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Clustering algorithm for intuitionistic fuzzy sets. (English) Zbl 1256.62040

Summary: The intuitionistic fuzzy set (IFS) theory, originated by K.T. Atanassov [Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986; Zbl 0631.03040)], has been used in a wide range of applications, such as logic programming, medical diagnosis, pattern recognition, decision making, etc. However, so far there has been little investigation of the clustering techniques of IFSs. We define the concepts of association matrices and equivalent association matrices, and introduce some methods for calculating the association coefficients of IFSs. Then, we propose a clustering algorithm for IFSs. The algorithm uses the association coefficients of IFSs to construct an association matrix, and utilizes a procedure to transform it into an equivalent association matrix. The \(\lambda\)-cutting matrix of the equivalent association matrix is used to cluster the given IFSs. Moreover, we extend the algorithm to cluster interval-valued intuitionistic fuzzy sets (IVIFSs), and finally, demonstrate the effectiveness of our clustering algorithm by experimental results.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H86 Multivariate analysis and fuzziness
03E72 Theory of fuzzy sets, etc.
65C60 Computational problems in statistics (MSC2010)

Citations:

Zbl 0631.03040
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References:

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