id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4467	Ahn, Sun Shin; Roh, Eun Hwan ; Jun, Young Bae	Ideals in BE-algebras Based on Lukasiewicz Fuzzy Set	2022	14	.pdf	application/pdf	7097	396	95	Hence Lεψ(x∗y) ≥ t, and so x∗y ∈ ( Lεψ, t)∈. Let x, y ∈ X and t ∈ (0.5, 1] be such that x ∈ ( Lεψ, t)∈ and y ∈ ( Lεψ, t)∈. Then Lεψ(x) ≥ t and Lεψ(y) ≥ t, which imply from (19) that 0.5 < t ≤ min{ Lεψ(x), Lεψ(y)} ≤ max{ Lεψ((x ∗ (y ∗ z)) ∗ z), 0.5} for all z ∈ X. Hence ⟨1/max{ta, tb}⟩ ∈ Lεψ by (22), and thus 1 ∈ ( Lεψ,max{ta, tb})∈. Let x, y, z ∈ X be such that x ∗ (y ∗ z) ∈ ( Lεψ,max{ta, tb})∈ and y ∈ ( Lεψ,max{ta, tb})∈. Then Lεψ(x ∗ (y ∗ z)) ≥ max{ta, tb} > 1 − max{ta, tb} and Lεψ(y) ≥ max{ta, tb} > 1 − max{ta, tb}, that is, ⟨(x ∗ (y ∗ z))/max{ta, tb}⟩ q Lεψ and ⟨y/max{ta, tb}⟩ q Lεψ.	cache/ejpam-4467.pdf	txt/ejpam-4467.txt