基于Jaynes最大熵的模糊多属性群决策投影方法

Multi-attribute group decision-making method with projection based on Jaynes' maximum entropy principle

为了解决属性权重完全未知的模糊多属性群决策问题,采用基于Jaynes最大熵原理的投影偏差模型确定指标权重,运用基于多准则妥协解排序法的妥协解排序框架实现决策过程。首先运用区间直觉模糊集表达决策者的犹豫模糊评价信息,然后运用集成算子获得综合决策矩阵,再运用Lingo11~求解获得属性权重,利用信息集结获得备选方案的加权投影,最后根据方案的最大群效应值、最小后悔值和综合指标值进行方案排序。实验显示,方案的排序结果与其它方法保持一致,趋势图显示此方法计算的各方案综合指标值变化趋势更明显。分析表明,该方法避免了其他权重确定方法的不足之处,消除了计算过程中的折衷损失,适用于属性权重完全未知的多属性群决策方案排序问题的评价。

To solve the problem of fuzzy multi-attribute group decision making with unknown attribute weights, a weighted projection bias model based on Jaynes＇s maximum entropy principle was presented and the method of VlseKriterijumska Optimizacija I Kompromisno Resenje（VIKOR） framework was used to rank the alternatives. Firstly, the interval-valued evaluation information of decision makers. Then, intuitionistic fuzzy set was used to express hesitant fuzzy the comprehensive decision matrix was obtained by ag- gregation operators. Moreover, the attribute weights were obtained through iterating of Lingo11 , and the weighted projections of the alternatives were obtained by integrating the weights. Finally, alternatives were ranked by the maximum group utility value, the minimum regret value and the comprehensive index value. Experiments show that the ranking results of alternatives are consistent with other methods, and the tendency chart shows that the comprehensive index value changes calculated by this approach are more obvious. Analysis shows that the proposed method avoids the weakness of the other weights determined methods and removed the loss of compromise in calculation and this approach is suitable for the alternatives ranking evalua- tion problems of fuzzy multi--attribute group decision making with unknown attribute weights.