基于粗糙集与层次分析相融合的多属性决策方法及应用研究

In real situations, decision problem often involves uncertainty, reference and complexity, so such decision systems are often encountered that include both the classification and ranking problems. Rough sets are a kind of classification method to deal with uncertainty, and AHP is a useful ranking method with quantitative and qualitative analysis. The former does not require any priori information, and the latter gives full play to the subjective initiative. However, neither rough sets nor AHP is able to handle the classification and the ranking decision problems at the same time. So, can these two decision-making methods be combined organically to play their respective strengths while overcoming their limitations, to fully reflect the subjective initiative while making full use of the objectivity of the currently obtained data, and to form a new kind of multi-attribute decision-making method? This project focuses on two aspects: (1) one is to extend the theory of AHP based on rough sets, drawing the objectivity of the rough sets into the classical AHP; (2) the other is to propose methods of attribute reduction and rule acquisition from the perspective of preserving the ranking results of the objects, leading the classification mechanism of AHP in to the rough sets. By doing this, we get a new multi-attribute decision-making method obtained by combining rough sets with AHP organically, which is of great importance in enriching the multi-attribute decision-making theory.

由于现实中的决策问题具有不确定性、偏好性与复杂性，常常需要处理既有分类问题又有分级（或排序）问题的决策系统。粗糙集理论是一种处理不确定问题的分类方法，层次分析法则是一种定性与定量相结合的分级或排序方法，前者不需要任何先验信息，后者可发挥人的主观能动性。但上述任一种方法均不能够处理同时具有分类与分级的决策问题。那么，能否有机地将这两种决策方法结合起来，在发挥它们各自长处的同时克服其局限性，既能充分利用现有数据的客观性，又能充分反映人的主观能动性，形成一种新的多属性决策方法呢？本项目将从两个方面入手，一方面提出基于粗糙集的层次分析法，将粗糙集的客观性引入层次分析法；另一方面提出基于排序（即保持排序结果不变）的属性约简与规则提取概念与方法，将层次分析的分级机制引入到粗糙集中。这样，我们获得了将粗糙集与层次分析法有机融合起来的多属性决策新方法，这对于丰富多属性决策理论具有重要的理论意义与应用价值。

在处理不确定决策问题中，粗糙集理论（RS）的客观性与层次分析（AHP）理论的主观性各有其优势，粗糙集理论主要研究分类问题，层次分析主要研究排序问题，但实际应用中往往是既要分类又要排序的混合问题。本项目研究其融合问题，提出了粗糙层次分析法与基于排序的属性约简概念，在如下各方面获得一些有趣的结果：关于粗糙层次分析法，对区间粗糙数的排序，提出了三个新方法；对基于区间粗糙数决策矩阵，提出了四种新的多属性决策方法；对不确定多属性决策，提出几种新方法；完整地提出了区间粗糙数层次分析法，从粗糙标度、区间粗糙判断矩阵构造、一致性定义与检验、基于区间粗糙数判断矩阵的排序方法等各个步骤提出了自己的方法，该方法既考虑了决策者在判断时具有的不确定性，又考虑到了判断中存在的部分精确性，同时所提出的权重排序方法还考虑决策者在决策中的风险偏好，以使排序方法更具有广泛的适应性与操作性。而关于基于排序的属性约简及粗糙集模型拓展，项目组首先提出了基于保持排序不变的属性约简概念，并对四种保序约简给出了定义，同时给出一些约简方法与步骤。此外，对一些粗糙集拓展模型进行了讨论；对本项目提出的方法也给出了若干应用领域的实际例子。