Characterizations of non-associative ordered semigroups by their fuzzy bi-ideals

Fuzzy Ideals on Ordered AG-Groupoids

“…In [25] An ordered AG-groupoid S, is a partially ordered set, at the same time an AG-groupoid such that a ≤ b, implies ac ≤ bc and ca ≤ cb for all a, b, c ∈ S. Two conditions are equivalent to the one condition We denote by L(a), S(a), I(a) the left ideal, the right ideal and the ideal of S, respectively generated by a. We have L(a) = {s ∈ S : s ≤ a or s ≤ xa for some x ∈ S} = (a ∪ Sa], S(a) = (a ∪ aS],…”

Anti Fuzzy Interior Ideals on Ordered AG-groupoids

“…In [31], an ordered AG-groupoid S, is a partially ordered set, at the same time an AGgroupoid such that a ≤ b, implies ac ≤ bc and ca ≤ cb for all a, b, c ∈ S. Two conditions are equivalent to the one condition (ca)d ≤ (cb)d, for all a, b, c, d ∈ S. An ordered AG-groupoid is also called a po-AG-groupoid for short. Example 1.…”

A Non-associative Ordered Semigroup Characterizated by Anti fuzzy Interior Ideals

“…In [31], an ordered AG-groupoid S, is a partially ordered set, at the same time an AGgroupoid such that a ≤ b, implies ac ≤ bc and ca ≤ cb for all a, b, c ∈ S. Two conditions are equivalent to the one condition (ca)d ≤ (cb)d, for all a, b, c, d ∈ S. An ordered AG-groupoid is also called a po-AG-groupoid for short. Then (S, •, ≤) is an ordered AG-groupoid with left identity e.…”