Approach for Establishing Intuitionistic Fuzzy Linear Regression Models Based on Weakest <i>T</i>-Norm Arithmetic

作     者：Chen, Liang-Hsuan Nien, Sheng-Hsing 

作者机构：Natl Cheng Kung Univ Dept Ind & Informat Management Tainan 70101 Taiwan 

出 版 物：《IEEE TRANSACTIONS ON FUZZY SYSTEMS》 (IEEE模糊系统汇刊)

年 卷 期：2021年第29卷第6期

页      面：1431-1445页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Ministry of Science and Technology  Taiwan [MOST 104-2410-H-006-054-MY3  MOST 107-2410-H-006-041-MY2] 

主　　题：Fuzzy linear regression model (FLRM) intuitionistic fuzzy number (IFN) intuitionistic fuzzy regression mathematical programming weakest T-norm arithmetic 

摘      要：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.