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Ordering in the Algebraic Hyperstructure Theory: Some Examples with a Potential for Applications in Social Sciences

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Book cover Models and Theories in Social Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 179))

Abstract

In this chapter we include several examples of concepts of the algebraic hyperstructure theory, which are all based on the concept of ordering. We also show how these concepts could be linked. The reason why we make this selection, is the fact that, in social sciences, objects are often linked in two different ways, which can be represented by an operation (or a hyperoperation) and a relation. The algebraic hyperstructure theory is useful in considerations of social sciences because, in this theory, the result of an interaction of two objects is, generally speaking, a set of objects instead of one particular object.

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Notes

  1. 1.

    We use the name “extensive” as this can be found in a number of works by Chvalina and / or his students and collaborators. However, some authors, such as Massouros, use a much more suitable name “closed” as this can be easily contrasted with “open” in the geometrical sense. For basic definitions see e.g. Massouros (2016), Massouros and Massouros (2011), Massouros (1999).

  2. 2.

    Notice that the lower index “n” in “\(\le _n\)” stands for “new” to distinguish (19) from (12), which is defined by means of \(x*y=0\).

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic

    Michal Novák

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  1. Michal Novák
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Correspondence to Michal Novák .

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Editors and Affiliations

  1. Faculty of Mathematics and Computer Science, Ovidius University of Constanţa, Constanţa, Romania

    Cristina Flaut

  2. Department of Mathematics and Physics, Faculty of Military Technology, University of Defence, Brno, Czech Republic

    Šárka Hošková-Mayerová

  3. Faculty of History and Political Science, Ovidius University of Constanţa, Constanţa, Romania

    Daniel Flaut

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Novák, M. (2019). Ordering in the Algebraic Hyperstructure Theory: Some Examples with a Potential for Applications in Social Sciences. In: Flaut, C., Hošková-Mayerová, Š., Flaut, D. (eds) Models and Theories in Social Systems. Studies in Systems, Decision and Control, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-030-00084-4_28

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