<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Our objective in this paper is to define and study the Rényi entropy and the Rényi divergence in the intuitionistic fuzzy case. We define the Rényi entropy of order of intuitionistic fuzzy experiments (which are modeled by IF-partitions) and its conditional version and we examine their properties. It is shown that the suggested concepts are consistent, in the case of the limit of <italic>q</italic> going to 1, with the Shannon entropy of IF-partitions. In addition, we introduce and study the concept of Rényi divergence in the intuitionistic fuzzy case. Specifically, relationships between the Rényi divergence and Kullback-Leibler divergence and between the Rényi divergence and the Rényi entropy in the intuitionistic fuzzy case are studied. The results are illustrated with several numerical examples.</p></abstract>

Our objective in this paper is to define and study the Rényi entropy and the Rényi divergence in the intuitionistic fuzzy case. We define the Rényi entropy of order of intuitionistic fuzzy experiments (which are modeled by IF-partitions) and its conditional version and we examine their properties. It is shown that the suggested concepts are consistent, in the case of the limit of q going to 1, with the Shannon entropy of IF-partitions. In addition, we introduce and study the concept of Rényi divergence in the intuitionistic fuzzy case. Specifically, relationships between the Rényi divergence and Kullback-Leibler divergence and between the Rényi divergence and the Rényi entropy in the intuitionistic fuzzy case are studied. The results are illustrated with several numerical examples.

Rényi Entropy and Rényi Divergence in the Intuitionistic Fuzzy Case

Institute of Mathematics, Slovak Academy of Sciences

Department of Mathematics, Faculty of Natural Sciences

Institute of Mathematics, Faculty of Natural Sciences CPU

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Rényi Entropy and Rényi Divergence in the Intuitionistic Fuzzy Case"}

Our objective in this paper is to define and study the Rényi entropy and the Rényi divergence in the intuitionistic fuzzy case. We define the Rényi entropy of...

Rényi Entropy and Rényi Divergence in the Intuitionistic Fuzzy Case

Published Online: Mar 12, 2019

Page range: 77 - 105

Received: Oct 09, 2018

DOI: https://doi.org/10.2478/tmmp-2018-0023

Keywords
intuitionistic fuzzy event, IF-partition, Rényi entropy, Rényi conditional entropy, Rényi divergence

© 2018 Beloslav Riečan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Rényi Entropy and Rényi Divergence in the Intuitionistic Fuzzy Case

Published Online: Mar 12, 2019

Page range: 77 - 105

Received: Oct 09, 2018

DOI: https://doi.org/10.2478/tmmp-2018-0023

Keywordsintuitionistic fuzzy event, IF-partition, Rényi entropy, Rényi conditional entropy, Rényi divergence

© 2018 Beloslav Riečan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
intuitionistic fuzzy event, IF-partition, Rényi entropy, Rényi conditional entropy, Rényi divergence