Cluster analysis for multidimensional objects in fuzzy data conditions

This article presents many different areas of practical applications multivariate cluster analysis under conditions fuzzy initial data that are described in the literature. New algorithms and formula expressions proposed for combining various multi-dimensional objects, parameters which given by fuzzy-sets, into clusters along with calculating coordinates centroids their membership functions. Various types clustering criteria formulated form minimizing weighted average sum distances between objects presented metrics, as well maximizing clusters. The formulations mathematical models three NP-hard problems multidimensional fuzzy-data proposed; while solving them any considered optimality can be used. Heuristic approximate solution two have been developed. algorithm 1st problem is illustrated a numerical example. obtained results serve direction further research wide applications.