基于非线性序转换的层次分析模型  

The hierarchy analysis model based on non-linear order conversion

作　　者：庞彦军[1] 刘立民[1] 马丽涛[1] 刘开第[1] 

机构地区：[1]河北工程大学理学院,河北邯郸056038

出　　处：《河北工程大学学报（自然科学版）》2011年第2期109-112,共4页Journal of Hebei University of Engineering:Natural Science Edition

基　　金：国家自然科学基金项目(60874116);河北省自然科学基金项目(F2008000857)

摘　　要：为了解决复杂层次结构中方案排序问题,将排序度量映射到高维状态空间,挖掘隐藏在指标隶属度中的分类信息,利用区分权滤波算法将一维空间上无法实现的非线性序关系转换转化为高维空间上隶属度向量间的非线性转换,通过计算底层方案对目标的影响度,实现底层指标排序,建立基于非线性序转换的层次分析模型。以某矿出现渗漏的污水坝为例,根据拟采用的4种防渗加固方案以及6种衡量方案优、劣的指标构建三层递阶层次结构,并进行验证分析,结果表明本模型能够实现非线性序转换,可以作为解决复杂层次结构中方案排序的一种实用方法。The ranking metric was mapped into high dimensional state space to discover the classification information hidden in the membership degree and the non-lienear order conversion,which could not achieve in the one dimensional space, was transformed into the conversion between membership degree vector in the high dimension space.The influence degree of the bottom plan to object was calculated to rank the bottom index,and then the hierarchy analysis model based on non-linear order conversion was established.The wastewater dam of a mine with foundation seepage was taken as an example to establish the three-layer hierarchical structure for verification,based on the 4 seepage reinforcement plans and 6 measurement indices.The results show that the model can implement the non-linear order conversion and serve as the method of ranking the complex hierarchical structural problem.

关 键 词：层次结构 隶属度 状态空间 区分权 

分 类 号：O141.4[理学—数学]