Fixed-Anchor Euclidean TOPSIS for Prefix-Pruning Label Search under a Global Lower-Envelope Condition

Can a TOPSIS score safely prune partial walks before the terminal alternative set is known? Classical set-relative Euclidean TOPSIS cannot meet this timing requirement because its normalization and ideal points depend on the candidate set. We instead study Euclidean TOPSIS with exogenous anchors L < U and prove that its closeness score is well defined and strictly componentwise antitone on [L, U]. Consider a finite directed graph with componentwise nonnegative additive arc costs, and suppose that L is a componentwise lower envelope of every complete s-t walk. Under this condition, criterion-wise suffix bounds support admissible score pruning and extension-safe same-node dominance. Together with closed-subwalk erasure and a graph-size search horizon, these properties yield an exact walk-based label search and equality of the optimal feasible-walk and simple-path scores. The optimization model and its generic bound/dominance architecture fit established nonlinear resource-constrained shortest-path theory. The contribution is therefore a TOPSIS-specific certification and boundary analysis: a mutually nondominated example exposes candidate-set dependence, while further counterexamples identify why dominance and terminal arguments can fail when the lower anchor is nonredundant.