Dual-centers type-2 fuzzy clustering framework and its verification and validation indices

• The clustering model considers dual-centers rather than single centers.
• The dual-centers type-2 clustering model and algorithm are proposed.
• The relations among parameters of the proposed model are explained.
• The degrees of belonging to the clusters are defined by type-2 fuzzy numbers.
• The verification and verification indices are developed for model evaluation.

In this paper we present a clustering framework for type-2 fuzzy clustering which covers all steps of the clustering process including: clustering algorithm, parameters estimation, and validation and verification indices. The proposed clustering algorithm is developed based on dual-centers type-2 fuzzy clustering model. In this model the centers of clusters are defined by a pair of objects rather than a single object. The membership values of the objects to the clusters are defined by type-2 fuzzy numbers and there are not any type reduction or defuzzification steps in the proposed clustering algorithm. In addition, the relation among the size of the cluster bandwidth, distance between dual-centers and fuzzifier parameter are indicated and analyzed to facilitate the parameters estimation step. To determine the optimum number of clusters, we develop a new validation index which is compatible with the proposed model structure. A new compatible verification index is also defined to compare the results of the proposed model with existing type-1 fuzzy clustering model. Finally, the results of computational experiments are presented to show the efficiency of the proposed approach.

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