Rényi and Tsallis and Shannon entropies on D-posets

Article type: Research Article

Authors: Alizadeh, Leila^{; *} | Ebrahimi, Mohammad

Affiliations: Department of Mathematics, University of Shahid Bahonar, Kerman, Iran

Correspondence: [*] Corresponding author. Leila Alizadeh, Department of Mathematics, University of Shahid Bahonar, Kerman, Iran. E-mail: leilaalizadeh1985@gmail.com.

Abstract: This paper is devoted to introduce and study Rényi and Tsallis entropy, conditional Tsallis entropy and Tsallis mutual information of D-posets on a state s. Several relations between the conditional entropies are derived. Finally we define Tsallis entropy of dynamical system on D-posets and a new version of Kolmogorove-Sinai Theorem has been proved.

Keywords: D-poset, Tsallis entropy, Rényi entropy, dynamical systems, partition, s-generator

DOI: 10.3233/JIFS-17930

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 4, pp. 2771-2781, 2018