A new method for computing continuous functions with fuzzy variable

Abstract

This study proposes a new method for computing f(U) where f is a real continuous function and U is a fuzzy interval. The computation of f(U) is performed by incorporating optimisation technique into Zadeh's extension principle. By discretising α up to n finite numbers, a set of n closed and bounded intervals is obtained. Here, the computation of f on closed and bounded intervals is the same idea of solving unconstrained optimisation problems. For every finite numbers of α, if the function to be optimised is unimodal, the authors apply Brent's method. One of the main advantages of using this method is that it does not require the calculation of derivative. In case where f is reduced to monotone or to a straight line, the optimal solutions are obtained at the endpoints of intervals. This new strategy gives better results and requires only few function evaluations. An example is provided to illustrate the effectiveness of the proposed method.