A New Approach for Computing Zadeh’s Extension Principle

Zadeh’s extension principle is one of the most fundamental principles in fuzzy set theory. It provides a powerful technique in order to extend a real continuous function to a function accepting fuzzy sets as arguments. If the function is monotone, then the endpoints of the output can be determined quite easily. However, the difficulty arises when the function is non-monotone. In that case, the computation of the output is not an easy task. The purpose of this paper is to provide a new method to reduce this difficulty. The method is based on the implementation of optimisation technique over the α-cuts of fuzzy set. By doing so, the endpoints of the output can be approximated. The method proposed in this paper is easy to implement and can be applied to many practical applications. Several examples are given to illustrate the effectiveness of the proposed method.