Bělohlávek, R. Fuzzy closure operators. (English) Zbl 0989.54006 J. Math. Anal. Appl. 262, No. 2, 473-489 (2001). 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. Reviewer: Bernhard Behrens (Göteborg) Cited in 2 ReviewsCited in 55 Documents 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. Keywords:fuzzy closure system; almost closed fuzzy set; subsethood degree; Galois connection PDF BibTeX XML Cite \textit{R. Bělohlávek}, J. Math. Anal. Appl. 262, No. 2, 473--489 (2001; Zbl 0989.54006) Full Text: DOI OpenURL References: [1] Bělohlávek, R., Fuzzy Galois connections, Math. logic quart., 45, 497-504, (1999) · Zbl 0938.03079 [2] R. Bělohlávek, Fuzzy closure operators. II. Induced relations, representation, and examples, submitted for publication. [3] Biacino, L.; Gerla, G., Closure systems and L-subalgebras, Inform. sci., 33, 181-195, (1984) · Zbl 0562.06004 [4] Biacino, L.; Gerla, G., An extension principle for closure operators, J. math. anal. appl., 198, 1-24, (1996) · Zbl 0855.54007 [5] Birkhoff, G., Lattice theory, Amer. math. soc., colloq. publ., 25, (1967), Amer. Math. Soc Providence [6] Gerla, G., Graded consequence relations and fuzzy closure operators, J. appl. non-classical logics, 6, 369-379, (1996) · Zbl 0872.03012 [7] G. Gerla, Fuzzy Logic, Kluwer Academic, Dordrecht, in press. [8] Goguen, J.A., L-fuzzy sets, J. math. anal. appl., 18, 145-174, (1967) · Zbl 0145.24404 [9] Hájek, P., Metamathematics of fuzzy logic, (1998), Kluwer Academic Dordrecht · Zbl 0937.03030 [10] Höhle, U., On the fundamentals of fuzzy set theory, J. math. anal. appl., 201, 786-826, (1996) · Zbl 0860.03038 [11] Ore, O., Galois connections, Trans. amer. math. soc., 55, 493-513, (1944) [12] Ward, M.; Dilworth, R.P., Residuated lattices, Trans. amer. math. soc., 45, 335-354, (1939) · Zbl 0021.10801 [13] Zadeh, L.A., Fuzzy sets, Inform. control, 8, 338-353, (1965) · Zbl 0139.24606 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.