规范化公式对无关方案独立性的影响

对决策矩阵进行规范化处理是MCDM决策的必要步骤，其目的是消除指标单位影响，使得不同指标的值具有可加性。目前针对不同类型的指标存在着不同的规范化公式，本文指出利用规范化公式对决策矩阵进行处理会破坏方案之间的独立性，导致评价违反无关方案独立性，并产生逆序；并以基于WAA算子的决策为例在数学上推导了决策矩阵规范化致使无关方案独立性的违背以及逆序的产生的必然性，最后用具体的数例验证了这一结论。

Effects of Normalizing Formulae on Independence from Irrelevant Alternatives

Normalizing decision matrix is one of the necessary steps for transacting the MCDM with the aim of eliminating the influence of the target's unit, so that different targets' expected values are additive. Now many normalizing formulae were proposed according to different kinds of the target. The paper point out that normalizing formulae' application will (result) in violations of independence from irrelevant alternatives and lead rank reversal; and take the WAA operator as an (example) to deduce in theory that violation of the independence is inevitability only if the normalizing formulae are utilized; and validate the conclusion using specific data at last.