Journal of Applied Mathematics

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

Yaoyao Lan and Chunlai Mu

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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.

Article information

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

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
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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