Uncertain linguistic Z-numbers (ULZNs), which inherit the prominent characteristics of linguistic term sets and Z-numbers, can flexibly describe qualitative information as well as its reliability. To cautiously solve a qualitative multi-criteria decision-making (MCDM) problem with larger number of criteria than alternatives, this paper develops an ULZN-based QUALIFLEX (QUALItative FLEXible multiple criteria method) by considering the decision-maker (DM)’s psychological behavior character. First, the likelihood and diversity degree of ULZNs are determined and a comparison method is proposed. Second, a decision model combining the QUALIFLEX and prospect theory is developed to address MCDM problems with ULZNs, considering the incomplete compensation of criteria. An extended maximizing deviation method is developed to objectively obtain the weights of the criteria. Subsequently, an illustrative example concerning risk evaluation of high-tech project investment with larger number of criteria than alternatives is provided to demonstrate the application of the proposed approach. Finally, sensitivity analysis and comparative analyses are conducted to validate the proposed approach. The result shows that the proposed approach can effectively address MCDM problems with ULZNs, considering the DM’s psychological behavior.
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