Martelli chaotic properties of a generalized form of Zadeh's extension principle

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. © 2014 yaoyao lan and chunlai mu.