关键词: 多属性群决策, 概率犹豫模糊集, Frank范数, 信息集成算子, 数据产品

Abstract: As a generalized form of hesitant fuzzy elements, the Probabilistic Hesitant Fuzzy Elements（PHFEs） can depict uncertainty more practically. In addition, because Frank’s operations have dexterity with parameters, it can reflect the subjective preferences of decision makers. Thus, combining the PHFEs and the Frank operations, the probabilistic hesitant fuzzy Frank operations are first defined, and the improved score function of PHFEs is presented. Then, a Probabilistic Hesitant Fuzzy Frank Weighted Average（PHFFWA） operator is investigated, and some propertied of the PHFFWA operator are studied. Based on which, a novel multi-attribute group decision making method is developed on the basis of PHFFWA operator. Finally, an example about selection of data products is provided to demonstrate that the effectiveness and feasibility of the proposed method.

Key words: multi-attribute group decision making, probabilistic hesitant fuzzy sets, Frank norms, information aggregation operator, data products