基于对数归一化的MADM方法的VIKOR和TOPSIS重点重新分析
A VIKOR and TOPSIS focused reanalysis of the MADM methods based on logarithmic normalization
摘要：
在多准则决策分析中，决策者和决策者考虑一些策略，以分析结果，并最终做出有效和更精确的决策。在这些策略中，由于多种规范化工具的对抗，多准则决策算法中规范化过程的修改仍然是一个问题。规范化是定义和求解多属性决策问题和多属性决策模型的基本动作。归一化是求解的第一步，也是必要的一步，即应用MADM方法。归一化方法的选择对结果有着直接的影响。最新引入的归一化方法之一是对数归一化（LN）方法。这种新方法有一个突出的优点，反映在标准的归一化值的总和总是等于1。这种归一化方法以前从未应用于任何MADM方法。本研究的重点是分析经典的基于对数归一化的多属性决策方法。本文选取了两种著名的多属性决策方法VIKOR和TOPSIS进行再分析研究。两个数值例子检查在这两种方法的基础上，经典的和新的方法的基础上的LN。结果表明，这两种方法之间存在差异。最后，通过敏感性分析验证了最终结果的可靠性.
英文摘要：
Decision and policy-makers in multi-criteria decision-making analysis take into account some strategies in order to analyze outcomes and to finally make an effective and more precise decision. Among those strategies, the modification of the normalization process in the multiple-criteria decision-making algorithm is still a question due to the confrontation of many normalization tools. Normalization is the basic action in defining and solving a MADM problem and a MADM model. Normalization is the first, also necessary, step in solving, i.e. the application of a MADM method. It is a fact that the selection of normalization methods has a direct effect on the results. One of the latest normalization methods introduced is the Logarithmic Normalization (LN) method. This new method has a distinguished advantage, reflecting in that a sum of the normalized values of criteria always equals 1. This normalization method had never been applied in any MADM methods before. This research study is focused on the analysis of the classical MADM methods based on logarithmic normalization. VIKOR and TOPSIS, as the two famous MADM methods, were selected for this reanalysis research study. Two numerical examples were checked in both methods, based on both the classical and the novel ways based on the LN. The results indicate that there are differences between the two approaches. Eventually, a sensitivity analysis is also designed to illustrate the reliability of the final results.
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