Abstract
We study several degrees in defining a fuzzy positive implicative filter, which is a generalization of a fuzzy filter in BE-algebras.
Highlights
We study several degrees in defining a fuzzy positive implicative filter, which is a generalization of a fuzzy filter in BE-algebras
We introduce a relation “≤” on a BE-algebra X by x ≤ y, if and only if x∗y = 1
A fuzzy subset μ of a BE-algebra X is called a fuzzy filter of X with degree (λ, κ), if it satisfies the following: (e1) (∀x ∈ X)(μ(1) ≥ λμ(x)), (e2) (∀x, y ∈ X)(μ(x) ≥ κ min{μ(y ∗ x), μ(y)})
Summary
A nonempty subset F of X is called a positive implicative filter of a BE-algebra X if it satisfies (F1) and (F4) x ∗ ((y ∗ z) ∗ y) ∈ F and x ∈ F imply y ∈ F, for all x, y, z ∈ X. A fuzzy subset μ of a BE-algebra X is called a fuzzy positive implicative filter of X, if it satisfies (d1) and (d4) μ(y) ≥ min{μ(x∗((y∗z)∗y)), μ(x)}, for all x, y ∈ X.
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