Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Residuated Lattice

  • Vilém Novák
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_5009

Synonyms

Structure of truth values

Definition

The residuated lattice is a basic algebraic structure accepted as a structure of truth values for fuzzy logic and fuzzy set theory. In general, it is an algebra
$$ \left\langle L,\vee, \wedge, \otimes, \to, 0,1\right\rangle $$
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Recommended Reading

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    Esteva F, Godo L. Monoidal t-norm based logic: towards a logic for left-continuous t-norms. Fuzzy Set Syst. 2001;124(3):271–88.MathSciNetzbMATHCrossRefGoogle Scholar
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    Hájek P. Metamathematics of fuzzy logic. Dordrecht: Kluwer; 1998.zbMATHCrossRefGoogle Scholar
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    Klement EP, Mesiar R, Pap E. Triangular norms. Dordrecht: Kluwer; 2000.zbMATHCrossRefGoogle Scholar
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    Novák V, Perfilieva I, Močkoř J. Mathematical principles of fuzzy logic. Boston/Dordrecht: Kluwer; 1999.zbMATHCrossRefGoogle Scholar
  5. 5.
    Gottwald S. A treatise on many-valued logics. Baldock, Herfordshire: Research Studies; 2001.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Research and Applications of Fuzzy ModelingUniversity of OstravaOstravaCzech Republic