无量纲化方法对属性权重影响的敏感性和方案保序性

针对多属性决策中属性值无量纲化处理方法对决策结果的影响问题，给出了6种无量纲化方法产生的属性值方差，并基于属性均方差方法求解属性权重。在此基础上，分析了不同无量纲化处理方法对属性权重影响的敏感性，研究了属性值发生变化以及增加或者减少方案情况下的方案保序性问题，得出了一些重要结论，为决策者选择合适的无量纲化处理方法提供理论参照。最后通过军队资金管理绩效案例对结论进行了检验。

Sensibility and alternative COP analysis of dimensionless methods on effect of attribute weight

According to the effect of attribute dimensionless on decision results in the process of multi-attribute decision-making, the attribute variance is supposed by six kinds of dimensionless approaches, and attribute weight can be gained based on attribute mean square deviation. On the basis of the results, the sensibility of attribute weight is studied for several dimensionless methods, the problem of condition of order preservation (COP) in the condition of attributes value or alternatives number transformation in detail is also analyzed, and some important results are obtained, which can help decision makers select appropriate dimensionless methods. Finally, an illustrative example of army capital management is given to examine the conclusion.