On modeling regression in full interval-valued fuzzy environment

Abstract

We apply the general extension-principle-based approach to make predictions based on a regression model in a full interval-valued fuzzy environment. We use triangular interval-valued fuzzy numbers that model the uncertainty of the observed inputs and outputs to derive the predicted outputs in full accordance with Zadeh's extension principle. On one side, we enhance the Monte Carlo based algorithm introduced in the literature for simulating the output predictions of a fuzzy regression model by reducing the universe of random selections still keeping the accuracy of the empirical results; and on the other side, we solve quadratic models to derive the left endpoints of the α-cut intervals of the exact results. We use one real-life problem from hydrology engineering with data recalled from the literature to carry out numerical experiments and illustrate our proposed methodology.