Linear Programming for Multi-Criteria Assessment with Cardinal and Ordinal Data: A Pessimistic Virtual Gap Analysis
| Source: ArXiv | Original article
A new pre‑print on arXiv (2604.09555v1) proposes a linear‑programming framework that merges cardinal and ordinal information for multi‑criteria assessment. The authors call the method “pessimistic virtual gap analysis” (PVGA). It formulates each alternative’s performance as a set of linear constraints that capture exact numeric scores (cardinal data) and rank‑order preferences (ordinal data). By minimizing the worst‑case “virtual gap” – the distance between an alternative’s achievable score and an ideal reference point – the model yields a single scalar value that can rank all options without forcing ordinal inputs into arbitrary numeric scales.
The contribution matters because most Multiple Criteria Decision‑Making (MCDM) tools either require fully quantified inputs or treat ordinal judgments as if they were cardinal, a practice that can distort outcomes in environmental planning, public procurement or AI model selection where qualitative rankings coexist with hard metrics. PVGA preserves the integrity of ordinal data, remains solvable with off‑the‑shelf simplex or interior‑point solvers, and produces a transparent worst‑case guarantee that decision makers can audit. Early simulations reported in the paper show tighter discrimination among alternatives compared with classic methods such as TOPSIS or weighted sum models, especially when data quality is uneven.
The next steps will reveal whether the approach moves beyond theory. Watch for an open‑source implementation, likely in Python’s PuLP or Julia’s JuMP, and for pilot studies in EU sustainability assessments where mixed data are the norm. Industry groups may test PVGA for supplier evaluation, while academic circles could benchmark it against existing MCDM suites. If the method proves scalable, it could become a standard tool for AI‑augmented decision pipelines that must reconcile quantitative outputs with expert rankings.
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