概率语言多属性群决策方法及其在新型智慧城市市民获得感评价中的应用

针对公众参与的语言信息多属性群决策问题，研究了考虑参与者满意度的概率语言多属性群决策方法。首先，根据参与者的语言评价信息确定并规范化概率语言决策矩阵。然后，对大群体进行共识分析，由最大化参与者群体的满意度构建线性规划模型，确定参与者群组的权重；构造正、负理想方案的评价向量，构建多目标规划模型，用拉格朗日乘子法求解属性权重；定义各方案的加权贴近度，并以此对方案进行排序和优选。最后，通过新型智慧城市市民获得感评价案例验证了模型的可行性和有效性。

Probabilistic linguistic multi-attribute group decision making method and its application to evaluation of citizens′ sense of gain in new smart city

Considering the satisfaction of participants, a probabilistic linguistic multi-attribute group decision making method is proposed. Firstly, according to the linguistic evaluation information, the probabilistic linguistic decision making matrices are established and normalized. Secondly, a linear programming model is constructed by maximizing the satisfaction of group of participants by analyzing the large-scale group consensus to obtain the weights of participant subsets. Then the evaluation vectors of the positive and negative ideal alternatives are generated. The multi-objective programming model is constructed and solved by applying the Lagrange multiplier method to obtain the weights of attributes. Finally, the weighted closeness degrees of alternatives are determined to rank the alternatives. The feasibility and effectiveness of the proposed method are verified by the evaluation example of citizens' sense of gain in the new smart city.