<p>With decision-making scenarios evolving constantly, complex decision-making has become more sophisticated and multidimensional, as seen in more uncertain attributes and growing interdependent criteria. (e.g., engineering decision-making has seen a 15–20% annual increase in uncertain attributes over the past decade.) Nested probabilistic linguistic term sets are an effective tool for describing complex and uncertain information due to its nested structure and flexibility. By considering the psychological behavior of decision makers, this paper aims to propose a three-way decision model based on cumulative prospect theory under nested probabilistic linguistic term sets. Firstly, it’s noteworthy that the existing distance formula of nested probabilistic linguistic term sets is flawed. To address this issue, we design a new distance formula of nested probabilistic linguistic term sets. On this basis, we adopt the maximizing deviation method to obtain objective attribute weights. Secondly, we construct a dominance relation on the alternative set based on net flows obtained by TODIM-PROMETHEE II, then conditional probability is estimated based on this relation. Subsequently, the problem of reference point selection in cumulative prospect theory is solved by using the conversion function of nested probabilistic linguistic term sets and relative utility functions are constructed by cumulative prospect values, the NPL-CPT-TWD model is constructed. Finally, the application of the proposed model is demonstrated through a case of ship construction material selection. Comparative analyses are also presented to verify the validity and stability of the proposed model. The Spearman correlation coefficients are all greater than 0.75 and the categorization indices are good, as far as we know, this indicates that the proposed model is superior to other existing models.</p>