A behavioral multi-attribute decision making (BMADM) problem with probabilistic-based expressions is studied by considering decision-maker’s (DM) risk attitude and pre-evaluation. With consideration of information expressions for uncertainty, probabilistic interval numbers (PINs) and probabilistic linguistic terms (PLTs) are utilized to depict pre-evaluation information with respect to quantitative and qualitative attributes, respectively. Then surrounding the two kinds of probabilistic-based expressions, we propose a BMADM method with DM’s risk attitude being included based on regret theory. First, through taking into account characteristics of risk, we develop a basic utility function and a regret–rejoice function by considering risk-averse, risk-neutral and risk-seeking preference coefficients. Second, risk-based utility functions are examined for measuring PINs and PLTs. The third element is the establishment of optimization models for handling probability incompleteness to fully utilize the information. In the fourth step, a weighted comprehensive risk-based utility measurement is presented as a basis for making a selection. The final phase of the research is the application of the proposed method to one case, along with sensitivity and comparative analyses, as a means of illustrating the applicability and feasibility of the new method.

通过考虑决策者（DM）的风险态度和预先评估，研究了基于概率表达的行为多属性决策（BMADM）问题。考虑到信息表达的不确定性，分别使用概率区间数（PIN）和概率语言术语（PLT）来描述有关定量和定性属性的评估前信息。然后围绕两种基于概率的表达式，我们提出了一种基于后悔理论的BMADM方法，其中包括了DM的风险态度。首先，通过考虑风险的特征，我们通过考虑规避风险，风险中立和寻求风险的偏好系数来开发基本效用函数和后悔喜悦函数。第二，检查了基于风险的实用程序功能，以测量PIN和PLT。第三个要素是建立用于处理概率不完整的优化模型，以充分利用信息。在第四步中，将基于加权的基于风险的综合效用度量作为选择的基础。研究的最后阶段是将提出的方法应用于一种情况，并进行敏感性分析和比较分析，以此说明该方法的适用性和可行性。