Abstract: Entropy is an important means to describe the uncertainty degree of fuzzy sets.To depict the uncertainty of interval-valued intuitionistic fuzzy sets,this paper first put forward the definition of core interval of interval-valued intui-tionistic fuzzy sets based on Hukuhara difference (H-difference) of interval numbers,which can effectively reflect the fuzziness generated by the force comparison between membership degree and non-membership degree of interval-valued intuitionistic fuzzy sets.Considering the uncertainty of interval-valued intuitionistic fuzzy sets is codetermined by the fuzziness and hesitancy,this paper proposed the basic criterion of the uncertainty measurement of interval-valued intui-tionistic fuzzy sets,which more accords with human intuition.Due to the difficulty for completely determining the proportion of fuzziness and hesitancy,in order to better describe the influence of the fuzziness and hesitancy on the uncertainty degree of interval-valued intuitionistic fuzzy sets,this paper presented a new interval-valued intuitionistic fuzzy entropy based on the exponential weighted method.Comparison example analysis under properties discussion and diffe-rent for interval-valued intuitionistic fuzzy entropy demonstrates that when hesitancy degree interval is the same,theinterval-valued intuitionistic fuzzy entropy decreases with the increase of the number of left and right intervals of the core interval,and when core interval is the same,the new fuzzy entropy increases with the increase of the number of left and right intervals of the hesitancy degree interval,which are accord with basic principle of uncertainty measurement.The proposed method completely shows that the uncertainty can increase with the increase of the fuzziness and hesitancy,which is accordance with human intuition.Secondly,this paper analyzed and verified that when the interval-valued intui-tionistic fuzzy sets degenerate into the intuitionistic fuzzy sets,the new fuzzy entropy constructed by the proposed me-thod can measure the degree of uncertainty of the intuitionistic fuzzy sets effectively.Finally,the proposed new entropy formula is applied effectively in multiple attributes decision-making analysis with unknown attribute weights and the rationality of the method is verified by an example,which provides a new way to solve multi-attribute decision-making problem.

Key words: Core interval, Fuzziness, Hesitancy, Hesitancy degree interval, Hukuhara difference (H-difference), Interval-valued intuitionistic fuzzy entropy