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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.

MSC:

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.
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References:

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