Potential Nondominance in Multi-Criteria Decision Analysis

Vladislav Podinovski () and Andrey Nelyubin
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Vladislav Podinovski: National Research University Higher School of Economics, Moscow 101000, Russian Federation
Andrey Nelyubin: ��Institute of Machines Science of the RAS, Moscow 101990, Russian Federation

International Journal of Information Technology & Decision Making (IJITDM), 2024, vol. 23, issue 03, 1401-1422

Abstract: In this paper, we consider multi-criteria decision-making problems of selecting the best decision alternative in which the preferences of the decision maker are given in the form of quasi-orders. If the decision maker’s preferences are modeled by a family of complete quasi-orders (in particular, by a parametric family of additive value functions) then a common approach to solving such problems is based on the notion of potential optimality. In this paper, we consider the case in which the decision maker’s preferences are modeled by a family of incomplete quasi-orders. We suggest a new approach to selecting decision alternatives by introducing the notion of potential nondominated alternatives. Such alternatives can be regarded as candidates for the best alternative. We investigate properties of the sets of potential nondominated alternatives and, for the case of a parametric family of partial quasi-orders, we develop a method of their identification. Our development is illustrated by numerical examples.

Keywords: Decision analysis; preference relations; nondominance; potential optimality (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0219622022500808

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