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Web-Geometric View on Uninorms and Structure of Some Special Classes

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Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 299))

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Abstract

This paper studies the relation between associativity of uninorms and geometry of their level sets which is enabled by adopting the concepts of web geometry, a branch of differential geometry, and the Reidemeister closure condition. Based on this result, the structure of some special classes of uninorms is described. Namely, it is the class of uninorms with involutive underlying t-norms and t-conorms and the class of uninorms with involutive underlying t-norms and idempotent underlying t-conorm (as well as the corresponding dual cases).

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic

    Milan Petrík

  2. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic

    Milan Petrík

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

    Radko Mesiar

  4. Centre of Excellence IT4Innovations, Division of the University of Ostrava, IRAFM, Ostrava, Czech Republic

    Radko Mesiar

Authors
  1. Milan Petrík
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  2. Radko Mesiar
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute — IONA College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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Petrík, M., Mesiar, R. (2012). Web-Geometric View on Uninorms and Structure of Some Special Classes. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31718-7_39

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  • DOI: https://doi.org/10.1007/978-3-642-31718-7_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31717-0

  • Online ISBN: 978-3-642-31718-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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