Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle

Source abstract

Let X denote a compact metric space and let f : X → X be a continuous map. It is known that a discrete dynamical system ( X , f ) naturally induces its fuzzified counterpart, that is, a discrete dynamical system on the space of fuzzy compact subsets of X . In 2011, a new generalized form of Zadeh’s extension principle, so-called g -fuzzification, had been introduced by Kupka 2011. In this paper, we study the relations between Martelli’s chaotic properties of the original and g -fuzzified system. More specifically, we study the transitivity, sensitivity, and stability of the orbits in system ( X , f ) and its connections with the same ones in its g -fuzzified system.