The aim of this work is to introduce a new category of Fuzzy d-algebra called Γ-Fuzzy d-algebra. This notion is more useful than Fuzzy d-algebra because in the old case the degree of membership of any in the Fuzzy set does not depend on the structure of d-algebra X. Therefore, in this work, we introduced a new construction of Fuzzy d-algebra that is depended on structure of d-algebra. Also, we show that for any d-algebra there is a Γ-Fuzzy d-algebra. Further, this new construction helps us to find the interesting relation between Γ-Fuzzy d-algebra and edge d-algebra in this work. For any d-algebra, we determined unique Γ-Fuzzy topological space using Γ-Fuzzy d-algebra. For any , a new class of d-algebra is introduced, where is the set of all equivalence classes . Finally, a new class of intuitionistic fuzzy set is called intuitionistic Γ-Fuzzy d-algebra is investigated and discussed.
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