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In this paper, the Choquet integral and the interval neutrosophic set theory are combined to make multi-criteria decision for problems under neutrosophic fuzzy environment. Firstly, a ranking index is proposed according to its geometrical structure, and an approach for comparing two interval neutrosophic numbers is given. Then, a ≤ L implied operation-invariant total order which satisfies order-preserving condition is proposed. Secondly, an interval neutrosophic number Choquet integral (INNCI) operator is established and a detailed discussion on its aggregation properties is presented. In addition, the procedure of multi-criteria decision making based on INNCI operator is given. Finally, a practical example for selecting the third party logistics providers is provided to illustrate the feasibility of the developed approach.