keywords: Fuzzy sets
    Type-2 fuzzy sets
    Similarity measure
    Inclusion measure
    Entropy
    Clustering
    LOGIC SYSTEMS
    FUZZIFICATION
    RECOGNITION
    Date: 2011-05
    Issue Date: 2013-01-18 16:09:51 (UTC+8)
    Abstract: 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.
    Relation: MATHEMATICAL AND COMPUTER MODELLING Volume: 53 Issue: 9-10 Pages: 1788-1797
    Appears in Collections:[Department of Applied Mathematics] journal articles

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