基于证据理论和Vague集的多属性群决策方法研究

为了解决人们在复杂环境中决策困难的问题,论文基于Vague集描述不确定事物的优势,通过证据理论对Vague集进行合成,得到一种信息集结的多属性群决策方法。该算法首先考虑专家评分的可信度,在分析Vague集与证据理论的数学关系后,使用证据理论将各方案在各属性下的专家集证据集结。然后通过Vague集记分函数进行属性权重的计算,将方案集在属性集下的Vague评价值进行加权修正,再通过证据理论将属性集证据集结得到各方案最终的Vague评价值。之后使用记分函数计算每一方案的得分来确定最优方案。最后通过算例进一步说明所提方法的可行性与有效性。文章给出的算法使决策者在不确定环境下可以进行理性决策,从而选出最优方案。

Research on Multi-attribute Group Decision-making Method Based on Evidence Theory and Vague Sets

In order to solve the problem of difficult decision-making in complex environments, a multi-attribute group decision-making method based on Vague sets and evidence theory is proposed. Vague sets have the advantage of describing uncertain information. Evidence theory can fuse the information of Vague sets. Firstly, after considering the credibility of expert evaluation information, this paper uses evidence theory to fuse the evaluation information of expert set under the analysis of mathematical relationship between Vague sets and evidence theory. Secondly, the weight of every attribute can be obtained through the use of score function and the Vague evaluation value of every solution under all attributes can be corrected through weighted average algorithm. Then, evidence theory is used to fuse the evaluation information of attribute set. Thirdly, the optimal solution is determined according to the score of every solution obtained from the score function. Finally, an example is used to further illustrate the feasibility and effectiveness of the proposed method. The decision-makers can make decisions rationally and select the optimal solution through the algorithm given in the paper.