Since the sufficient conditions for the maximum value of the intuitionistic fuzzy entropy are not unified and the hesitant fuzzy entropy cannot be compared when the lengths of the hesitation fuzzy elements are not equal, improved axiomatic definitions of intuitionistic fuzzy entropy and hesitant fuzzy entropy are proposed, and new intuitionistic fuzzy entropy and hesitant fuzzy entropy based on the improved axiomatic definitions are established. This paper defines the fuzzy entropy that satisfies the properties based on the axiomatized definition of fuzzy entropy and, based on the fuzzy entropy, defines new intuitionistic fuzzy entropy and hesitant fuzzy entropy, so that the three are unified in form. The validity and rationality of the proposed intuitionistic fuzzy entropy and hesitant fuzzy entropy are verified by analysis.