Multivariate Least Squares Regression using Interval-Valued Fuzzy Data and based on Extended Yao-Wu Signed Distance

Abstract

The purpose of this study is to introduce a new regression model, based on the least squares method, when the available data of both explanatory variable(s) and response variable are interval-valued fuzzy (IVF) numbers. The proposed method is based on a new metric on the space of IVF numbers, which is an extended version of the signed distance introduced by Yao and Wu (2000). In order to evaluate the goodness of fit of the proposed model, we introduce some new indices based on the similarity measure and the coefficient of multiple determination. Finally, the application of proposed approach is provided to model some real data.

Keywords:

• Coefficient of multiple determination
• Goodness of fit
• Interval-valued fuzzy set
• Multivariate least squares regression
• Similarity measure