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Rényi entropy of fuzzy dynamical systems

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  • Eslami Giski, Zahra
  • Ebrahimzadeh, Abolfazl
  • Markechová, Dagmar

Abstract

The present paper is devoted to the study of Rényi entropy in the fuzzy case. We define the Rényi entropy of a fuzzy partition and its conditional version and derive basic properties the suggested entropy measures. In particular, it was shown that the Rényi entropy of a fuzzy partition is monotonically decreasing. Consequently, using the proposed concept of Rényi entropy, the notion of Rényi entropy of a fuzzy dynamical system is introduced. Finally, it is proved that the Rényi entropy of a fuzzy dynamical system is invariant under isomorphism of fuzzy dynamical systems.

Suggested Citation

  • Eslami Giski, Zahra & Ebrahimzadeh, Abolfazl & Markechová, Dagmar, 2019. "Rényi entropy of fuzzy dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 244-253.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:244-253
    DOI: 10.1016/j.chaos.2019.01.039
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    References listed on IDEAS

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    1. Oikonomou, Thomas & Tirnakli, Ugur, 2009. "Generalized entropic structures and non-generality of Jaynes’ Formalism," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3027-3034.
    2. Stefanini, Luciano & Sorini, Laerte & Guerra, Maria Letizia, 2006. "Simulation of fuzzy dynamical systems using the LU-representation of fuzzy numbers," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 638-652.
    3. Li, Lixiang & Yang, Yixian & Peng, Haipeng, 2009. "Fuzzy system identification via chaotic ant swarm," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 401-409.
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