Abstract
-groupoids (non-associative structure) 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
-groupoids called (
,
)-fuzzy bi-ideals, (
,
)-fuzzy interior ideals, (
̄,
̄)-fuzzy bi-ideals, and (
̄,
̄)-fuzzy interior ideals, where
,
∈{∈
,
, ∈
, ∈
} and
̄,
̄∈{⋶
,
, ⋶
, ⋶
}, with
≠∈
and
̄≠⋶
. An important milestone achieved by this paper is providing the connection between classical algebraic structures (ordinary bi-ideals, interior ideals) 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.