应用规范化公式的MCDM保序研究

规范化公式的应用会破坏方案之间的独立性，导致逆序的产生。提出了两种改进规范化公式的方法以消除逆序，并以加权算术平均（WAA）集结算子的多属性决策分析(MCDM)为例验证了所提出方法的合理性和有效性。改进后的规范化公式不仅可以应用于WAA算子，还可以应用到其他类似的决策算子中。改进后规范化公式的应用可以降低和消除规范化公式对无关方案独立性的影响，使得MCDM决策过程更加合理、科学。

Study on Rank Preservation of the MCDM With Normalizing Formula

The application of the normalizing formula will result in violations of independence from irrelevant alternatives and lead to rank reversal. In the paper, the two methods that improve the original normalizing formula to erase the rank reversal are proposed; and a MCDM example based on the WAA operator is deduced to validate the conclusion using specific data at last. The methods mentioned can also be applied into other decision operators. The application of these methods can remove the influence of the normalizing formula to the independence from irrelevant alternatives and make the decision making more reasonable and scientific.