Fuzzy ideals of ordered semigroups with fuzzy orderings
Keyword(s):
AbstractThe 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.
Keyword(s):
2020 ◽
Vol 13
(1)
◽
pp. 113-129
1970 ◽
Vol 68
(3)
◽
pp. 211-228
1968 ◽
Vol 8
(3)
◽
pp. 547-556
◽
Keyword(s):
Keyword(s):
2015 ◽
Vol 08
(01)
◽
pp. 1550001
Keyword(s):