FUZZY LINEAR-REGRESSION ANALYSIS FOR FUZZY INPUT-OUTPUT DATA

A class of fuzzy linear regression models, where both input data and output data are fuzzy numbers, is introduced by using the three indices for equalities between fuzzy numbers. For some fixed degree-alpha of the fuzzy threshold for the three indices, three types of optimization problems for obtaining fuzzy linear regression models are formulated, putting special emphasis on the relation to the least squares problems for the usual linear regression models. Then linear programming based methods for solving the formulated problems are developed. A numerical example demonstrates the feasibility and efficiency of the proposed method.