Infinite Series 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 first obtain that a continuous function f (x) can be transformed into a fuzzy mapping f (u) by using the extension principle. Furthermore we discuss some properties of the series of fuzzy numbers. From these properties we get that f (u) has the analytic properties similar to those of the analytic function f (x). Finally as applications, the author gives some examples.