Abstract
An ordered AG-groupoid can be referred to as a non-associativeordered semigroup, as the main di¤erence between an ordered semigroup and anordered AG-groupoid is the switching of an associative law. In this paper, wede ne the smallest left (right) ideals in an ordered AG-groupoid and use them tocharacterize a (2; 2)-regular class of a unitary ordered AG-groupoid along with itssemilattices and (2 ;2 _q)-fuzzy left (right) ideals. We also give the conceptof an ordered A*G**-groupoid and investigate its structural properties by usingthe generated ideals and (2 ;2 _q)-fuzzy left (right) ideals. These concepts willverify the existing characterizations and will help in achieving more generalizedresults in future works.
Highlights
(S, ◦e, ≤) becomes an ordered semigroup [17]
The concept of fuzzy sets was first proposed by Zadeh [19] in 1965, which has a wide range of applications in various fields such as computer engineering, artificial intelligence, control engineering, operation research, management science, robotics and many more
Murali [8] defined the concept of belongingness of a fuzzy point to a fuzzy subset under a natural equivalence on a fuzzy subset
Summary
The concept of fuzzy sets was first proposed by Zadeh [19] in 1965, which has a wide range of applications in various fields such as computer engineering, artificial intelligence, control engineering, operation research, management science, robotics and many more. [18] A fuzzy subset f of an ordered AG-groupoid S is called an (∈γ, ∈γ ∨qδ)-fuzzy left (right) ideal of S if for all a, b ∈ S and γ, δ ∈ [0, 1], the following conditions hold:. [18] Let f be a fuzzy subset of an ordered AG-groupoid S and γ, δ ∈ [0, 1], f is an (∈γ, ∈γ ∨qδ)-fuzzy left (right) ideal of S if and only if f satisfies the following conditions. On (2, 2)-regular ordered AG-groupoids via (∈γ, ∈γ ∨qδ)-fuzzy one-sided ideals By a unitary ordered AG-groupoid, we shall mean an ordered AG-groupoid with left identity unless otherwise satisfied
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