云模型双重积分算子的层次多属性决策方法

Hierarchical Multi-attribute Decision-Making Method with Twofold Integral Operator of Cloud Model

由于实际决策问题的复杂性,大多数指标间都具有相互依赖的特征,因此针对不确定环境下指标间具有关联性的多属性决策问题,提出了一种以层次结构为框架、云模型双重积分(C-TI)为聚合算子的决策方法。首先为了体现决策者在确定指标权重时的不确定思维提出了云模型模糊测度;其次在云模型模糊测度的基础上构建了云模型双重积分算子,该算子将云模型作为决策信息的表征,充分体现出决策信息的模糊性和随机性,且应用结合Choquet积分与Sugeno积分优势的双重积分聚合各指标值,其不仅可以有效处理指标间的交互性问题,还能够考虑到指标值与权重的侧重关系;随后讨论了云模型双重积分算子的定理和性质以及特定条件的变化形式,并给出了相应证明;最后构建出云模型双重积分算子的层次多属性决策方法,并将该方法应用到企业社会责任的评估问题上,通过与其他模型的比较,进一步说明所构建的方法适用于处理模糊与随机的不确定问题,并且能够在指标具有关联性的条件下同时考虑到整体的决策效果。

Due to the complexity of the actual decision-making problem,most indicators have the characteristics of mutual dependence.Therefore,for the multi-attribute decision-making problem with correlation between indicators under uncertain environment,a decision method with hierarchical structure as the framework and cloud model twofold integral(C-TI)as the aggregation operator is proposed.Firstly,in order to reflect the uncertain thinking of decision makers in determining the index weights,a cloud model fuzzy measure is proposed.Secondly,the cloud model twofold integral operator is constructed on the basis of cloud model fuzzy measure,which takes the cloud model as the representation of decision information,fully reflects the fuzzy and random nature of decision information.And twofold integral combining the advantages of Choquet integral and Sugeno integral is applied to aggregating the index values,which can not only effectively deal with the interaction problem between indexes,but also take into account the focus relationship between the index value and the weight.Subsequently,the theorems and properties of the cloud model twofold integral operator and the variation form of specific conditions are then discussed and the corresponding proofs are given.Finally,a hierarchical multi-attribute decision making method for cloud model twofold integral operator is constructed and applied to the corporate social responsibility assessment problem.Compared with other models,it is further shown that the method constructed in this paper is suitable for dealing with fuzzy and stochastic uncertainty problems and can take into account the overall decision effect while the indicators are correlated.