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Information reliability has a remarkable effect on decision-making outcome. Zadeh's Z-number considers information fuzziness and reliability, and can, therefore, help the decision-maker to manage complicated problems. However, due to its complex construct, several issues concerning the computation of Z-numbers require further research. This study develops a novel likelihood-based method of comparing two Z-numbers to solve multi-criteria decision-making (MCDM) problems. Four main parts can be outlined. First, the likelihood of fuzzy restriction of Z-numbers is defined based on the conversion method of Z-number. Second, the likelihood of underlying probability distributions of Z-numbers is also proposed to compare the difference of randomness of Z-information. Third, by adding to a risk preference parameter, this study constructs a comprehensive weighted likelihood of Z-numbers. Finally, a likelihood-based qualitative flexible approach is extended to address the MCDM problems under Z-evaluation. In addition, a numerical example of the selection of ERP systems for ABC enterprise is placed to illustrate the applicability, validity, and effectiveness of the proposed method.