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Information Journal Paper

Title

Sensitivity and strong sensitivity on induced dynamical systems

Pages

  69-78

Abstract

 Given a metric space X, we consider the family of all normal upper semicontinuous Fuzzy sets on X, denoted by F(X), and a discrete dynamical system (X; f). In this paper, we study when (F(X); b f) is (strongly) sensitive, where b f is the Zadeh's extension of f and F(X) is equipped with different metrics: The uniform metric, the Skorokhod metric, the sendograph metric and the endograph metric. We prove that the sensitivity in the induced dynamical system (K(X); f) is equivalent to the sensitivity in b f: F(X)! F(X) with respect to the uniform metric, the Skorokhod metric and the sendograph metric. We also show that the following conditions are equivalent: a) (X; f) is strongly sensitive; b) (F(X); b f) is strongly sensitive, where F(X) is equipped with the uniform metric; c) (F(X); b f) is strongly sensitive, where F(X) is equipped with the Skorokhod metric; d) (F(X); b f) is strongly sensitive, where F(X) is equipped with the sendograph metric.

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    • Cite

    APA: Copy

    Jardon, D., & SANCHEZ, I.. (2021). Sensitivity and strong sensitivity on induced dynamical systems. IRANIAN JOURNAL OF FUZZY SYSTEMS, 18(4 ), 69-78. SID. https://sid.ir/paper/413970/en

    Vancouver: Copy

    Jardon D., SANCHEZ I.. Sensitivity and strong sensitivity on induced dynamical systems. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2021;18(4 ):69-78. Available from: https://sid.ir/paper/413970/en

    IEEE: Copy

    D. Jardon, and I. SANCHEZ, “Sensitivity and strong sensitivity on induced dynamical systems,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 18, no. 4 , pp. 69–78, 2021, [Online]. Available: https://sid.ir/paper/413970/en

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