Fuzzy closure operators. (English) Zbl 0989.54006

For a set \(X\) and a complete residuated lattice \(L\), the author introduces and investigates graduated closure operators \(L^X\to L^X\), closure systems \(\subseteq L^X\) and systems of “almost closed fuzzy sets” \(L^X\to L\) in \(X\). He shows that they characterize each other and studies the relationship to fuzzy Galois connections.


54A40 Fuzzy topology
06A15 Galois correspondences, closure operators (in relation to ordered sets)
54A05 Topological spaces and generalizations (closure spaces, etc.)
03E72 Theory of fuzzy sets, etc.
Full Text: DOI


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