Taylor Expansion on the Fuzzy Number Space

Abstract

It is well known that fuzzy mapping plays an important and fundamental role in fuzzy analysis. In this paper, we attempt to determine extensive classes of these fuzzy mappings that are represented by their Taylor expansion. We have first obtained that the continuous function f(x) can transform a fuzzy mapping f(u) using the extension principle. And we discuss some properties of the series of fuzzy numbers. From these properties we have seen that f(u) has the property of being analytic for the analytic function f(x). Finally as applications, we give some examples.