\(ILI\)-ideals and prime \(LI\)-ideals in lattice implication algebras.

DOI10.1016/S0020-0255(03)00159-2zbMath1040.03046OpenAlexW1966289666MaRDI QIDQ1425298

Yang Xu, Yong Lin Liu, Keyun Qin, San-Yang Liu

Publication date: 15 March 2004

Published in: Information Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0020-0255(03)00159-2

zbMATH Keywords

\(ILI\)-idealLattice implication algebraMaximal \(LI\)-idealPrime \(LI\)-ideal

Mathematics Subject Classification ID

Logical aspects of lattices and related structures (03G10)

Related Items (8)

Fuzzy prime Boolean filters and their operations in IMTL-algebras ⋮ On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras ⋮ Lattice implication ordered semigroups ⋮ Some kinds of falling fuzzy filters of lattice implication algebras ⋮ Fuzzy implicative and Boolean filters of \(R_{0}\) algebras ⋮ On fuzzy ordered semigroups. ⋮ Ultra LI-ideals in lattice implication algebras and MTL-algebras ⋮ On WLI-ideal space and the properties of WLI-ideals in lattice implication algebra (LIA)

Cites Work

• Filters and structure of lattice implication algebra
• Lattice-valued logic. An alternative approach to treat fuzziness and incomparability
• \(L\)-valued propositional logic \(L_{\text{vpl}}\)
• Fuzzy reasoning based on the extension principle
• \(\alpha\)-resolution principle based on first-order lattice-valued logic \(\text{LF}(X)\)
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