A Novel Method for Objective Weighting in MCDM: The Lorentzian Distance Approach (LDA) Model

The objective determination of criterion weights in Multi-Criteria Decision-Making (MCDM) processes is of critical importance for ensuring the validity and reliability of decision outcomes. However, most existing methods primarily focus on internal variations or linear relationships among criteria, often overlooking external distributional effects and complex interdependencies. To address these methodological limitations, this study introduces an innovative framework the Lorentzian Distance Approach (LDA) which simultaneously considers both internal and external distributions of criteria. LDA statistically models the normalized distributions of criteria and employs the Lorentzian distance metric to measure inter-criterion divergence with high sensitivity. Empirical analyses conducted on the 2024 Global Innovation Index (GII) dataset (Criteria: Institutions, Human Capital and Research, Infrastructure, Market Sophistication, Business Sophistication, Knowledge and Technology Outputs, Creative Outputs; Alternatives: Indonesia, Mauritius, Mexico, Georgia, North Macedonia, Russian Federation, Ukraine) revealed that LDA demonstrates strong consistency and robustness in maintaining alternative rankings. In the rank reversal analysis, LDA exhibited a high degree of structural alignment with the ENTROPY (rho = 0.964, p < 0.01) and SVP (rho = 0.964, p < 0.01) methods. Furthermore, case studies based on the World Competitiveness Booklet and the Global Sustainable Index confirmed that LDA maintains ranking stability and preserves its homogeneous structure throughout simulation analyses. The selected datasets were chosen for their qualitative representation of global and international characteristics and their quantitative suitability, ensuring that no dominant criterion values existed among countries. In conclusion, the LDA method emerges as a methodologically robust, flexible, and adaptable approach, offering a compelling alternative to classical weighting models and demonstrating strong potential for application in decision-making environments under uncertainty.