RankabilityRanking

Given a set of $n$ alternatives, each evaluated against criteria that assign real-valued ratings, a ranking can be generated by ordering the alternatives in accordance with their ratings, when only one criterion exists. When $m$ criteria are present, each induces its own ranking, making the reconciliation of these orderings a fundamental problem in Multicriteria Decision-Making (MCDM) and Artificial Intelligence (AI). This paper introduces the concept of dominance (or nondominance) between alternatives. The recently proposed notion of rankability characterizes the feasibility of generating a meaningful ranking from a set of alternatives. However, current rankability methods produce inconsistent results. An alternative is considered efficient if it is nondominated. In principle, an ideal ranking method should satisfy two conditions: (1) place all nondominated alternatives above dominated ones, and (2) properly order nondominated alternatives relative to each other through appropriate parameter adjustments. Existing methods frequently fail to meet both requirements and they can suggest less accurate rankings. This paper makes two key contributions: (1) A novel rankability index that quantifies rankability through dominance analysis, measuring how closely the data approximates complete dominance; and (2) an Extension of VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje, or Multicriteria Optimization and Compromise Solution), called EVIKOR, which generates rankings that preserve total dominance relationships. We demonstrate the effectiveness of our methodology through applications to both a basketball dataset and a world university ranking dataset, showing significant improvements over existing approaches.