The interval neutrosophic set (INS) can be better to express the incomplete, indeterminate and inconsistent information, and the power average (PA) operator can take all the decision arguments and their relationships into account, and the generalized

In actual decision making, there are many multiple criteria decision making (MCDM) problems with prioritization and interaction among the criteria. In this study, we proposed a novel method to handle the intuitionistic fuzzy MCDM problems with weakly ordered prioritization and interaction among the criteria. Firstly, we presented some novel Einstein operations of intuitionistic fuzzy sets (IFSs), which could capture the relationship between non-membership and membership functions of various IFSs. Then, we proposed a novel operator called prioritized interactive Choquet (PIC) operator based on fuzzy measure, generalized prioritized measure and Choquet integral. Meanwhile, three fundamental features of this operator were discussed. Besides, we combined the PIC operator and Einstein operations to IFSs, and proposed the intuitionistic fuzzy prioritized interactive Einstein Choquet (IFPIEC) operator, which could consider the prioritization and interaction among the criteria. Additionally, we utilized O’Hagan’s maximum entropy to obtain the quantity of each priority level in the generalized prioritized measure. Finally, the detailed decision making steps for the intuitionistic fuzzy MCDM problems with weakly ordered prioritization and interaction were developed, and two practical cases were given to check the created approach and to illustrate its validity and superiority.