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Z-number that proposed by Zadeh is an effective tool to describe the information with uncertainty in decision-making problems. However, most of the researches on Z-numbers employed linguistic cardinalities with uniformly distributed scales. In fact, unbalance situation is much common in terms of the psychology of experts. In this paper, we propose a new computational method based on Probabilistic Linguistic Z-number with Unbalanced semantics(UPLZ), which can represent the linguistic evaluations of experts precisely combined with individual risk appetite. A new score function of UPLZs is provided based on hesitant degree and linguistic scale function to reduce the computational complexity. Afterward, a linear programming is constructed to determine weights of criteria by considering cross entropy maximization. The robust decision result can be obtained by applying MULTIMOORA method since it is specific with peculiarities of three subordinate models. Finally, a case study concerning medicine selection for the patients with mild symptoms of the COVID-19 is provided to illustrate the feasibility and effectiveness of the proposed method. The advantages of it are highlighted by sensitivity analysis and comparative analysis with two outstanding multi-criteria decision-making methods.

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A New Computational Method Based on Probabilistic Linguistic Z-Number With Unbalanced Semantics and Its Application to Multi-Criteria Group Decision Making