Abstract: A group decision making model based on optimization model and consistency adjustment algorithm was established for the group decision problems with incomplete occurrence probability information of hesitant fuzzy elements. First of all, some new concepts were introduced, including Probability Incomplete Hesitant Fuzzy Preference Relations (PIHFPRs), the expected consistency of PIHFPRs and the acceptable additive expected consistency of PIHFPRs. Secondly, the minimization of deviations between PIHFPRs and the weight vectors was regarded as the objective function, a linear optimization model was constructed to calculate the probability information of the PIHFPRs. Then, by using the integrated operator for weighted probability incomplete hesitant fuzzy preference relations, the comprehensive PIHFPR was determined. A group consistency adjustment algorithm was further designed, which not only makes the adjusted PIHFPRs are acceptable expected consistent, but also can obtain the weight vectors for alternatives. Finally, the proposed group decision-making model was applied to a numerical example about the selection of block chain. Experimental results show that the decision-making results are reasonable and reliable, and the actual situation can be reflected.

Key words: probability incomplete information, hesitant fuzzy preference relation, group decision-making model, expected consistency, group consistency adjustment algorithm

摘要： 针对犹豫模糊元中元素发生的概率信息不完备的群决策问题，提出一种基于最优化模型和一致性调整算法的群决策模型。该模型首先引入了概率不完备犹豫模糊偏好关系（PIHFPR）、概率不完备犹豫模糊偏好关系的期望一致性以及概率不完备犹豫模糊偏好关系的满意加性期望一致性等概念；其次，以PIHFPR和排序权重向量间的偏差最小化作为目标函数，构建线性最优化模型计算得到PIHFPR中不完备的概率信息；随后，通过提出的加权概率不完备犹豫模糊偏好关系集成算子确定综合的PIHFPR，同时设计一种群体一致性调整算法，不仅使得调整后的PIHFPR具有满意加性期望一致性，还可以计算方案的排序权重。最后，将群决策模型应用于区块链的选择实例中。实验结果表明，决策结果合理可靠，且更能反映实际决策情况。

关键词: 概率不完备信息, 犹豫模糊偏好关系, 群决策模型, 期望一致性, 群体一致性调整算法