Fuzzy correlation and fuzzy non-linear regression analysis

Abstract

In this chapter, we will deal with fuzzy correlation and fuzzy non-linear regression analyses. Both correlation and regression analyses that are useful and widely employed statistical tools have been redefined in the framework of fuzzy set theory in order to comprehend relation and to model observations of variables collected as either qualitative or approximately known quantities which are no longer being utilized directly in classical sense. When fuzzy correlation and fuzzy non-linear regression are concern, dealing with several computational complexities emerging due to the nature of fuzzy set theory is a challenge. It should be noted that there is no well-established formula or method in order to calculate fuzzy correlation coefficient or to estimate parameters of the fuzzy regression model. Therefore, a rich literature will accompany with the readers. While extension principle based methods are utilized in the computational procedures for fuzzy correlation coefficient, the distance based methods preferred rather than mathematical programming ones are employed in parameter estimation of fuzzy regression models. That extension principle combined with either fuzzy arithmetic or non-linear programming is two different methods proposed in the literature will be examined with small but illustrative examples in detail for fuzzy correlation analysis. Fuzzy non-linear regression has been a relatively new studied method when compared to fuzzy linear regression. However, both employ similar tools. S-curve fuzzy regression and two types of quadratic fuzzy regression models in the literature will be discussed.