Abstract: For the serious loss of important level of information when decision making information is described by interval-valued hesitant fuzzy set, a new multi-attribute group decision making model is investigated on the basis of probabilistic interval-valued hesitant fuzzy geometric operator. Firstly, the concept of probabilistic interval-valued hesitant fuzzy set is introduced, and the new probabilistic interval-valued hesitant fuzzy operational laws are defined by using the Archimedean norm. Then, based on the defined operational laws, the Probabilistic Interval-Valued Hesitant Fuzzy Ordered Weighted Geometric（PIVHFOWG） operator is proposed. Furthermore, some basic properties of PIVHFOWG operator are discussed, and several common forms of PIVHFOWG operator are studied. Finally, a novel multi-attribute group decision making model is developed under the probabilistic interval-valued hesitant fuzzy information environment, and a numerical example about the network public opinion prediction system selection is provided to illustrate the effectiveness of the developed model.

Key words: multi-attribute group decision making, probabilistic interval-valued hesitant fuzzy sets, Archimedean norm, geometric operator, network public opinion prediction system

摘要： 针对区间犹豫模糊集在描述决策信息时会导致决策信息重要性程度损失这一问题，构建了一种基于概率区间犹豫模糊几何算子的新的多属性群决策模型。引入了概率区间犹豫模糊集的概念，将Archimedean范数引入到概率区间犹豫模糊环境下，定义了新的概率区间犹豫模糊运算法则；运用新的运算法则，提出了概率区间犹豫模糊有序加权几何（Probabilistic Interval-Valued Hesitant Fuzzy Ordered Weighted Geometric，PIVHFOWG）算子；讨论了PIVHFOWG算子的一些基本性质，并研究了其两种常见形式；在概率区间犹豫模糊信息环境下，建立了一种新的多属性群决策模型，且通过网络舆情预测系统的选择实例验证了提出的决策模型是可行的和有效的。

关键词: 多属性群决策, 概率区间犹豫模糊集, Archimedean范数, 几何算子, 网络舆情预测系统