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Note on Aggregation Functions and Concept Forming Operators

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Book cover New Trends in Aggregation Theory (AGOP 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 981))

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Abstract

A certain connection between the theory of aggregation functions and the theory of concept lattices is discussed. We describe a generalization of residuated mappings, convenient for creating a monotone analogue of antitone concept lattices. Examples of such mappings are also presented.

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Notes

  1. 1.

    The authors are aware that this notion can be defined in other contexts under another name.

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Acknowledgments

The first author was supported by the Slovak Research and Development Agency under the contract no. APVV-16-0213. The second author was supported by the project of Grant Agency of the Czech Republic (GAČR) no. 18-06915S and by the Slovak Research and Development Agency under the contract no. APVV-16-0073. The third author was supported by the Slovak VEGA Grant 1/0365/19.

Author information

Authors and Affiliations

  1. Department of Cybernetics and Artificial Intelligence, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 04200, Košice, Slovakia

    Peter Butka

  2. Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Jozef Pócs

  3. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovakia

    Jozef Pócs

  4. Institute of Control and Informatization of Production Processes, BERG Faculty, Technical University of Košice, Boženy Němcovej 3, 043 84, Košice, Slovakia

    Jana Pócsová

Authors
  1. Peter Butka
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  2. Jozef Pócs
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  3. Jana Pócsová
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Corresponding author

Correspondence to Peter Butka .

Editor information

Editors and Affiliations

  1. Faculty of Science, Palacký University, Olomouc, Czech Republic

    Radomír Halaš

  2. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Marek Gagolewski

  3. Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

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Butka, P., Pócs, J., Pócsová, J. (2019). Note on Aggregation Functions and Concept Forming Operators. In: Halaš, R., Gagolewski, M., Mesiar, R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, vol 981. Springer, Cham. https://doi.org/10.1007/978-3-030-19494-9_26

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