Abstract
The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. In this paper, using Atanassov idea, we continue the study on intuitionistic fuzzy sets in Γ-semihypergroups initiated recently by Ersoy and Davvaz [25]. We give some further properties of intuitionistic fuzzy Γ-hyperideals and intuitionistic fuzzy bi-Γ-hyperideals in a Γ-semihypergroup and use the intuitionistic fuzzy left, right, two-sided and bi-Γ-hyperideals to characterize some classes of Γ-semihypergroups. We introduce and study (λ, μ)-intuitionistic fuzzy Γ-hyperideals. We also introduce the notion of an intuitionistic fuzzy M (resp. N)-hypersystem of a Γ-semihypergroup and some properties of them are investigated.