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Linear Representation of Residuated Lattices

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Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 298))

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Abstract

We reconsider the notion of semilinear space and consider it as a couple of two semimodules connected by residuated scalar multiplications. We show that under certain conditions the semigroup of endomorphisms of a semilinear space is a residuated, commutative ℓ-monoid. By this, we obtain what can be regarded as a linear representation of a residuated, commutative ℓ-monoid.

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Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modeling, Centre of Excellence IT4Innovations, Division of the University of Ostrava, Ostrava, Czech Republic

    Irina Perfilieva

Authors
  1. Irina Perfilieva
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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. Université Pierre et Marie Curie - Paris6, CNRS UMR 7606, DAPA, LIP6 8, 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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Perfilieva, I. (2012). Linear Representation of Residuated Lattices. 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 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31715-6_23

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  • DOI: https://doi.org/10.1007/978-3-642-31715-6_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31714-9

  • Online ISBN: 978-3-642-31715-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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