Incomplete analytic hierarchy process with minimum weighted ordinal violations
Abstract
Incomplete pairwise comparison matrices offer a natural way of expressing preferences in decision-making processes. Although ordinal information is crucial, there is a bias in the literature: cardinal models dominate. Ordinal models usually yield nonunique solutions; therefore, an approach blending ordinal and cardinal information is needed. In this work, we consider two cascading problems: first, we compute ordinal preferences, maximizing an index that combines ordinal and cardinal information; then, we obtain a cardinal ranking by enforcing ordinal constraints. Notably, we provide a sufficient condition (that is likely to be satisfied in practical cases) for the first problem to admit a unique solution and we develop a provably polynomial-time algorithm to compute it. The effectiveness of the proposed method is analyzed and compared with respect to other approaches and criteria at the state of the art.
- Publication:
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International Journal of General Systems
- Pub Date:
- August 2020
- DOI:
- 10.1080/03081079.2020.1786380
- arXiv:
- arXiv:1904.04701
- Bibcode:
- 2020IJGS...49..574F
- Keywords:
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- Mathematics - Optimization and Control
- E-Print:
- preprint submitted to the International Journal of General Systems