Entropy of Dynamical Systems on Interval-Valued Intuitionistic Fuzzy Sets

Zohreh Nazari, Batool Mosapour (), Elham Zangiabadi () and Abolfazl Ebrahimzadeh ()
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Zohreh Nazari: Department of Mathematics, Vali-e-Asr, University of Rafsanjan, Rafsanjan, Iran
Batool Mosapour: Department of Mathematics, Farhangian, University, Kerman, Iran
Elham Zangiabadi: Department of Mathematics, Vali-e-Asr, University of Rafsanjan, Rafsanjan, Iran
Abolfazl Ebrahimzadeh: Young Researchers and Elite Club, Zahedan Branch, Islamic Azad University, Zahedan, Iran

New Mathematics and Natural Computation (NMNC), 2023, vol. 19, issue 02, 541-556

Abstract: In this work, we introduce the concepts of Shannon entropy and conditional entropy of experiments in the interval-valued intuitionistic fuzzy case, and study the basic properties of the information measures. Subsequently, by means of the suggested notion of entropy of partitions, we define the entropy of a dynamical system on interval-valued intuitionistic fuzzy sets (IVIF). A version of the Kolmogorov–Sinai theorem on generators for dynamical systems on the IVIF is proved. It is shown that this entropy is an invariant under isomorphisms of interval-valued intuitionistic fuzzy dynamical systems; thus, we obtain a tool for distinguishing some non-isomorphic interval-valued intuitionistic fuzzy dynamical systems. The proposed measure can be used as a measure of information of experiment whose outcomes are interval-valued intuitionistic fuzzy events.

Keywords: Interval-valued intuitionistic fuzzy set; Shannon entropy; conditional entropy; dynamical system (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S1793005723500217

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