We firstly generalize the fuzzy way-below relation on an L-poset, and consider its continuity by means of this relation. After that, we introduce a kind of stratified L-generalized convergence structure on an L-poset. In terms of that, L-fuzzy Scott topology and fuzzy Scott topology are considered, and the properties of fuzzy Scott topology are discussed in detail. At last, we investigate the Scott convergence of stratified L-filters on an L-poset, and show that an L-poset is continuous if and only if the Scott convergence on it coincides with the convergence with respect to the corresponding topological space.
@article{bwmeta1.element.doi-10_1515_math-2017-0067,
author = {Hongping Liu and Ling Chen},
title = {Scott convergence and fuzzy Scott topology onL-posets},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {815-827},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0067}
}
Hongping Liu; Ling Chen. Scott convergence and fuzzy Scott topology onL-posets. Open Mathematics, Tome 15 (2017) pp. 815-827. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0067/