Approach for Establishing Intuitionistic Fuzzy Linear Regression Models Based on Weakest T-Norm Arithmetic

This article establishes an intuitionistic fuzzy linear regression model (IFLRM) under the consideration that the explanatory and response variables in the observation data set as well as the parameters of the model are intuitionistic fuzzy numbers (IFNs). The weakest T-norm arithmetic is applied in the formulation of the IFLRMs to avoid wide spreads in the predicted IFN responses. The sign of the parameters is determined in the formulation process. We propose a mathematical programming problem to find the optimal IFN parameters. The goal of the optimization is to minimize the absolute distances between the observed and predicted IFNs. To enhance computational efficiency, a three-step procedure is proposed for solving a mathematical programming problem when the number of explanatory variables or the size of the observation data set is large. Comparisons with existing approaches indicate that the proposed approach has outstanding performance in terms of similarity and distance measures.

I. Introduction

Fuzzy linear regression models (FLRMs) are used to investigate the relationship between explanatory and response variables for fuzzy observations. Based on the fuzzy set theorem [1], fuzzy numbers are defined and characterized by membership functions for constructing FLRMs through various approaches, such as mathematical programming, goal programming, the least-squares method, and the two-stage method. The construction criteria include maximum similarity, minimum total distance, least square error, and least absolute deviation [2]. FLRMs relax the strict assumptions of the traditional regression model, such as the normality of error terms and predictions and random measurement errors in collected observations [3]. When an FLRM is used, observational uncertainties or fuzziness is represented by the fuzzy parameters related to the indefinite structure of the system.