Fuzzy entropy in fuzzy weighted linear regression model under linear restrictions with simulation study

Abstract

In fuzzy set theory, it is well known that a fuzzy number can be uniquely determined through its position and entropy. Hence, by using the concept of fuzzy entropy the estimators of the fuzzy regression coefficients may be estimated. In the present communication, a fuzzy linear regression (FLR) model with some restrictions in the form of prior information has been considered. The estimators of regression coefficients have been obtained with the help of fuzzy entropy for the restricted/unrestricted FLR model by assigning some weights in the distance function. Some numerical examples have also been provided in order to illustrate the proposed model along with the obtained weighted estimators. Further, in order to compare the performance of unrestricted estimator and restricted estimator, a simulation study has been conducted by using two fundamental criteria of dominance – mean squared error matrix (MSEM) and absolute bias.