Intuitionistic Fuzzy Clustering Algorithms
Since the fuzzy set theory was introduced by Zadeh (1965), many scholars have investigated the issue how to cluster the fuzzy sets, and a lot of clustering algorithms have been developed for fuzzy sets. However, the studies on clustering problems with int
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Intuitionistic Fuzzy Clustering Algorithms
Since the fuzzy set theory was introduced (Zadeh 1965), many scholars have investigated the issue how to cluster the fuzzy sets, and a lot of clustering algorithms have been developed for fuzzy sets, such as the fuzzy c-means clustering algorithm (Fan et al. 2004), the maximum tree clustering algorithm (Christopher and Burges 1998), and the net-making clustering method (Wang 1983), etc. However, the studies on clustering problems with intuitionistic fuzzy information are still at an initial stage (Wang et al. 2011, 2012; Xu 2009; Xu and Cai 2012; Xu and Wu 2010; Xu et al. 2008, 2011; Zhang et al. 2007; Zhao et al. 2012a, b). Zhang et al. (2007) first defined the concept of the intuitionistic fuzzy similarity degree and constructed an intuitionistic fuzzy similarity matrix, and then proposed a procedure for deriving an intuitionistic fuzzy equivalence matrix by using the transitive closure of the intuitionistic fuzzy similarity matrix. After that, they presented a clustering technique of IFSs on the basis of the λ-cutting matrix of the interval-valued matrix. Xu et al. (2008) defined the concepts of the association matrix and the equivalent association matrix, they introduced some methods for calculating the association coefficients of IFSs, and used the derived association coefficients to construct an association matrix, from which they derived an equivalent association matrix. Based on the equivalent association matrix, a clustering algorithm for IFSs was developed and extended to cluster interval-valued intuitionistic fuzzy sets (IVIFSs). Xu (2009) introduced an intuitionistic fuzzy hierarchical algorithm for clustering IFSs, which is based on the traditional hierarchical clustering procedure, the intuitionistic fuzzy aggregation operator, and some basic distance measures, such as the Hamming distance, the normalized Hamming distance, the Euclidean distance, and the normalized Euclidean distance, etc. Xu and Wu (2010) developed an intuitionistic fuzzy C-means algorithm to cluster IFSs, which is based on the well-known fuzzy C-means clustering method (Bezdek 1981) and the basic distance measures between IFSs. Then, they extended the algorithm for clustering IVIFSs. Xu et al. (2011) extended the fuzzy closeness degree (Wang 1983) to the intuitionistic fuzzy closeness degree, and defined an intuitionistic fuzzy vector, the inner and outer products of intuitionistic fuzzy vectors. Based on the intuitionistic fuzzy closeness degree, they put forward a new method of constructing intuitionistic fuzzy similarity matrix. Zhao et al. (2012a) developed an Z. Xu, Intuitionistic Fuzzy Aggregation and Clustering, Studies in Fuzziness and Soft Computing 279, DOI: 10.1007/978-3-642-28406-9_2, © Springer-Verlag Berlin Heidelberg 2012
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2 Intuitionistic Fuzzy Clustering Algorithms
intuitionistic fuzzy minimum spanning tree (MST) clustering algorithm to deal with intuitionistic fuzzy information. Zhao et al. (2012b) gave a measure for calculating the association coefficient bet
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