AbstractIn this paper, we introduce the notion of a fuzzy soft tri-ideal over Γ−semiring. We characterize the regular Γ−semiring in terms of fuzzy soft tri-ideals, and study some of the properties. M is a regular Γ−semiring, E be a parameters set and A ⊆ E. If (µ, A) is a fuzzy soft left tri-ideal over M, then (µ, A) is a fuzzy soft right ideal over M.