The purpose of this paper is to introduce the notions of ∈, ∈ ∨qk-fuzzy ideals of a fuzzy ordered semigroup with the ordering being a fuzzy relation. Several characterizations of ∈, ∈ ∨qk-fuzzy left (resp. right) ideals and ∈, ∈ ∨qk-fuzzy interior ideals are derived. The lattice structures of all ∈, ∈ ∨qk-fuzzy (interior) ideals on such fuzzy ordered semigroup are studied and some methods are given to construct an ∈, ∈ ∨qk-fuzzy (interior) ideals from an arbitrary fuzzy subset. Finally, the characterizations of generalized semisimple fuzzy ordered semigroups in terms of ∈, ∈ ∨qk-fuzzy ideals (resp. ∈, ∈ ∨qk-fuzzy interior ideals) are developed.
@article{bwmeta1.element.doi-10_1515_math-2016-0076,
author = {Xiaokun Huang and Qingguo Li},
title = {Fuzzy ideals of ordered semigroups with fuzzy orderings},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {841-856},
zbl = {1354.06009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0076}
}
Xiaokun Huang; Qingguo Li. Fuzzy ideals of ordered semigroups with fuzzy orderings. Open Mathematics, Tome 14 (2016) pp. 841-856. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0076/