Incomplete analytic hierarchy process with minimum weighted ordinal violations |
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Authors: | L Faramondi Sándor Bozóki |
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Affiliation: | 1. Unit of Automatic Control, Department of Engineering, Università Campus Bio-Medico di Roma, Rome, Italy;2. Laboratory on Engineering and Management Intelligence, Research Group of Operations Research and Decision Systems, Institute for Computer Science and Control (SZTAKI), Budapest, Hungary;3. Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest, Budapest, Hungary https://orcid.org/0000-0003-4170-4613 |
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Abstract: | 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. |
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Keywords: | Pairwise comparison matrix incomplete data logarithmic least squares ordinal constraints decision making process |
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