INTUITIONISTIC FUZZY CLUSTERING ALGORITHM BASED ON BOOLE MATRIX AND ASSOCIATION MEASURE

Hua Zhao (), Zeshui Xu () and Zhong Wang ()
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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

International Journal of Information Technology & Decision Making (IJITDM), 2013, vol. 12, issue 01, 95-118

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.

Keywords: Atanassov's intuitionistic fuzzy set; interval-valued intuitionistic fuzzy set; association coefficients; association matrix; λ-cutting matrix; clustering algorithm; 90B50; 91B06 (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219622013500053

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