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Closure systems and L-subalgebras. (English) Zbl 0562.06004

A subset of a complete lattice is called a closure system if it is closed under the inf-operation. In the lattice of L-fuzzy sets [cf. J. A. Goguen, J. Math. Anal. Appl. 18, 145-174 (1967; Zbl 0145.244)] many closure systems can be described by systems of inequalities, which lead to the simple computation of the respective closure operation. The authors have collected a long list of L-fuzzy subalgebras which are defined by suitable systems of inequalities (and therefore form closure systems), and they have obtained certain formulas for the determination of the respective generated L-fuzzy algebras.
Reviewer: J.Drewniak

MSC:

06B23 Complete lattices, completions
06A15 Galois correspondences, closure operators (in relation to ordered sets)
08A30 Subalgebras, congruence relations

Citations:

Zbl 0145.244
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References:

[1] Anthony, J.M.; Sherwood, H., Fuzzy groups redefined, J. math. anal. appl., 69, 124-130, (1979) · Zbl 0413.20041
[2] Anthony, J.M.; Sherwood, H., A characterization of fuzzy subgroups, Fuzzy sets and systems, 7, 297-305, (1982) · Zbl 0524.20050
[3] Capocelli, R.M., On some free subsemigroups of a free semigroup, (), 125-135 · Zbl 0393.20042
[4] G. Gerla, L-subsemigroups of a free semigroup, Rend. Mat., to appear. · Zbl 0631.20048
[5] G. Gerla, Pavelka’s fuzzy logic and free L-subsemigroups, Z. Math. Logik Grundlag. Math., to appear. · Zbl 0584.03015
[6] G. Gerla, Generalized fuzzy points, J. Math. Anal. Appl., to appear. · Zbl 0659.54003
[7] G. Gerla, Codex theory and fuzzy subsemigroups, manuscript. · Zbl 0634.94027
[8] Goguen, J.A., L-fuzzy sets, J. math. anal. appl., 18, 145-171, (1967) · Zbl 0145.24404
[9] Gratzer, G., Universal algebra, (1968), Van Nostrand · Zbl 0182.34201
[10] Negoita, C.V.; Ralescu, D.A., Applications of fuzzy sets to systems analysis, (1975), Birkhäuser Basel · Zbl 0326.94002
[11] Kuroki, N., Fuzzy semiprime ideals in semigroups, Fuzzy sets and systems, 8, 71-79, (1972) · Zbl 0488.20049
[12] Kuroki, N., On fuzzy bi-ideals in semigroups, Comment. math. univ. st. paul., 28, 17-21, (1979) · Zbl 0428.20041
[13] Kuroki, N., On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy sets and systems, 5, 203-215, (1981) · Zbl 0452.20060
[14] Liu, W., Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and systems, 8, 133-139, (1982) · Zbl 0488.20005
[15] Rosenfeld, A., Fuzzy groups, J. math. anal. appl., 35, 512-517, (1971) · Zbl 0194.05501
[16] Das, P.Sivaramakrishna, Fuzzy groups and level subgroups, J. math. anal. appl., 84, 264-269, (1981) · Zbl 0476.20002
[17] Spehner, J.C., Quelques constructions et algorithmes relatifs aux sous-monoïdes d’un monoïde libre, (), 334-353 · Zbl 0298.20046
[18] Tilson, B., The intersection of free submonoids of a free monoid is free, (), 345-350 · Zbl 0261.20060
[19] Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
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