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

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  • Yaoyao Lan
  • Chunlai Mu

Abstract

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.

Suggested Citation

  • Yaoyao Lan & Chunlai Mu, 2014. "Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-6, March.
    • Handle: RePEc:hin:jnljam:956467
    DOI: 10.1155/2014/956467
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