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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。
In reality, many phenomena approximate the normal distribution. In order to solve the multi-criteria decision problem whose criterion value is a normal random variable and the risk attitude of decision makers is uncertain, an IPOWA operator and probability coefficient method based on interval possible ordered weighted averaging . Through the linear combination of normal random variables, the linear weighted normal random variables of each scheme are calculated. According to the 3σ principle of normal random variables, linear weighted normal random variables are transformed into random intervals. Comparing the number of random intervals with each other, we get the matrix of probability. Using the weighted average operator in the interval, the value of each row of elements in the probability matrix can be collected. Using the probability coefficient of risk attitude, we can calculate the comprehensive evaluation value of each program and then determine the final ranking of each program. Finally, the comparative analysis of two examples shows that the proposed method has the characteristics of stable ranking results and sufficient support information.