Soft Computing

, Volume 23, Issue 24, pp 13035–13053 | Cite as

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

  • Adel MehrpooyaEmail author
  • Yamin Sayyari
  • MohammadReza MolaeiEmail author


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.


Algebraic entropy Shannon entropy Chemical algebra Information source Hypergroupoid Hyperdynamical system 


Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mahani Mathematical Research CenterShahid Bahonar University of KermanKermanIran
  2. 2.Department of Mathematics, Faculty of Mathematics and Computer ScienceSirjan University of TechnologySirjanIran
  3. 3.Department of Pure Mathematics, Faculty of Mathematics and ComputerShahid Bahonar University of KermanKermanIran

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