Pythagorean Neutrosophic Mathematical Modelling

Survey-based assessments often suffer from ambiguity, inconsistency, and uncertainty, which weaken the reliability of decision-making outcomes. To address these challenges, this study proposes a novel decision-support framework for data fuzzification, ranking, and agility measurement using Pythagorean Neutrosophic Fuzzy Sets (PNFS). The proposed method offers three major advantages: (i) enhanced ability to capture high levels of indeterminacy compared with classical fuzzy and intuitionistic models, (ii) improved ranking accuracy through a newly developed score function and ranking algorithm, and (iii) greater robustness in scenarios involving conflicting, incomplete, or imprecise expert judgments. The framework includes a refined Pythagorean Neutrosophic fuzzification technique, mathematically supported propositions, a score-based ranking mechanism, and a Pythagorean Neutrosophic Agility Index (PNAI) to measure responsiveness and flexibility under uncertain conditions. A case study on the Ennum Ezhuthum (Foundational Literacy and Numeracy - FLN) program in Tamil Nadu demonstrates the practical applicability of the approach, where decision-maker inputs are analyzed, criteria are established, and algorithms are implemented through MATLAB. The results show that PNFS-based modelling more effectively represents indeterminacy, enhances discrimination among alternatives, and provides a strong, reliable tool for educational policy evaluation and other uncertainty-driven domains.