Han, S., Lu, L. (2019). A kind of fuzzy upper topology on L-preordered sets. Iranian Journal of Fuzzy Systems, 16(1), 191-203. doi: 10.22111/ijfs.2019.4493

Sang-Eon Han; Ling-Xia Lu. "A kind of fuzzy upper topology on L-preordered sets". Iranian Journal of Fuzzy Systems, 16, 1, 2019, 191-203. doi: 10.22111/ijfs.2019.4493

Han, S., Lu, L. (2019). 'A kind of fuzzy upper topology on L-preordered sets', Iranian Journal of Fuzzy Systems, 16(1), pp. 191-203. doi: 10.22111/ijfs.2019.4493

Han, S., Lu, L. A kind of fuzzy upper topology on L-preordered sets. Iranian Journal of Fuzzy Systems, 2019; 16(1): 191-203. doi: 10.22111/ijfs.2019.4493

A kind of fuzzy upper topology on L-preordered sets

^{2}School of Mathematics and Science, Hebei GEO University, Shijiazhuang City, China

Abstract

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completely distributive L-ordered set, the fuzzy S-upper topology has a special base such that it looks like the usual upper topology on the set of real numbers. For every complete L-ordered set, the fuzzy S-upper topology coincides the fuzzy Scott topology.

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