Stronger Forms of Sensitivity for Induced Fuzzified Map

Abstract

Every dynamical system on a compact metric space X induces a fuzzy dynamical system on the space of fuzzy sets , by Zadeh's extension principle. In this paper we consider stronger forms of sensitivity, viz. strong sensitivity, asymptotic sensitivity, syndetic sensitivity, multi-sensitivity and cofinite sensitivity. Some examples are given to expound the interrelation between them. Our main concern here is to find the relationship between f and in terms of these forms of sensitivity. We Prove that these forms of sensitivity for f partially imply the same for and in other way we also get partial induction.