Fuzzy regression methods – a comparative assessment

Abstract

The fundamental differences between fuzzy regression and ordinary regression are identified in this paper. Fuzzy regression can be used to fit fuzzy data and crisp data into a regression model, whereas ordinary regression can only fit crisp data. Through a comprehensive literature review, three approaches of fuzzy regression are summarized. The first approach of fuzzy regression is based on minimizing fuzziness as an optimal criterion. The second approach uses least-squares of errors as a fitting criterion, and two methods are summarized in this paper. The third approach can be described as an interval regression analysis. For each fuzzy regression method, numerical examples and graphical presentations are used to evaluate their characteristic and differences with ordinary least-squares regression. Based on the comparative assessment, the fundamental differences between ordinary least-squares regression and conventional fuzzy regression are concluded – that is, ordinary least-squares regression modeling data with randomness type of uncertainty, and conventional fuzzy regression modeling data with fuzziness type of uncertainty. In order to integrate both randomness and fuzziness types of uncertainty into one regression model, the concept of hybrid fuzzy least-squares regression analysis is proposed in this paper, and the details of its method are derived in the accompanying paper.