In this paper, we have introduced a new method of entropy measure of an interval-valued intuitionistic fuzzy set (IVIFS) which is defined as membership and non-membership interval valued of IVIFS with the extension form of Deluca-Termini axioms for fuzzy entropy. The relationship between the existing information measure of IVIFSs, and the entropy proposed. Including that we have discussed some more examples by using the application of the decision-making, clustering analysis are proposed entropy of an interval-valued intuitionistic fuzzy set IVIFS.