Some Approaches for Estimating the Parameters of Fuzzy Intuitionistic Fuzzy Regression Models

Abstract

In the last few years, several approaches have been proposed in the literature to estimate the parameters (regression coefficients) of fuzzy/ intuitionistic fuzzy regression models (regression models in which some or all the variables and parameters are represented as fuzzy/ intuitionistic fuzzy numbers). In this thesis, limitations and flaws of some existing approaches have been pointed out. Also, to resolve the flaws/ to overcome the limitations of the existing approaches, new approaches have been proposed. The chapter-wise summary of the thesis is as follows: Chapter 1 Introduction In this chapter, the need of interval/ fuzzy set/ intuitionistic fuzzy set in regression analysis is discussed. Also, a brief review of some existing approaches for estimating the parameters of interval/ fuzzy / intuitionistic fuzzy regression models is discussed. Chapter 2 Mehar approach for estimating the parameters of fully interval linear regression models. Souza et al. [158] proposed an approach for estimating the parameters of fully interval linear regression models (linear regression models in which the values of all the input variables, output variable and the coefficients are represented as intervals). In this chapter, limitations of Souza et al. approach [158] are pointed put. Also, it is pointed out that Souza et al. [158] have used some mathematical incorrect assumptions in their proposed approach. Therefore, it is mathematically incorrect to use Souza et al. approach [158]. Furthermore, a new approach (named as Mehar approach) is proposed for estimating the parameters of fully Interval linear regression models. Finally, the proposed Mehar approach has been illustrated with the help of numerical examples. Chapter 3 Modified mathematical programming method for estimating the parameters of FLR model of type-I Chen and Hsueh [41] pointed out the flaws of some existing methods for estimating the parameters of fuzzy linear regression (FLR) models of type-I (linear regression models in which the values of the input variables