| Authors: | Šešelja, Branimir Tepavčević, Andreja |
Affiliations: | Computer Science Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | Lattice-Valued Algebraic Structures Via Residuated Maps | Series/Report no.: | Studies in Computational Intelligence | First page: | 7 | Last page: | 13 | Related Publication(s): | Computational Intelligence and Mathematics for Tackling Complex Problems 3 | Conference: | 12th European Symposium on Computational Intelligence and Mathematics, ESCIM 2020, Budapest4-7 October 2020 | Issue Date: | 2022 | Rank: | M33 | ISBN: | 978-3-030-74969-9 | ISSN: | 1860-949X | DOI: | 10.1007/978-3-030-74970-5_2 | 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 Ω-algebras, with a special reference to separation property. |
Keywords: | Cuts | Lattice valued fuzzy algebraic structures | Residuated maps | Ω-algebras | Publisher: | Springer Link |
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