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On fuzzy LI-ideals in negative non-involutive residuated lattices. (Chinese. English summary) Zbl 1424.03065

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)
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