In this paper, notions of multi and soft multi LA-Γ-semigroup are defined. Some generalizations of certain operations on the families of the soft and fuzzy soft multisets are introduced. A concept of fuzzy multi LA-Γ-semigroup is presented. The concept of fuzzy soft multisets is applied to LA-Γ-semigroups and various characteristics of these all structures defined on LA-Γ-semigroups are investigated. Some properties of generalized operations on multi soft and fuzzy multi soft LA-Γ-semigroups are studied