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2014 Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle
Yaoyao Lan, Chunlai Mu
J. Appl. Math. 2014: 1-6 (2014). DOI: 10.1155/2014/956467


Let X denote a compact metric space and let f : XX 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.


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Yaoyao Lan. Chunlai Mu. "Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle." J. Appl. Math. 2014 1 - 6, 2014.


Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010807
MathSciNet: MR3193640
Digital Object Identifier: 10.1155/2014/956467

Rights: Copyright © 2014 Hindawi


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