In practical multiple attribute decision making (MADM) problems, the interest groups or individuals intentionally set attribute weights to achieve their own benefits. In this case, the rankings of different alternatives are changed strategically, which is called the strategic weight manipulation inMADM. Sometimes, the attribute values are given with imprecise forms. Several theories and methods have been developed to deal with uncertainty, such as probability theory, interval values, intuitionistic fuzzy sets, hesitant fuzzy sets, etc. In this paper, we study the strategic weight manipulation based on the belief degree of uncertainty theory, with uncertain attribute values obeying linear uncertain distributions. It allows the attribute values to be considered as a whole in the operation process. A series of mixed 0-1 programming models are constructed to set a strategic weight vector for a desired ranking of a particular alternative. Finally, an example based on the assessment of the performance of COVID-19 vaccines illustrates the validity of the proposed models. Comparison analysis shows that, compared to the deterministic case, it is easier to manipulate attribute weights when the attribute values obey the linear uncertain distribution. And a further comparative analysis highlights the performance of different aggregation operators in defending against the strategic manipulation, and highlights the impacts on ranking range under different belief degrees.

中文翻译：

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基于不确定性理论的多属性策略权重操作混合0-1规划方法

在实际的多属性决策（MADM）问题中，利益集团或个人有意设置属性权重以实现自身利益。在这种情况下，策略性地改变不同备选方案的排名，这在MADM中称为策略权重操纵。有时，属性值以不精确的形式给出。已经发展了几种处理不确定性的理论和方法，如概率论、区间值、直觉模糊集、犹豫模糊集等。本文研究了基于不确定性理论置信度的策略权重操纵。服从线性不确定分布的不确定属性值。它允许在操作过程中将属性值作为一个整体来考虑。构建了一系列混合的 0-1 编程模型，为特定备选方案的所需排名设置战略权重向量。最后，一个基于 COVID-19 疫苗性能评估的例子说明了所提出模型的有效性。对比分析表明，与确定性情况相比，当属性值服从线性不确定分布时，更容易操纵属性权重。进一步的比较分析突出了不同聚合运营商在防御战略操纵方面的表现，并突出了不同信任度下对排名范围的影响。一个基于 COVID-19 疫苗性能评估的例子说明了所提出模型的有效性。对比分析表明，与确定性情况相比，当属性值服从线性不确定分布时，更容易操纵属性权重。进一步的比较分析突出了不同聚合运营商在防御战略操纵方面的表现，并突出了不同信任度下对排名范围的影响。一个基于 COVID-19 疫苗性能评估的例子说明了所提出模型的有效性。对比分析表明，与确定性情况相比，当属性值服从线性不确定分布时，更容易操纵属性权重。进一步的比较分析突出了不同聚合运营商在防御战略操纵方面的表现，并突出了不同信任度下对排名范围的影响。