A novel connection between rough sets, hypergraphs and hypergroups

Abstract

This paper presents a general framework for the study of the relations between hypergraphs and hypergroups based on approximation operators. Indeed, by a given hypergraph [Formula: see text], an equivalence relation [Formula: see text] on the set of vertices and using the notion of lower and upper approximations, we investigate two new hyperoperations on the set of vertices. In particular, by considering certain conditions on the equivalence relation [Formula: see text], we obtain two related [Formula: see text]-groups and we prove some results in this respect.

Hypergroups constructed from hypergraphs

“…The connections between hyperstructure theory, binary relations and graph theory have been analyzed by many researchers (see for instance [4,6,[10][11][12][13][14][15][16][17]21]). In [4], Corsini present a commutative quasihypergroup H Γ associated to a given hypergraph Γ.…”

“…Further, they studied the degree hypergroupoid associated with cartesian product of hypergraphs. In [21], Maryati and Davvaz investigated a general framework for the study of the relations between hypergraphs and hypergroups based on approximation operators.…”