Fuzzy regression model with monotonic response function

Abstract

Fuzzy linear regression model has been widely studied with many successful applications but there have been only a few studies on the fuzzy regression model with monotonic response function as a generalization of the linear response function. In this paper, we propose the fuzzy regression model with the monotonic response function and the algorithm to construct the proposed model by using α-level set of fuzzy number and the resolution identity theorem. To estimate parameters of the proposed model, the least squares (LS) method and the least absolute deviation (LAD) method have been used in this paper. In addition, to evaluate the performance of the proposed model, two performance measures of goodness of fit are introduced. The numerical examples indicate that the fuzzy regression model with the monotonic response function is preferable to the fuzzy linear regression model when the fuzzy data represent the non-linear pattern. © 2018 Korean Mathematical Society.