A Novel Method for Performance Evaluation of Alternatives: Lorentzian Distance Performance Measurement (LDPM)

This study proposes the Lorentzian Distance Performance Measurement (LDPM), a novel squared difference based approach developed for multi-criteria decision-making (MCDM) problems, enabling the comparative assessment of decision alternatives with respect to both ideal and anti-ideal reference points. In contrast, a substantial portion of conventional MCDM methods prevalent in the literature rely on one-sided distance measures, restrictive metric frameworks, or reference systems that overlook the relative configurations among alternatives. Such methodological constraints create a critical gap, particularly in decision environments where distributional characteristics exert a significant influence. The LDPM method addresses this gap by employing the Lorentzian Distance (LD) metric, distinguished by its high structural sensitivity and strong validity. This metric accentuates subtle differences while minimizing the disproportionate impact of large values, thereby effectively mitigating scale sensitivity issues. In an empirical application using the 2024 Global Innovation Index (GII) dataset, the method was evaluated with Entropy-based criterion weights, and its performance was rigorously examined through sensitivity analysis, comparative evaluation, and simulation scenarios. The results demonstrate that LDPM produces statistically consistent and reliable rankings, exhibiting a high degree of correlation with widely recognized MCDM techniques. Accordingly, LDPM emerges as a robust, flexible, and scientifically rigorous evaluation framework, particularly well-suited for deterministic and uncertainty free decision-making contexts.