Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2014 (2014), Article ID 956467, 6 pages.
Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle
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.
J. Appl. Math., Volume 2014 (2014), Article ID 956467, 6 pages.
First available in Project Euclid: 2 March 2015
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Lan, Yaoyao; Mu, Chunlai. Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle. J. Appl. Math. 2014 (2014), Article ID 956467, 6 pages. doi:10.1155/2014/956467. https://projecteuclid.org/euclid.jam/1425305650