A modified axiomatic foundation of the analytic hierarchy process
Fang Liu, Wei-Guo Zhang

TL;DR
This paper introduces a modified axiomatic foundation for the analytic hierarchy process that relaxes the reciprocal property, allowing for better modeling of decision-making under uncertainty and addressing ranking reversal phenomena.
Contribution
It proposes the concept of reciprocal symmetry breaking and develops a new axiomatic basis for AHP, enhancing flexibility in representing decision information and uncertainty.
Findings
Incorporates uncertainty into AHP axioms
Addresses ranking reversal with a new index
Defines ranking equilibrium under modified axioms
Abstract
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…
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