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International Summer School on Aggregation Operators

AGOP 2017: Aggregation Functions in Theory and in Practice pp 138–146Cite as

Generalization of Czogała-Drewniak Theorem for n-ary Semigroups

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 581))

Abstract

We investigate n-ary semigroups as a natural generalization of binary semigroups. We refer it as a pair \((X,F_n)\), where X is a set and an n-associative function \(F_n:X^n\rightarrow X\) is defined on X. We show that if \(F_n\) is idempotent, n-associative function which is monotone in each of its variables, defined on an interval \(I\subset \mathbb {R}\) and has a neutral element, then \(F_n\) is combination of the minimum and maximum operation. Moreover we can characterize the n-ary semigroups \((I, F_n)\) where \(F_n\) has the previous properties.

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References

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Acknowledgements

The results based on the article [7], which is an extended version of the current paper. This research is partly supported by the internal research project R-AGR-0500-MRO3 of University of Luxembourg.

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Authors and Affiliations

  1. Université du Luxembourg, 2, l’Université L-4365, Avenue de l’Universite, Esch-sur-Alzette, Luxembourg

    Gergely Kiss

  2. Eötvös Loránd University, 1/C, HU-1117, Pázmány Péter sétány, Budapest, Hungary

    Gabor Somlai

Authors
  1. Gergely Kiss
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  2. Gabor Somlai
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Correspondence to Gergely Kiss .

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Editors and Affiliations

  1. School of Informatics, University of Skövde, Skövde, Sweden

    Vicenç Torra

  2. Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  3. KERMIT Research Unit Knowledge-based Systems, Ghent University, Ghent, Belgium

    Bernard De Baets

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Kiss, G., Somlai, G. (2018). Generalization of Czogała-Drewniak Theorem for n-ary Semigroups. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_14

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  • DOI: https://doi.org/10.1007/978-3-319-59306-7_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59305-0

  • Online ISBN: 978-3-319-59306-7

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