The motive of this paper is to conduct the detailed analysis on fuzzy d-algebra and Intuitionistic fuzzy d-algebra. The intuitionistic fuzzy set theory is a valuable method for presenting and manipulating information. Also, it investigates the use of fuzzy d-ideals with its properties and relations. The most relevant properties of the fuzzy d sub-algebras have been analyzed with the sample illustrations. Based on this, it investigated that the degree of membership functions in the fuzzy set are not depends on the structure of d-algebra in the set Moreover, the intuitionistic fuzzy set with the degree of non-membership functions is highly. accurate for efficiently solving the problems related to the knowledge base and observations. In this paper th he notion of a mapping on intuitionistic fuzzy d -algebra set, several Proposition and definitions of intuitionistic fuzzy d -algebra are presented.