Abstract: In reality, most of the phenomena can approximately obey the normal distribution. In order to solve multi-criterion decision-making problems with normal stochastic criterion evaluations and uncertain risk attitude of decision makers, this paper proposes a method based on interval possible ordered weighted averaging (IPOWA) operator and possibility coefficients. Firstly, by the linear combination method of normal stochastic variables, the linear weighted normal stochastic variables of alternatives are gotten. Then, according to the 3σ principle of normal stochastic variables, the linear weighted normal stochastic variables are transformed into stochastic interval numbers. Furthermore, through the comparison of stochastic interval numbers, the possible degree matrix is attained. After that, using the IPOWA operator, the items of each row are integrated in the matrix. Accordingly, via the possibility coefficients of risk attitudes, the comprehensive evaluation values of alternatives are calculated. Moreover, the ranking order comes out. Finally, the comparative analysis of two illustrative examples shows the method has some features such as stable ranking result, sufficient support information and so on.

Key words: multi-criterion decision-making, normal stochastic variable, interval possible ordered weighted averaging operator, possible degree matrix, possibility coefficient of risk attitude

摘要： 现实中，很多现象近似服从正态分布。为了解决准则值为正态随机变量且决策者风险态度不确定的多准则决策问题，提出了一种基于区间可能有序加权平均（interval possible ordered weighted averaging，IPOWA）算子与可能性系数的方法。通过正态随机变量的线性组合方法，算出各方案的线性加权正态随机变量。根据正态随机变量的3σ原则，将线性加权正态随机变量转化为随机区间数。对随机区间数进行两两比较，得到可能度矩阵，利用区间可能有序加权平均算子，集结可能度矩阵中每行元素的值。采用风险态度的可能性系数，计算各方案的综合评价值，进而确定各方案的最终排序。最后，通过两个算例的对比分析，表明所提方法具有排序结果稳定，支持信息充分等特点。

关键词: 多准则决策, 正态随机变量, 区间可能有序加权平均算子, 可能度矩阵, 风险态度的可能性系数