层次分析法的一种改进的公理化基础
A modified axiomatic foundation of the analytic hierarchy process
摘要：
本文提出了一种改进的层次分析法（AHP）的公理化基础，打破了配对比较的互逆性。提出了倒易对称破缺的新概念来描述所考虑的无倒易性质的情况。结果发现，决策者所经历的不确定性可以自然地纳入修改后的公理。利用新的公理，引入近似一致性的概念和优先级的提取方法，得到了一些结果。在修正的公理化基础上，从理论的角度重新审视了排序反转现象。没有排名逆转的情况下，解决和所谓的排名均衡。排名逆转的可能性是通过引入一个可能性程度指数的基础上肯德尔的和谐系数。修正后的公理和推导出的事实构成了不确定条件下AHP选择模型的一个新的操作基础。结果表明，与具有互反性质的判断相比，决策信息的表达更灵活。
英文摘要：
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.
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