A Conditional, Boundary-Aware, and Auditable Deletion-Effect Weighting Framework for MCDM with Positive Decision Matrices and a Fixed Set of Alternatives

Source abstract

In objective-weighted multi-criteria decision-making (MCDM), a deletion-effect weight is not automatically identifiable when the normalization scale and its reference boundary are determined by the same candidate set. We develop a conditional, auditable framework for fixed-candidate decision matrices with benefit and cost criteria. Log-Ratio Composite Normalization (LRCN) maps each direction-aligned positive value to its log ratio relative to a declared criterion boundary, preserving within-criterion ratio gaps. LRCN-conditioned Deletion-Effect Weighting (LRCN-DEW) assigns each criterion a normalized weight proportional to the change in equal-weight row score under leave-one-criterion-out recalculation. The framework makes the structural, resolution, and candidate-set conditions for interpreting these effects explicit. Deterministic identities, controlled perturbations, ten public matrices, and semi-synthetic generators examine numerical consistency, boundary behavior, module coupling, and recovery. The frozen-boundary coordinate preserves the audited pair gap (1.000 versus 0.009 after re-estimating a min–max boundary). The proposed LRCN–LRCN-DEW configuration is favored under the declared ratio-scale generator, with recovery and Kendall’s agreement of 0.9332 and 0.9716, respectively, but other configurations lead under additive noise and in some public cases. The public matrices are used to examine numerical portability; their criterion-level ratio semantics and native measurement resolution were not verified. These findings show that the method provides boundary-consistent and reproducible weighting, while its comparative advantage depends on the measurement and perturbation mechanism.