Algorithm of Fuzzy c-Regression Based on Least Absolute Deviations

Abstract

This paper proposes an algorithm of fuzzy c-regression based on least absolute deviations. Theoretical properties of the algorithm and the solutions are moreover investigated. Objective functions for the standard c-regression as well as the regularization using an entropy term are studied. The calculation of the regression coefficients is reduced to the solution of a set of linear programming problems. Convergence of the alternative algorithm of the fuzzy c-regression is proved and theoretical properties of the classification functions are observed. Numerical examples show effectiveness of the present method of least absolute deviations.