NEW ALGORITHMS FOR SOLVING THE FUZZY CLUSTERING PROBLEM

Two new algorithms for fuzzy clustering are presented. Convergence of the proposed algorithms is proved. An empirical study of their convergence behavior is discussed. The performance of the new algorithms is compared with the fuzzy c-means algorithm by testing them on four published data sets. Experimental results show that the new algorithms are faster and lead to computational savings

NEW ALGORITHMS FOR SOLVING THE FUZZY CLUSTERING PROBLEM

Two new algorithms for fuzzy clustering are presented. Convergence of the proposed algorithms is proved. An empirical study of their convergence behavior is discussed. The performance of the new algorithms is compared with the fuzzy c-means algorithm by testing them on four published data sets. Experimental results show that the new algorithms are faster and lead to computational savings

Кластерный анализ для многомерных объектов в условиях нечетких данных

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