In this study, we concentrate on multiple attribute decision-making (MADM) problems in the probabilistic linguistic preference information surroundings based on novel aggregation operators. Considering interrelationships among the multi-input arguments of probabilistic linguistic term sets (PLTSs), we extend dual Muirhead mean (DMM) operators to the probabilistic linguistic preference environment and develop a decision-making approach to deal with probabilistic linguistic MADM (PLMADM) problems. In specific, we define probabilistic linguistic dual Muirhead mean operators, i.e., probabilistic linguistic dual Muirhead mean (PLDMM) operator and probabilistic linguistic weighted dual Muirhead mean (PLWDMM) operator, and further investigate their corresponding propositions, theorems as well as properties. In the light of VIKOR method, a novel decision-making approach for PLMADM problems has been carefully explored. Finally, an application of hospitals selection can fruitfully demonstrate and signify the practicality and feasibility of the proposed decision-making approach.

在这项研究中，我们集中在基于新型聚合算子的概率语言偏好信息环境中的多属性决策（MADM）问题。考虑到概率语言术语集（PLTS）的多输入参数之间的相互关系，我们将双重Muirhead均值（DMM）运算符扩展到了概率语言偏好环境，并开发了一种决策方法来处理概率语言MADM（PLMADM）问题。具体来说，我们定义了概率语言对偶Muirhead均值算子，即概率语言对偶Muirhead均值算子和概率语言加权对偶Muirhead均值算子，并进一步研究了它们的对应命题，定理和性质。根据VIKOR方法，仔细研究了PLMADM问题的新颖决策方法。最后，医院选择的应用可以有效地证明和表明所提出的决策方法的实用性和可行性。