With respect to the interval neutrosophic Multi-Attribute Decision-Making (MADM) problems, the MADM method is developed based on some interval neutrosophic aggregation operators. Firstly, the Induced Generalized Interval Neutrosophic Hybrid Arithmetic Averaging (IGINHAA) operator and the Induced Generalized Interval Neutrosophic Hybrid Geometric Mean (IGINHGM) operator are proposed, which can weight all the input arguments and their ordered positions. Further, regarding the situation where the input elements are interdependent, the Induced Generalized Interval Neutrosophic Shapley Hybrid Arithmetic Averaging (IGINSHAA) operator and the Induced Generalized Interval Neutrosophic Shapley Hybrid Geometric Mean (IGINSHGM) operator are proposed, which are extensions of IGINHAA and IGINHGM operators, respectively, and some properties of these given operators are investigated. Furthermore, the interval neutrosophic cross
entropy, which is an extension of single-valued neutrosophic cross entropy, is dened, and the models based on the interval neutrosophic cross entropy and generalized Shapley function are respectively constructed to determine the optimal fuzzy measures on the attribute and ordered sets. Finally, an approach to interval neutrosophic MADM with interactive conditions and incomplete known weight information is proposed based on these given operators, and a practical example is shown to verify the practicality and feasibility of the new approach.