Evidential reasoning (ER) approach is a representative method for analyzing uncertain multi-criteria decision-making (MCDM) and multi-criteria group decision-making (MCGDM) problems. Its core is ER algorithm used to combine belief distributions on criteria, which is developed based on Dempster’s rule of combination and probability theory. The ER algorithm is nonlinear and more computationally complex than linear combination of belief distributions. To address the necessity of the ER algorithm in MCDM and MCGDM, it is compared with linear combination from three perspectives by simulation. The first is to examine differences between the aggregated assessments derived from the ER algorithm and linear combination. The second is to examine error rates of best alternatives derived from two combination ways. The third is to examine alternative ranking differences derived from two combination ways. To facilitate the comparison, difference between aggregated assessments is designed and score function of alternative is developed from the expected utilities of alternative. Simulation experiments show that differences between the aggregated assessments are influenced by the number of assessment grades, and error rates of best alternatives and alternative ranking differences are influenced by the numbers of criteria and alternatives.

中文翻译：

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证据推理与线性组合决策方法的比较

证据推理（ER）方法是用于分析不确定的多标准决策（MCDM）和多标准组决策（MCGDM）问题的代表性方法。它的核心是用于根据标准组合信念分布的ER算法，它是基于Dempster的组合规则和概率论开发的。ER算法是非线性的，比置信度分布的线性组合要复杂得多。为了解决MCDM和MCGDM中ER算法的必要性，通过仿真从三个角度将其与线性组合进行了比较。首先是检查从ER算法和线性组合得出的汇总评估之间的差异。第二个是检查从两种组合方式得出的最佳替代方案的错误率。第三是研究从两种组合方式得出的替代排名差异。为了便于比较，设计了汇总评估之间的差异，并根据替代方案的预期效用开发了替代方案的得分函数。仿真实验表明，汇总评估之间的差异受评估等级数量的影响，最佳替代品和替代品排名差异的错误率受标准和替代品的数量影响。