In this paper, we develop a multicriteria group decision-making methodology with probabilistic linguistic q-rung orthopair fuzzy sets (PLqROFSs). The benefit of choosing PLqROFSs is that they consider the simultaneous occurrence of stochastic and nonstochastic uncertainty and so are superior to probabilistic hesitant fuzzy sets, linguistic intuitionistic fuzzy sets, and linguistic Pythagorean fuzzy sets. To develop the methodology, we first propose two types of operators, namely, probabilistic linguistic q-rung orthopair fuzzy weighted Generalized Dombi operator which gives the flexibility of choosing the parameter values and probabilistic linguistic q-rung orthopair fuzzy weighted Generalized Dombi Bonferroni mean operator which can consider the interrelationships between criteria. Since both the subjective and objective weights of experts are hardly considered in the current PLqROFSs-based research, so in our proposed methodology, we deploy the thought of consistency and similarity between the experts to calculate the subjective and objective weights, respectively, of the experts and as a result the evaluation results do not get malformed. For measuring the weights of criteria, the gray correlation coefficient of the assessment value of criteria is used to reflect the similarity between the criteria and its reference value. To exhibit the applicability of the proposed operators, we provide a case study on biomass feedstock selection. Moreover, to make sure that our model is stable, we have investigated a sensitivity analysis of parameters. At the end, we make a comparison of our approach to different existing schemes.

中文翻译：

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概率语言 q-rung orthopair 模糊广义 Dombi 和 Bonferroni 均值算子用于具有未知专家权重的群体决策

在本文中，我们开发了一种具有概率语言q - rung orthopair 模糊集 (PLqROFS)的多标准群决策方法。选择 PLqROFS 的好处是它们考虑了随机和非随机不确定性的同时发生，因此优于概率犹豫模糊集、语言直觉模糊集和语言勾股模糊集。为了开发该方法，我们首先提出两种类型的算子，即概率语言q- rung orthopair 模糊加权广义 Dombi 算子，它提供了选择参数值的灵活性和概率语言q-梯级 orthopair 模糊加权广义 Dombi Bonferroni 均值算子，可以考虑标准之间的相互关系。由于目前基于PLqROFSs的研究几乎没有同时考虑专家的主观和客观权重，因此在我们提出的方法中，我们采用专家之间的一致性和相似性的思想来分别计算专家的主观和客观权重因此，评估结果不会出现格式错误。在衡量标准的权重时，采用标准评价值的灰色相关系数来反映标准与其参考值的相似程度。为了展示提议的运营商的适用性，我们提供了一个关于生物质原料选择的案例研究。此外，为了确保我们的模型稳定，我们研究了参数的敏感性分析。最后，我们将我们的方法与不同的现有方案进行比较。