An uncertainty-induced axiomatic foundation of the analytic hierarchy process and its implication

• Published in: Expert systems with applications 2021-11, Vol.183, p.115427, Article 115427
• Main Authors: Liu, Fang, Qiu, Mei-Yu, Zhang, Wei-Guo
• Format: Article
• Language: English
• Subjects: Analytic hierarchy process; Analytic hierarchy process (AHP); Axiomatic foundation; Axioms; Broken symmetry; Consistency; Decision analysis; Decision making; Hierarchies; Reciprocal symmetry breaking (RSB); Uncertainty
• ISSN: 0957-4174; 1873-6793
• DOI: 10.1016/j.eswa.2021.115427

Uncertainty is always encountered by decision makers (DMs) when addressing a complex decision-making problem. The existing axiomatic foundation of the analytic hierarchy process (AHP) cannot reflect the uncertainty experienced by DMs. In this paper, it is first to find that the uncertainty experienced by DMs can be characterized by the non-reciprocal property of pairwise comparisons. The novel concept of reciprocal symmetry breaking (RSB) is proposed to capture the situation without reciprocal property. Then an uncertainty-induced axiomatic foundation of the AHP model is reported, where the RSB is one of the proposed axioms. Some interesting results are derived from the new axioms involving the concept of approximate consistency and the method of eliciting priorities. An index is constructed to measure approximate consistency degree of pairwise comparison matrices (PCMs). Some comparisons with the typical AHP model are offered by carrying out some numerical examples. The obtained results reveal that the proposed axiomatic foundation and the derived facts form a novel operational basis of the AHP model under uncertainty. •An uncertainty-induced axiomatic foundation of AHP is proposed.•A novel concept of reciprocal symmetry breaking is introduced.•Some interesting facts are derived using the proposed axiomatic foundation.•An index is proposed to measure approximate consistency of pairwise comparison matrices.