A two-stage approach for formulating fuzzy regression models

• A simple two-stage approach is proposed to construct a fuzzy regression model.
• The fuzzy model contains the crisp coefficients and a fuzzy adjustment term.
• The negative coefficients are taken into account in the fuzzy regression model.
• The fuzzy model has the highest explanatory performance using various criteria.

Fuzzy regression models have been widely applied to explain the relationship between explanatory variables and responses in fuzzy environments. This paper proposes a simple two-stage approach for constructing a fuzzy regression model based on the distance concept. Crisp numbers representing the fuzzy observations are obtained using the defuzzification method, and then the crisp regression coefficients in the fuzzy regression model are determined using the conventional least-squares method. Along with the crisp regression coefficients, the proposed fuzzy regression model contains a fuzzy adjustment variable so that the model can deal with the fuzziness from fuzzy observations in order to reduce the fuzzy estimation error. A mathematical programming model is formulated to determine the fuzzy adjustment term in the proposed fuzzy regression model to minimize the total estimation error based on the distance concept. Unlike existing approaches that only focus on positive coefficients, the problem of negative coefficients in the fuzzy regression model is taken into account and resolved in the solution procedure. Comparisons with previous studies show that the proposed fuzzy regression model has the highest explanatory power based on the total estimation error using various criteria. A real-life dataset is adopted to demonstrate the applicability of the proposed two-stage approach in handling a problem with negative coefficients in the fuzzy regression model and a large number of fuzzy observations.