Fuzzy clustering of data with uncertainties using minimum and maximum distances based on L{sub}1 metric

摘要

Fuzzy c-means is well-known among various methods of fuzzy cluster analysis. L1 based fuzzy c means is also studied in recent years. The aim of the present paper is to discuss L1 based fuzzy c-means of data with fuzzy uncertainties. Data unit is suposed to be Cartesian product of fuzzy numbers. The metric between a data unit with uncertainty and a cluster center is defined using Minimum and Maximum Distances. Fuzzy c-means algorithm is altenate optimization procedure of the cluster center and the membership, while the solutions of cluster center for the data with uncertainties can not be obtained directly. The algorithm for the solution of cluster centers based on L1 metric for the data with uncertainties are developed in this paper. Using this algorithm, exact alternate optimization procedure is obtained. Numerical examples show that the results for the data with uncertainties are different from the results for the data without uncertainties.