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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 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.

Suggested Citation

  • Yaoyao Lan & Chunlai Mu, 2014. "Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:956467
    DOI: 10.1155/2014/956467
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    References listed on IDEAS

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    1. Yaoyao Lan & Qingguo Li & Chunlai Mu & Hua Huang, 2012. "Some Chaotic Properties of Discrete Fuzzy Dynamical Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Román-Flores, Heriberto & Chalco-Cano, Y., 2005. "Robinson’s chaos in set-valued discrete systems," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 33-42.
    3. Yaoyao Lan & Qingguo Li & Chunlai Mu & Hua Huang, 2012. "Some Chaotic Properties of Discrete Fuzzy Dynamical Systems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, December.
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