Double-framed soft set theory applied to Abel-Grassmann’s hypergroupoids

Abstract

In this paper, we apply the concept of double-framed soft sets to Abel-Grassmann’s hypergroupoids (AG-hypergroupoids). We define double-framed soft AG-hypergroupoids (DFS AG-hypergroupoids) and double-framed soft left (respectively, right) (briefly DFS-left (respectively, DFS-right)) hyperideals of AG-hypergroupoids. It is shown that an idempotent DFS-left hyperideal is a DFS-hyperideal. Also a DFS right hyperideal becomes DFS hyperideal when pure left identity is adjoined to an AG-hypergroupoid, but the converse is not true. We also discuss some properties of these hyperideals in regular AG-hypergroupoids.