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Intuitionistic Fuzzy Clustering Algorithm Based On Boole Matrix And Association Measure

Author

Listed:
  • HUA ZHAO

    (College of Sciences, PLA University of Science and Technology, Nanjing, Jiangsu 210007, China)

  • ZESHUI XU

    (College of Sciences, PLA University of Science and Technology, Nanjing, Jiangsu 210007, China)

  • ZHONG WANG

    (College of Sciences, PLA University of Science and Technology, Nanjing, Jiangsu 210007, China)

Abstract

In this paper we develop a measure for calculating the association coefficient between Atanassov's intuitionistic fuzzy sets (A-IFSs), and show its desirable axiomatic properties. Then we present an algorithm for clustering A-IFSs. The algorithm first utilizes the association coefficient of A-IFSs to construct an association matrix, and then calculates the λ-cutting matrix of the association matrix no matter whether it is an equivalent matrix or not. After that, the λ-cutting matrix is used to cluster A-IFSs (if the λ-cutting matrix is just only a similarity matrix, then we can easily transform it into an equivalent matrix). Three examples are used to show the effectiveness of the association coefficient and the algorithm for clustering A-IFSs. Furthermore, we extend the algorithm to cluster interval-valued intuitionistic fuzzy sets (IVIFSs), and finally, we use another numerical example to illustrate the latter algorithm.

Suggested Citation

  • Hua Zhao & Zeshui Xu & Zhong Wang, 2013. "Intuitionistic Fuzzy Clustering Algorithm Based On Boole Matrix And Association Measure," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 95-118.
    • Handle: RePEc:wsi:ijitdm:v:12:y:2013:i:01:n:s0219622013500053
    DOI: 10.1142/S0219622013500053
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    Cited by:

    1. Shuangsheng Wu & Jie Lin & Zhenyu Zhang & Yushu Yang, 2021. "Hesitant Fuzzy Linguistic Agglomerative Hierarchical Clustering Algorithm and Its Application in Judicial Practice," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
    2. Deng-Feng Li & Shu-Ping Wan, 2017. "Minimum Weighted Minkowski Distance Power Models for Intuitionistic Fuzzy Madm with Incomplete Weight Information," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1387-1408, September.

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