Liu, Chunhui On fuzzy LI-ideals in negative non-involutive residuated lattices. (Chinese. English summary) Zbl 1424.03065 Fuzzy Syst. Math. 32, No. 1, 66-76 (2018). Summary: In this paper, we further study the problem of fuzzy LI-ideals in negative non-involutive residuated lattices by using the principle and method of fuzzy sets and analysis. It is proved that the set of all fuzzy LI-ideals \(\mathbf{FLI} (L)\) in a given negative non-involutive residuated lattice \(L\), under fuzzy set-inclusion order \(\subseteq\), forms a complete Heyting algebra. Finally, a representation theorem of implication in the complete Heyting algebra \( (\mathbf{FLI} (L),\subseteq)\) is given. MSC: 03G10 Logical aspects of lattices and related structures 06B10 Lattice ideals, congruence relations 06D20 Heyting algebras (lattice-theoretic aspects) Keywords:negative non-involutive residuated lattice; fuzzy LI-ideal; complete Heyting algebra; implication operator PDFBibTeX XMLCite \textit{C. Liu}, Fuzzy Syst. Math. 32, No. 1, 66--76 (2018; Zbl 1424.03065)