论文标题
分析层次结构过程的修改的公理基础
A modified axiomatic foundation of the analytic hierarchy process
论文作者
论文摘要
本文报告了分析层次结构过程（AHP）修改的公理基础，其中配对比较的相互属性被打破了。提出了相互对称性破坏的新颖概念，以表征没有相互特性的考虑情况。发现决策者所经历的不确定性可以自然地纳入修改后的公理中。一些结果来自新的公理，涉及近似一致性的新概念和提出优先级的方法。从修改后的公理基础下的理论观点重新审视了排名逆转的现象。没有排名逆转的情况被解决并称为排名均衡。通过基于肯德尔的一致性系数引入可能性度指数来捕获对逆转的可能性。在某些不确定性下，修改后的公理和派生事实形成了AHP选择模型的新运作基础。观察结果表明，与具有相互属性的判断相比，可以接受更灵活的决策信息表达。
This paper reports a modified axiomatic foundation of the analytic hierarchy process (AHP), where the reciprocal property of paired comparisons is broken. The novel concept of reciprocal symmetry breaking is proposed to characterize the considered situation without reciprocal property. It is found that the uncertainty experienced by the decision maker can be naturally incorporated into the modified axioms. Some results are derived from the new axioms involving the new concept of approximate consistency and the method of eliciting priorities. The phenomenon of ranking reversal is revisited from a theoretical viewpoint under the modified axiomatic foundation. The situations without ranking reversal are addressed and called ranking equilibrium. The likelihood of ranking reversal is captured by introducing a possibility degree index based on the Kendall's coefficient of concordance. The modified axioms and the derived facts form a novel operational basis of the AHP choice model under some uncertainty. The observations reveal that a more flexible expression of decision information could be accepted as compared to the judgments with reciprocal property.
