区间粗糙数群组G1法的随机聚合求解及应用

Stochastic Integrated Solution of Interval Rough Number Group G1 Method and Its Application

针对复杂不确定环境下的群体评价问题,采用区间粗糙数表征专家偏好,在G1法的基础上,结合蒙特卡洛仿真技术,提出了一种随机模拟聚合算法.首先,通过随机抽样的方式模拟权重系数,并依据序相关性和区间粗糙数贴近度确定专家权重.其次,综合所有专家意见得到指标的最终权重,并将其与预处理后的指标值线性集结,求得一次模拟的综合评价值,据此判断被评价对象间的优劣.通过充分模拟得出优胜度矩阵,并从中推导出包含优胜概率的可能性排序,弥补了不确定信息环境下绝对排序呈现的不足.最后,通过算例说明了方法的有效性,并与现有方法对比阐述了所提方法的优势.

For the problem of group evaluation in complex uncertain environments,an interval rough number is used to characterize experts’preferences,and a stochastic simulation integrated algorithm is proposed based on the G1 method combined with Monte Carlo simulation techniques.Firstly,the weighting coefficients are simulated by random sampling and the weighting of experts are determined based on ordinal correlation and interval rough number closeness.Secondly,the final weights of indicators can be obtained by combining all the experts’opinions,and they are linearly aggregated with the pre-processed indicator values to obtain the comprehensive evaluation value of one simulation,which can be used to assess the advantages and disadvantages of the evaluated objects.Through full simulation,the preference ratio matrix is calculated,and the probability ranking with the probability of superiority is derived from it,which makes up for the deficiency of absolute ranking in the uncertain information environment.Finally,the effectiveness of the method is illustrated by an example and the advantages of the method are described in comparison with the existing methods.