On intuitionistic fuzzy version of Zadeh's extension principle

Abstract

In this paper, by using \alpha- and \beta-cuts approach and the intuitionistic fuzzy Zadeh’s extension principle, we have proved a result which reveals that the \alpha- and \beta-cuts of an intuitionistic fuzzy number obtained by the intuitionistic fuzzy Zadeh’s extension principle coincide with the images of the \alpha- and \beta-cuts by the crisp function. Then we have given a corollary about monotonicity of the extension principle. Finally, we have extended these results to IF_N(\mathbb{R}) \times IF_N(\mathbb{R}).