Multiobjective fuzzy linear regression analysis and its application

This paper tests three formulations of linear programming problems used to derive a fuzzy linear regression model, which are based on three different indices representing the necessity and of sufficiency equivalence relations between fuzzy numbers. It is shown that those formulations are extensions of three traditional formulations for fuzzy data. The trade-off between “fit” (between the model and the observed data) and the “fuzziness” (of the model) is considered to be a multiobjective decisionmaking problem. This leads to the formulation of a multiobjective programming problem for deriving the fuzzy linear regression model. Corresponding to this situation, an interactive decision-making procedure is proposed, which is applied to the problem of estimating the pork demand.