基于Vague集模糊熵和D-S证据理论的多属性群决策方法

针对方案属性值为Vague值且考虑专家评分可信度的多属性群决策问题,提出了一种基于Vague集模糊熵和D-S证据理论的多属性群决策分析方法。该方法充分考虑各专家给出的Vague值评价信息中所蕴含的模糊性与不确定性,借助模糊熵来获取与专家自身意见相匹配的评分可信度序列,其完全由数据驱动,弥补了传统方法对可信度主观统一设定的不足。首先,基于各专家原始决策矩阵获得各属性下的Vague集模糊熵,以构建与专家集相对应的评分可信度矩阵;其次,对经可信度调整后的各专家决策矩阵使用证据合成进行信息集结,利用Vague集记分函数并经可信度调整得到属性权重;最后,将专家群体集结信息经属性权重加权修正后算出各方案最终的Vague评价值,进而使用记分函数获得各方案综合得分,筛选出最优方案。利用证据理论在不确定信息融合方面的优势和Vague集记分函数的信息转化功能,通过证据合成和记分函数集结专家群体的评价信息,所得出的决策结果更加客观、合理,并通过一个具体算例验证了所提方法的可行性和有效性。

A Multi-attribute Group Decision Making Method Based on Fuzzy Entropy of Vague Sets and D-S Evidence Theory

Aiming at the multi-attribute group decision-making problems with Vague value and considering the reliability of expert rating, a multi-attribute group decision-making analysis method based on Vague set fuzzy entropy and D-S evidence theory was proposed. The method took into full account the fuzziness and uncertainty embedded in the Vague value evaluating information given by various experts, and used fuzzy entropy to obtain the scoring credibility sequence matching experts''opinions. It is completely data-driven, which makes up for the deficiency of the traditional method in the subjective unified setting of credibility. Firstly, based on the original decision matrix of each expert, the fuzzy entropy of Vague set under each attribute was obtained to construct the scoring credibility matrix corresponding to the expert set. Secondly, the information of each expert decision matrix adjusted by credibility was gathered through evidence synthesis, and the attribute weight was obtained by using score function of Vague sets and credibility adjustment. Finally, the final Vague evaluation value of each scheme was calculated by modifying the aggregation information of expert group by attribute weight, and then the comprehensive score of each scheme was obtained by using the score function to screen the optimal scheme. By using the advantages of evidence theory in uncertain information fusion and the information transformation function of score function of Vague sets, the evaluation information of expert group was gathered through evidence synthesis and score function of Vague sets, the decision-making results were more objective and reasonable, and the feasibility and effectiveness of the proposed method were verified by a specific numerical example.