Picture fuzzy clustering for complex data

Fuzzy clustering is a useful segmentation tool which has been widely used in many applications in real life problems such as in pattern recognition, recommender systems, forecasting, etc. Fuzzy clustering algorithm on picture fuzzy set (FC-PFS) is an advanced fuzzy clustering algorithm constructed on the basis of picture fuzzy set with the appearance of three membership degrees namely the positive, the neutral and the refusal degrees combined within an entropy component in the objective function to handle the problem of incomplete modeling in fuzzy clustering. A disadvantage of FC-PFS is its capability to handle complex data which include mix data type (categorical and numerical data) and distinct structured data. In this paper, we propose a novel picture fuzzy clustering algorithm for complex data called PFCA-CD that deals with both mix data type and distinct data structures. The idea of this method is the modification of FC-PFS, using a new measurement for categorical attributes, multiple centers of one cluster and an evolutionary strategy - particle swarm optimization. Experiments indicate that the proposed algorithm results in better clustering quality than others through clustering validity indices.