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.


54A40 Fuzzy topology


Zbl 0705.54007
Full Text: DOI


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