Formulating Intuitionistic Fuzzy Linear Regression Models

Abstract

Fuzzy linear regression models (FLRMs) are typically formulated to characterize the relation between responses and explanatory variables in fuzzy environments Based on a literature review of existing studies on FLRMs an FLRM based on the least absolute deviation (LAD) is more robust than other approaches However some critical problems still exist such as the uncertainty arising and the determination of the sign of the parameters of the FLRMs In addition observations described by intuitionistic fuzzy sets (IFSs) can contain more information than those described by fuzzy sets However there are only two approaches that have been proposed for developing intuitionistic fuzzy linear regression models (IFLRMs) To establish an intuitionistic fuzzy linear regression model (IFLRM) in this study the fuzzy product core (FPC) operator is first proposed for the purpose of formulating fuzzy linear regression models with fuzzy parameters using fuzzy observations with the fuzzy response and explanatory variables Compared to existing approaches the proposed approach improves the weaknesses of the relevant approaches The proposed approach outperforms existing models in terms of distance and similarity measures even when crisp explanatory variables are used Then an IFLRM based on LAD is proposed that considers that the explanatory and response variables in the observation dataset as well as the parameters of the model are triangular intuitionistic fuzzy numbers (TIFNs) Based on the LAD FLRM some improved approaches are considered such as randomness and fuzziness as well as the use of the strongest T-norm the weakest T-norm and intuitionistic FPC (IFPC) These IFLRMs can avoid the wide spreads in the predicted TIFN responses where the sign of the parameters is determined during the formulation process Furthermore some example illustrations and comparisons are discussed

Date of Award	2020
Original language	English
Supervisor	Liang-Hsuan Chen (Supervisor)