## Journal of Applied Mathematics

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

#### Abstract

Let $X$ denote a compact metric space and let $f : X\to X$ 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.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 956467, 6 pages.

Dates
First available in Project Euclid: 2 March 2015

https://projecteuclid.org/euclid.jam/1425305650

Digital Object Identifier
doi:10.1155/2014/956467

Mathematical Reviews number (MathSciNet)
MR3193640

Zentralblatt MATH identifier
07010807

#### Citation

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

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