Multiple attribute group decision making based on interval-valued hesitant fuzzy information measures

•Three axiomatic definitions of information measures are introduced.•Several continuous information measure formulas for IVHFEs are constructed.•The relationship among the entropy, similarity measures and cross-entropy are discussed.•MAGDM method based on the proposed continuous information measures is developed.•A numerical example is given to illustrate the behavior of the proposed MAGDM method.

Under the interval-valued hesitant fuzzy environment, we investigate a multiple attribute group decision making (MAGDM) method on the basis of some information measures. We first introduce three axiomatic definitions of information measures under interval-valued hesitant fuzzy environment, including the entropy, similarity measures and cross-entropy. Several information measure formulas for interval-valued hesitant fuzzy elements (IVHFEs) are further constructed, which is based on the continuous ordered weighted averaging (COWA) operator. Then, the relationship among the entropy, similarity measures and cross-entropy is discussed, from which we find that three information measures can be transformed by each other based on their axiomatic definitions. The programming model is established to determine optimal weight of attribute with the principle of minimum entropy and maximum cross-entropy. Furthermore, an approach to MAGDM is developed, in which the attribute values take the form of IVHFEs. Finally, a numerical example for emergency risk management (ERM) evaluation is provided to illustrate the application of the developed approach.