Neutrosophic parameterized time-effective soft sets: theory, properties, and a TOPSIS-based decision-making application

Abstract

The parameterized time neutrosophic soft set supplies a time-indexed family of neutrosophic soft sets together with its basic operations, while the effective-parameter mechanism, which revises an assessment once external confirmatory evidence arrives, has so far been developed either for static neutrosophic soft sets or for time-indexed fuzzy soft sets, where each assessment is a single membership value. This paper places an effective-parameter operator, the Λ-adjustment, natively on neutrosophic truth--indeterminacy--falsity triples inside the parameterized time-indexed structure, giving the neutrosophic parameterized time-effective soft set (N-PTEFSS). The base structure and its operations are recalled from earlier work and are not claimed as new; what is established here is the adjustment itself and its algebraic behaviour, including a bound-preservation result showing that it respects the neutrosophic constraint T + I + F ≤ 3, which has no counterpart in the single-valued fuzzy setting, together with monotonicity, Lipschitz continuity and order preservation. A neutrosophic TOPSIS decision procedure is developed downstream of the adjustment and applied to a medical-diagnosis ranking problem in which indeterminacy is a genuine and unavoidable part of clinical judgment. The model reduces, term for term at the definitional layer, to the time-effective fuzzy soft set when indeterminacy and falsity vanish, so it is a proper generalization of that fuzzy predecessor rather than a relabelling. In the worked application, time-weighting alone leaves the top of the ranking unchanged while the effective-parameter adjustment reverses the top two alternatives, showing that post-assessment confirmatory evidence is decision-relevant and that no purely pre-implementation analysis can capture it.