Probabilistic linguistic Z number (PLZN) is considered as an effective information representation model. It not only describes the decision-making information, but also demonstrates its reliability. To handle the increasing problems of complexity and uncertainty in real-life, PLZN is widely used to indicate qualitative information. In this paper, a novel decision-making method with PLZNs is proposed, focusing on multiple attribute group decision-making (MAGDM) problems with fewer alternatives and more interacted attributes in PLZN environment. Firstly, all basic theories of PLZNs are shown, where the possibility degree of PLZNs is defined. Then, an integration model based on evidential reasoning theory is constructed to aggregate numerous PLZNs, which fully considers the incomplete probability distributions in PLZNs. The mathematical programming model with the generalized Shapley function is introduced to determinate the important degrees of attributes and reflect the interactive characteristics among them. In addition, the probabilistic linguistic Z QUALIFLEX (PLZ-QUALIFLEX) method with the generalized Shapley function is proposed to rank small numbers of alternatives with respect to large numbers of attributes with heterogeneous relationships. Lastly, after demonstrating the rationalities and superiorities of the proposed method, it is applied to solve some numerical cases, in which is compared with other methods.

概率语言 Z 数 (PLZN) 被认为是一种有效的信息表示模型。它不仅描述了决策信息，而且展示了其可靠性。为了处理现实生活中日益增加的复杂性和不确定性问题，PLZN 被广泛用于表示定性信息。在本文中，提出了一种具有 PLZN 的新型决策方法，重点解决 PLZN 环境中具有更少替代方案和更多交互属性的多属性组决策 (MAGDM) 问题。首先，展示了PLZNs的所有基本理论，定义了PLZNs的可能性程度。然后，构建基于证据推理理论的集成模型来聚合众多PLZN，充分考虑PLZN中的不完全概率分布。引入具有广义Shapley函数的数学规划模型来确定属性的重要程度并反映它们之间的交互特征。此外，提出了具有广义 Shapley 函数的概率语言 Z QUALIFLEX (PLZ-QUALIFLEX) 方法，以针对具有异构关系的大量属性对少量备选方案进行排名。最后，在论证了所提方法的合理性和优越性后，将其应用于一些数值案例的求解，并与其他方法进行了比较。提出了具有广义 Shapley 函数的概率语言 Z QUALIFLEX (PLZ-QUALIFLEX) 方法，以针对具有异质关系的大量属性对少量备选方案进行排名。最后，在论证了所提方法的合理性和优越性后，将其应用于一些数值案例的求解，并与其他方法进行了比较。提出了具有广义 Shapley 函数的概率语言 Z QUALIFLEX (PLZ-QUALIFLEX) 方法，以针对具有异质关系的大量属性对少量备选方案进行排名。最后，在论证了所提方法的合理性和优越性后，将其应用于一些数值案例的求解，并与其他方法进行了比较。