A measure is necessary for various decision‐making problems, but it is inherently difficult for fuzzy information. This paper defines an extended probabilistic hesitant I‐fuzzy set (PHIFS), and develops a simple and effective measure based on weighted area index. The measure can consider players' risk preferences and it has appealing properties such as linearity. Then it is applied in multiattribute decision making and game decision making (GDM) without difficulty, and the validity and simplicity are shown by comparing the performances. Especially, the optimal strategies of GDM with payoffs of PHIFSs are obtained by the parameterized linear programming models, and the results shows that the measure is flexible and practical in interactive decision making.

中文翻译：

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用于策略选择的概率犹豫模糊集和决策制定的度量

各种决策问题都需要采取措施，但是对于模糊信息而言，内在就很难。本文定义了一个扩展的概率犹豫I-模糊集（PHIFS），并基于加权面积指数开发了一种简单有效的方法。该度量可以考虑参与者的风险偏好，并且具有线性等吸引人的属性。然后将其毫不费力地应用于多属性决策和游戏决策（GDM），并通过比较性能来证明其有效性和简单性。尤其是，通过参数化线性规划模型获得了带有PHIFS收益的GDM最优策略，结果表明该方法在交互式决策中是灵活而实用的。