Incorporating optimisation technique into Zadeh’s extension principle for computing non-monotone functions with fuzzy variable

Abstract

This paper proposes a new computational method for computing non-monotone functions that take a fuzzy interval as their arguments. The proposed method represents an implementation of optimisation technique into Zadeh’s extension principle. By taking into account the dependency problem that exists in fuzzy environment, the proposed method can avoid the effect of overestimation in computation. This problem usually arises when the same fuzzy interval is computed separately in fuzzy interval computation. The proposed method is simple to use and can be implemented in many practical applications. In order to show the capability of the proposed method, several non-monotone functions with trapezoidal fuzzy intervals are studied.