Generalized Rough Γ-Hyperideals in Γ-Semihypergroups

Abstract

Davvaz (2008) introduced the concept of set-valued homomorphism and $T$-rough sets in a group. In this paper, we consider the set-valued homomorphism $\mathrm{T}$ on $\mathrm{\Gamma }$-semihypergroup $H$ to interpret the lower and upper approximations. We study the roughness of $(\mathrm{m},\mathrm{n})$ bi-$\mathrm{\Gamma }$-hyperideals and $(\mathrm{m},\mathrm{n})$ quasi-$\mathrm{\Gamma }$-hyperideals in terms of set-valued homomorphisms, which are extended notions of $(\mathrm{m},\mathrm{n})$ bi-$\mathrm{\Gamma }$-hyperideals and $(\mathrm{m},\mathrm{n})$ quasi-$\mathrm{\Gamma }$-hyperideals of $\mathrm{\Gamma }$-semihypergroups.