Abstract

AG-groupoids are basic structures in Flocks theory. This theory mainly focuses on distance optimization, motion replication, and leadership maintenance with a wide range of applications in physics and biology. In this paper, we define some new types of fuzzy ideals of AG-groupoids called -fuzzy bi-ideals, -fuzzy interior ideals, -fuzzy bi-ideals, and -fuzzy interior ideals, where α, β∈{∈γ, qδ, ∈γ∨qδ, ∈γ∧qδ} and ᾱ, β̄∈{⋶γ, q̄δ, ⋶γ∨q̄δ, ⋶γ∧q̄δ}, with α≠∈γ∧qδ and β̄≠⋶γ∧q̄δ. An important milestone achieved by this paper is providing the connection between classical algebraic structures and new types of fuzzy algebraic structures [-fuzzy bi-ideals, -fuzzy interior ideals]. Special attention is given to -fuzzy bi-ideals and -fuzzy bi-ideals.