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04-09-2019 | Foundations

Algebraic and Shannon entropies of commutative hypergroups and their connection with information and permutation entropies and with calculation of entropy for chemical algebras

Authors: Adel Mehrpooya, Yamin Sayyari, MohammadReza Molaei

Published in: Soft Computing | Issue 24/2019

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Abstract

Studying the evolution of a system and dealing with its complexity are key issues in analyzing and predicting its future behavior. In this respect, the uncertainty problem for a wide variety of mathematical structures such as hyper MV–algebras and stochastic processes (information sources) that provide models for varied systems has been studied. This paper presents the algebraic and Shannon entropies for hypergroupoids and commutative hypergroups, respectively, and studies their fundamental properties. These notions are established in a way that they are technically feasible to be adapted to other algebraic hyperstructures. Moreover, it is investigated that how these two types of entropies are connected for the case of commutative hypergroups. In addition, conditions under which the algebraic entropy is connected with the information and permutation entropies are detected. In the end, the algebraic entropy is calculated for some hypergroupoids and chemical algebras.

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Title: Algebraic and Shannon entropies of commutative hypergroups and their connection with information and permutation entropies and with calculation of entropy for chemical algebras
Authors: Adel Mehrpooya
Yamin Sayyari
MohammadReza Molaei
Publication date: 04-09-2019
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 24/2019
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-019-04314-7

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