多准则排序中的路径问题及层次分析法推广  

Path problem in multi-criteria ranking and generalization of AHP

作　　者：刘开第[1] 庞彦军[1] 周少玲[1] 马丽涛[1] 栗文国[1] 

机构地区：[1]河北工程大学不确定研究所,邯郸056038

出　　处：《系统工程理论与实践》2015年第4期973-983,共11页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(60874116;61375003)

摘　　要：本文指出,在多准则排序中层次分析法用矩阵乘法实现排序度量转换是不正确的.实际上排序度量转换与把排序指标的重要性传递到目标的路径有关,多准则排序是多路径的,多路径排序度量转换不是线性转换,不能用矩阵乘法实现.为此,将排序度量映射到高维状态空间上、用不确定性隶属度向量表征,进而把排序度量转换转化为隶属度转换.通过揭示指标隶属度中包含着确定目标隶属度的冗余值来论证隶属度转换是非线性转换,用区分权滤波算法实现隶属度非线性转换.由此建立多准则排序的非线性排序模型.It is pointed out that multi-criteria ranking metric transformation is realized by matrix multiplication in AHP is wrong. In fact this kind of transformation is concerned with path. Multi-criteria ranking is multipath. Multipath ranking metric transformation is nonlinear and can＇t use matrix multiplication. So ranking metric is mapped into high dimensional spaces and is expressed by uncertain membership vector. Then ranking metric transformation is changed into membership transformation. It is proved that mem- bership transformation is nonlinear and can be realized by classification weight filter. Nonlinear ranking model of multi-criteria is built up.

关 键 词：层次分析法 多准则排序 排序度量转换 非线性 区分权滤波 

分 类 号：O29[理学—应用数学]