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In this paper, we have decomposed an AG-groupoid. Let S be an AG-groupoid with left identity and a relation γ be defined on S as: aγb if and only if there exist positive integers m and n such that b m ∈ (Sa)S and a n ∈ (Sb)S for all a and b in S. We have proved that S/γ is a maximal separative semilattice homomorphic image of S. Every AG-groupoid S is uniquely expressible as a semilattice Y of archimedean AG-groupoids S α (α ∈ Y ). The semilattice Y is isomorphic to S/γ and the S α (α ∈ Y ) are the equivalence classes of S mod γ.

In this paper, we introduce complex fuzzy soft matrices and define some new operations on these matrices. Moreover we develop an algorithm using complex fuzzy soft matrices and apply it to a decision making problem in signal processing.

In this study, we have introduced the notion of Γ-fuzzification in Γ-AG-groupoids which is in fact the generalization of fuzzy AG-groupoids. We have studied several properties of an intra-regular Γ-AG **-groupoids in terms of fuzzy Γ-left (right, two-sided, quasi, interior, generalized bi-, bi-) ideals. We have proved that all fuzzy Γ-ideals coincide in intra-regular Γ-AG **-groupoids. We have also shown that the set of fuzzy Γ-two-sided ideals of an intra-regular Γ-AG **-groupoid forms a semilattice structure.