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Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

Author

Listed:
  • Irina Cristea

    (Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia)

  • Juš Kocijan

    (Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia
    Department of Systems and Control, Jožef Stefan Institut, Jamova Cesta 39, 1000 Ljubljana, Slovenia)

  • Michal Novák

    (Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 10, 61600 Brno, Czech Republic)

Abstract

The aim of this paper is to study, from an algebraic point of view, the properties of interdependencies between sets of elements (i.e., pieces of secrets, atmospheric variables, etc.) that appear in various natural models, by using the algebraic hyperstructure theory. Starting from specific examples, we first define the relation of dependence and study its properties, and then, we construct various hyperoperations based on this relation. We prove that two of the associated hypergroupoids are H v -groups, while the other two are, in some particular cases, only partial hypergroupoids. Besides, the extensivity and idempotence property are studied and related to the cyclicity. The second goal of our paper is to provide a new interpretation of the dependence relation by using elements of the theory of algebraic hyperstructures.

Suggested Citation

  • Irina Cristea & Juš Kocijan & Michal Novák, 2019. "Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures," Mathematics, MDPI, vol. 7(10), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:885-:d:269936
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    Cited by:

    1. Gerasimos G. Massouros & Christos G. Massouros, 2022. "State Machines and Hypergroups," Mathematics, MDPI, vol. 10(14), pages 1-25, July.

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