Interactive Decision Making for Multiobjective Fuzzy Linear Regression Analysis

Abstract

In this paper, to cope with the fuzzy environment where human subjective estimation is influential in the linear regression models, fuzzy linear regression models are introduced via the concepts of possibility and necessity. In fuzzy linear regression models, deviations between the observed values and the estimated values are assumed to be depending on the fuzziness of the parameters of the system. Given the fuzzy threshold for the three indices, three types of single-objective programming problems for obtaining fuzzy linear regression models, where input data is a vector of nonfuzzy numbers and output data is a fuzzy number, are formulated as natural extension of usual linear regression models. As an obvious advantage of these formulations, it is shown that all of the formulated problems can be reduced to linear programming ones. Moreover, by considering the conflict between the fuzzy threshold for the three indices and the fuzziness of the fuzzy linear regression model, the multiobjective programming problems for obtaining the fuzzy linear regression models are formulated, where both the fuzzy threshold and the fuzziness of the models are optimized corresponding to the three indices. Then on the basis of the linear programming method an interactive decision making method to derive the satisficing solution for the decision maker for the formulated multiobjective programming problems is developed. Finally, the proposed method is applied to the identification problem of the pork demand function to demonstrate its appropriateness and efficiency.