Concerning the discrete stochastic multi-attribute decision making (SMADM) problems in which attribute values are interval neutrosophic numbers and the attribute weight is incompletely known, a novel SMADM method based on the cumulative prospect theory (CPT) and generalized Shapley function is proposed. Firstly, the value prospect of each attribute under interval neutrosophic environment is calculated as well as subjective probability weights respectively, and the prospect function values are obtained according to the formulation of prospect function. Then, following the maximum deviation principle, the optimization model with respect to the incompletely known attribute weight information is constructed to obtain the optimal fuzzy measure, and the optimal weights of each attribute based on the formulation of generalized Shapley function are generated. Further, by aggregating the above prospect function values and the optimal weights, the values of the comprehensive prospect function are obtained and then alternatives are ranked. Finally, an illustrate example is presented to demonstrate the validity and feasibility of the proposed method.
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