Abstract
The combination of rough set theory and algebraic systems provide more new interesting research topics, which have drawn attention of many mathematicians and computer scientists. In this paper, we study the roughness of sub Gamma-semihypergroups, Gamma-hyperideals and bi-Gamma-hyperideals in terms of set valued homomorphisms. We applied generalized lower and upper approximation operators to Gamma-semihypergroups. We proved that the generalized lower and upper approximations of a Gamma-hyperideal, by mean of a set valued mapping, is a Gamma-hyperideal which is an extended notion of rough Gamma-hyperideals introduced in [ 11]. Also we introduced the notion of generalized rough M-hypersystems and generalized rough N-hypersystems in Gamma-semihypergroups and proved that the generalized upper rough approximation of an M-hypersystem (resp., N-hypersystem) is an M-hypersystem (resp., N-hypersystem).