A kind of fuzzy upper topology on L-preordered sets

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.

کلیدواژه ها:

Commutative unital quantale ، (Complete) L-(pre)ordered set ، Stratified L-filter ، Stratified L-topology ، Fuzzy S-upper topology ، Fuzzy Scott topology