A Linear-Programming Approach to Interval-Valued Fuzzy Regression Analysis

A fuzzy interval-valued regression model, on the basis of a mathematical programming approach, is introduced for when the observations of the response variable and the independent variables are crisp. Using a distance on the space of interval-valued fuzzy numbers, a linear-programming algorithm is developed to estimate the interval-valued fuzzy coefficients of the model. The applicability of the proposed model is investigated by three real data sets on soil sciences and hydrology engineering. The predictive ability of the obtained models is evaluated by three goodness of fit indices. Moreover, cross-validation is employed for further evaluation of the models.