Bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate multiplicative interior and additive closure operators (mi- and ac-operators) generalizing topological interior and closure operators on such algebras. We describe connections between mi- and ac-operators, and for residuated lattices with Glivenko property we give connections between operators on them and on the residuated lattices of their regular elements.
@article{bwmeta1.element.doi-10_2478_s11533-013-0349-y,
author = {Ji\v r\'\i\ Rach\r unek and Zden\v ek Svoboda},
title = {Interior and closure operators on bounded residuated lattices},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {534-544},
zbl = {06271176},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0349-y}
}
Jiří Rachůnek; Zdeněk Svoboda. Interior and closure operators on bounded residuated lattices. Open Mathematics, Tome 12 (2014) pp. 534-544. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0349-y/
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