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Lattice-Valued Algebraic Structures Via Residuated Maps

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Computational Intelligence and Mathematics for Tackling Complex Problems 3

Part of the book series: Studies in Computational Intelligence ((SCI,volume 959))

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Abstract

It is proved recently that cuts of a lattice valued fuzzy set determine a residuated map from the codomain lattice to the power set of the domain ordered dually to inclusion. Conversely, every residuated map from a complete lattice to the power set of the domain determines a lattice valued fuzzy set whose cuts coincide with the values of that map. These connections are applied here to the lattice valued algebraic structures and in particular to \(\varOmega \)-algebras, with a special reference to separation property.

Partially supported by Ministry of Education, Science and Technological Development, Republic of Serbia through Mathematical Institute SASA and Faculty of Science, University of Novi Sad and by the European Cooperation in Science and Technology (COST) Action CA17124.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia

    Branimir Šešelja & Andreja Tepavčević

  2. Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001, Belgrade, Serbia

    Andreja Tepavčević

Authors
  1. Branimir Šešelja
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  2. Andreja Tepavčević
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Corresponding author

Correspondence to Andreja Tepavčević .

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Editors and Affiliations

  1. Department of Mathematics and Computational Sciences, Széchenyi István University, Győr, Hungary

    István Á. Harmati

  2. Department of Information Technology, Széchenyi István University, Győr, Hungary

    László T. Kóczy

  3. Department of Mathematics, Science Faculty, Universidad de Cádiz, Cádiz, Spain

    Jesús Medina

  4. Department of Mathematics, Faculty of Economics and Business, University of Cádiz, Cádiz, Spain

    Eloísa Ramírez-Poussa

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Šešelja, B., Tepavčević, A. (2022). Lattice-Valued Algebraic Structures Via Residuated Maps. In: Harmati, I.Á., Kóczy, L.T., Medina, J., Ramírez-Poussa, E. (eds) Computational Intelligence and Mathematics for Tackling Complex Problems 3. Studies in Computational Intelligence, vol 959. Springer, Cham. https://doi.org/10.1007/978-3-030-74970-5_2

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