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Published in:
01-03-2014 | Foundations
Characterization of extended filters in residuated lattices
Published in: Soft Computing | Issue 3/2014
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Abstract
We give a characterization theorem of extended filters on residuated lattices, from which many results are immediately obtained. We show that, for a bounded integral commutative residuated lattice X, (1) an extended filter \(E_F (B)\) associated with \(B\) is characterized by \(E_F (B) = [B) \rightarrow F\), where \(B\subseteq X\) and \(F\) is a filter of \(X\); (2) the class \(E(B)\) of all extended filters associated with \(B\) is a complete Heyting algebra. (3) the class \(S(B)\) of all stable filters relative to \(B\subseteq X\) is also a complete Heyting algebra.