Fuzzy Regression Analysis with an Application

Abstract

This work investigates the analysis of fuzzy regression in case of the data being fuzzy or non-fuzzy. The analysis is performed by several methods , such as fuzzy linear regression (FLR) and modified one, and fuzzy linear regression with least squares (FLSLR), in which linear programming (LP) is used in the analysis. Estimation of fuzzy parameters is carried out in case of fuzzy and non-fuzzy (crisp) data where the regression model is detected by fuzzy set theory. These methods are applied on real data of Osteoporosis which are obtained by measuring the bone density of 30 patients (10 male and 20 female) by DEXA. The results of the analysis show that, Tanaka model is better than fuzzy linear regression model (FLR) so that to avoid the appearance of non-fuzzy estimated parameters ,and . (FLSLR) is better than (FLR) in the sense of degree of membership of the model.