Convergence of the complete intuitionistic fuzzy C-means clustering algorithm

Dung Thi Thu Nguyen

Abstract


This paper discusses the convergence of the complete intuitionistic fuzzy C_means clustering method (CIFCM). The complete intuitionistic fuzzy C-means clustering method based on the modification of the target function considering the index hesitance is a more efficient method to modify the intuitionistic fuzzy C_means clustering method. The target function of the clustering algorithm is a series of Picard iterations according to the updating of the membership matrix and cluster centers. Usually, fixed point theorems, of which the contracting mapping theorem is a classical case, are used to solve the convergence problem of Picard sequences. Picard sequences based on the fuzzy clustering method C-means algorithm (FCM) does not allow to verify the contraction property mainly due to the two-component compositional nature of one iteration. Therefore, in this paper, the convergence of the complete intuitionistic fuzzy C_means clustering method is examined using Zangwill's theorem, The iterative sequence generated by the algorithm of the complete intuitionistic fuzzy C-means clustering method ends at a local minimum or saddle point, or, at most, contains a sub-sequence that ends at a local minimum or saddle point of the target function of the complete intuitionistic fuzzy C_means clustering algorithm.

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