## 1 Introduction  
Since [PERSON] [1] put forward the theory of the fuzzy set (FSs), the decision making problem of fuzziness and uncertainty existing in real life has been dealt with better. Then, several extensions of fuzzy sets were proposed. On the basis of membership degree, the membership degree and hesitant degree were added, and the concept of intuitionistic fuzzy sets (IFSs) was introduced by [PERSON] [2], which is used to process decision information. [PERSON] [3] proposed the concept of hesitant fuzzy set, which effectively solves the hesitation of experts in group decision making and is better used to express decision information. In real life, many decision making problems are difficult to represented by an accurate value, and a relatively reasonable interval-value is chosen to describe them. On the basis of intuitionistic fuzzy sets, [PERSON] [4] introduced interval-valued concept, and put forward interval-valued intuitionistic fuzzy sets to solve decision problems. With the concept of interval-valued intuitionistic fuzzy sets, some scholars have studied the basic operations and basic properties of interval-valued intuitionistic fuzzy sets. In the context of interval-valued intuitionistic fuzzy sets, [PERSON] [5] defined a new score function by adding weighted average of hesitant degree in membership function to deal with the decision process. Subsequently, [PERSON] [6] reviewed the literature [5] and commented on the shortcomings of [PERSON]'s paper. Under interval-valued intuitionistic fuzzy sets, entropy measures have been studied by different researchers, which can describe the uncertainty information more fully [7; 8; 9; 10]. [PERSON] [11] proposed a new multi attribute decision making (MADM) method based on the interval-valued intuitionistic fuzzy weighted geometric average (IIFWGA) operator of interval-valued intuitionistic fuzzy values (IVIFVs), the accuracy function of IVIFVs and Particle Swarm Optimization techniques, which can overcome the drawbacks of the existing MADM methods for MADM in interval-valued intuitionistic fuzzy (IVIF) environments. The decision making process of actual problems has certain uncertainty. In order to depict the uncertainty in decision process more effectively, a new interval-valued hesitant fuzzy sets is defined by [PERSON] [12], which is based on the properties of hesitant fuzzy sets and the situation where the evaluation values are interval values. Under the interval-valued hesitant fuzzy sets, based on the continuous ordered weighted averaging (COWA) operator, [PERSON] [13] constructed several information measure formulas for interval-valued hesitant fuzzy elements (IVHFEs) and discussed the relationship among these information measures for IVHFEs. [PERSON] [14] studied the multi attribute group decision making (MAGDM) method which combines the improved Hamacher aggregation operators and continuous entropy. To address the lack of flexibility in decision making and lack of original information, [PERSON] [15] proposed some priority formulas of interval-valued hesitant fuzzy sets. Simultaneously, the expectation property of priority degree is also studied. In the multi attribute group decision making analysis of interval valued intuitionistic fuzzy information, the determination of attribute weight has a direct impact on the choice of the optimal scheme [16]. In view of complex group decision making problem, a multi-criteria weighting and ranking model is introduced with interval-valued hesitant fuzzy sets by [PERSON] [17], which operates properly under uncertainties. Furthermore, the attribute weights of interval numbers are discussed by both [PERSON] [18] and [PERSON] [19] to solve the MAGDM problem. [PERSON] et al. [20] constructed a new group decision making model for interval-valued hesitant fuzzy MAGDM problems with priority relations among attributes. The uncertainty of individual decision making is an important factor that ultimately affects the consistency of group decision making.