Fuzzy ideals of ordered semigroups with fuzzy orderings

Xiaokun Huang, and Qingguo Li. "Fuzzy ideals of ordered semigroups with fuzzy orderings." Open Mathematics 14.1 (2016): 841-856. <http://eudml.org/doc/287089>.

@article{XiaokunHuang2016,
abstract = {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.},
author = {Xiaokun Huang, Qingguo Li},
journal = {Open Mathematics},
keywords = {Fuzzy set, (∈, ∈ ∨qk)-Fuzzy ideal; (∈, ∈ ∨qk)-Fuzzy interior ideal; Generalized semisimple fuzzy ordered semigroup; fuzzy set; -fuzzy ideal; -fuzzy interior ideal; generalized semisimple fuzzy ordered semigroup},
language = {eng},
number = {1},
pages = {841-856},
title = {Fuzzy ideals of ordered semigroups with fuzzy orderings},
url = {http://eudml.org/doc/287089},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Xiaokun Huang
AU - Qingguo Li
TI - Fuzzy ideals of ordered semigroups with fuzzy orderings
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 841
EP - 856
AB - 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.
LA - eng
KW - Fuzzy set, (∈, ∈ ∨qk)-Fuzzy ideal; (∈, ∈ ∨qk)-Fuzzy interior ideal; Generalized semisimple fuzzy ordered semigroup; fuzzy set; -fuzzy ideal; -fuzzy interior ideal; generalized semisimple fuzzy ordered semigroup
UR - http://eudml.org/doc/287089
ER -