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Lower set-valued fuzzy topologies. (English) Zbl 0890.54005

The authors introduce a construction of an \((L,M)\)-topology in terms of a decreasing family of \((L,M)\)-topologies. It is shown that the level topologies of the resulting \((L,M)\)-topology can also be constructed from those of the members of the family. An \((L,M)\)-topology, a level \(L\)-topology, the construction as well as the result are generalizations of [A. P. Shostak, Mat. Vesn. 41, No. 1, 51-64 (1989; Zbl 0705.54007)]. Here instead of two unit intervals complete lattices \(L\), \(M\) with \(M\) completely distributive are used.

MSC:

54A40 Fuzzy topology

Citations:

Zbl 0705.54007
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References:

[1] Diskin Z., Topological Spaces and Mappings pp 59– (1985)
[2] Gierz G., A Compendium of Continuous Lattices (1980) · Zbl 0452.06001
[3] DOI: 10.1016/0020-0255(86)90040-X · Zbl 0614.54008
[4] Hamburg P., Conf. Nationale de Geometrie si Topologie, Iasi pp 215– (1984)
[5] DOI: 10.1016/0022-247X(80)90173-0 · Zbl 0462.54002
[6] Kubiak T., fuzzy topologies (1985)
[7] Kubiak T., (L, M)
[8] Matutu P. P., (L, M)-fuzzy topological (1992)
[9] DOI: 10.1090/S0002-9939-1953-0058568-4
[10] Šostak A. P., Serie II no 11 pp 89– (1985)
[11] Šostak A. P., Mat. Vesnik 41 pp 51– (1989)
[12] DOI: 10.1070/RM1989v044n06ABEH002295 · Zbl 0716.54004
[13] Šostak A. P., Rhodes University Preprint pp 1– (1993)
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