In this paper we define the concept of fuzzy set valued homomorphism of LA-Γ-semigroups and mention some features of them. We also investigate the approximations of a generalized fuzzy approximation space constructed on LA-Γ-semigroups and derived by fuzzy set valued homomorphisms of LA-Γ-semigroups. Especially, we focus on some algebraic properties of fuzzy subsets in terms of protection of some properties under these approximations.
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