Let denote a compact metric space and let be a continuous map. It is known that a discrete dynamical system () naturally induces its fuzzified counterpart, that is, a discrete dynamical system on the space of fuzzy compact subsets of . In 2011, a new generalized form of Zadeh’s extension principle, so-called -fuzzification, had been introduced by Kupka 2011. In this paper, we study the relations between Martelli’s chaotic properties of the original and -fuzzified system. More specifically, we study the transitivity, sensitivity, and stability of the orbits in system () and its connections with the same ones in its -fuzzified system.
"Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle." J. Appl. Math. 2014 1 - 6, 2014. https://doi.org/10.1155/2014/956467