对AHP单准则排序方法的改进
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摘要
层次分析法(AHP)用两两比较的方法,通过构造比例标度判断矩阵为排序提供了一种合理的数据条件;对比例标度判断矩阵进行基于最大特征根的一致性检验,是为了把最大特征值对应的归一化特征向量作为排序向量;但终因理论上不能提供比例标度判断矩阵保序的充分条件,所以特征根排序法受到质疑,AHP需要改进.指出,改进AHP的正确途径是回归基于判断矩阵数据的排序方法研究.排序可行的条件是标度具有可加性;为此定义具有可加性的评分标度,建立标度转换公式将比例标度转换为评分标度;阐述为什么一致性检验无助于正确排序的原因并剖析为什么基于评分标度排序与一致性检验无关;由此建立基于评分标度判断矩阵中数据的评分排序方法.
Analytic Hierarchy Process(AHP),by constructing scale judgment matrix through pair wise comparison,provides a reasonable data qualification for ranking.To process consistency test for the scale judgment matrix basing on maximum characteristic root is to use normalized eigenvector corresponding the maximum characteristic root as the ranking vector.However the theory couldn't provide sufficient condition for the scale judgment matrix' s order preserving.Thus the ranking method of characteristic root is questioned and need improving.This paper pointed out that the correct approach to improve AHP is to go back to ranking method research basing on data in judgment matrix.Besides the condition that approves ranking is to confirm that the scale is additive.Therefore this paper defines rating scale which is additive,builds formula to transfer scale into rating scale and presents the reason why consistency check makes no contribution to correct sorting.Besides the paper explains why sequencing basing on rating scale is not relevant to consistency check and builds sorting method basing on data in scale of judgment matrix.
Analytic Hierarchy Process(AHP),by constructing scale judgment matrix through pair wise comparison,provides a reasonable data qualification for ranking.To process consistency test for the scale judgment matrix basing on maximum characteristic root is to use normalized eigenvector corresponding the maximum characteristic root as the ranking vector.However the theory couldn't provide sufficient condition for the scale judgment matrix' s order preserving.Thus the ranking method of characteristic root is questioned and need improving.This paper pointed out that the correct approach to improve AHP is to go back to ranking method research basing on data in judgment matrix.Besides the condition that approves ranking is to confirm that the scale is additive.Therefore this paper defines rating scale which is additive,builds formula to transfer scale into rating scale and presents the reason why consistency check makes no contribution to correct sorting.Besides the paper explains why sequencing basing on rating scale is not relevant to consistency check and builds sorting method basing on data in scale of judgment matrix.
引文
[1]Saaty T C.The Analytic Hierarchy Process[M].University of Pittsburge,1988.
[2]许树柏,王莲芬.层次分析法原理[M].天津:天津大学出版社,1989.
[3]王莲芬,许树柏编著.层次分析法引论[M]北京:中国人民大学出版社,1990.
[4]Saaty T C.Decision making with the analytic hierarchy process[J].International Journal of Service Sciences,2008,1(1):83-98.
[2]许树柏,王莲芬.层次分析法原理[M].天津:天津大学出版社,1989.
[3]王莲芬,许树柏编著.层次分析法引论[M]北京:中国人民大学出版社,1990.
[4]Saaty T C.Decision making with the analytic hierarchy process[J].International Journal of Service Sciences,2008,1(1):83-98.