基于贝叶斯网络的模糊语言多属性决策模型

摘要

针对模糊语言多属性决策问题,提出了一种多属性决策贝叶斯网络模型（MADMBN）。该模型根据因果依赖关系把多属性决策层次结构转化成贝叶斯网络结构,降低了多属性决策层次结构的复杂度。分析了模糊语言多属性决策的层次结构（MADMHS）,根据MADMHS建立MADMBN;详述了MADMHS的元素在二态和多态情况下向MADMBN节点的转化方法;利用模糊综合评价法指标体系等级域的模糊关系矩阵和属性权重计算MADMBN节点的条件概率,并给出了MADMBN节点的重要度分析。通过科研项目申请实例与层次分析法对比验证了该模型的有效性和实用性,结果表明了MADMBN通过计算与理想解的相对接近程度不仅选择了最优方案,而且确定了该方案的状态,并且基于重要度分析对MADMBN节点进行灵敏度分析,识别影响方案的关键瓶颈。%With the multiple-attribute decision-making model,we convert the hierarchical structure of multiple-attribute decision making into the Bayesian Network structure from binary state to multiple states,thus reducing the complexity of the hierarchical structure.Then,we calculate the conditional probabilities of the nodes of the Bayesian Network,using the fuzzy relational matrix of the grade field of the fuzzy comprehensive evaluation indexes and the attribute weights.We also analyze the importance of the Bayesian network nodes.Finally,we verify the effectiveness of the multiple-attribute decision-making model by comparing the application example from our research project with the hierarchical analysis method.The comparison results show that our multiple-attribute decision-making model can not only select one optimal scheme and determine its state by calculating the degree of closeness to the ideal solution but also find out the bottleneck that affects the optimal scheme by doing the importance analysis.