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

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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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Authors and Affiliations

  1. Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, 7616914111, Iran

    Adel Mehrpooya & MohammadReza Molaei

  2. Department of Mathematics, Faculty of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, Iran

    Yamin Sayyari

  3. Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, 7616914111, Iran

    MohammadReza Molaei

Authors
  1. Adel Mehrpooya
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  2. Yamin Sayyari
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  3. MohammadReza Molaei
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Correspondence to Adel Mehrpooya or MohammadReza Molaei.

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Communicated by A. Di Nola.

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Mehrpooya, A., Sayyari, Y. & Molaei, M. Algebraic and Shannon entropies of commutative hypergroups and their connection with information and permutation entropies and with calculation of entropy for chemical algebras. Soft Comput 23, 13035–13053 (2019). https://doi.org/10.1007/s00500-019-04314-7

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