A Novel Explainable Neutrosophic Entropy–PROMETHEE Framework for Robust Crop Selection under Uncertainty

Abstract

Crop selection under climatic and agronomic uncertainty is a multi-criteria decision-making (MCDM) problem for which classical, deterministic approaches are poorly suited, as they cannot represent the indeterminacy inherent in field data. This study proposes a Neutrosophic Entropy–PROMETHEE (NE-PROMETHEE) framework that combines single-valued neutrosophic sets, for representing truth, indeterminacy, and falsity membership in criteria evaluations, with an entropy-based weighting scheme for deriving objective, data-driven criteria weights, free of subjective bias. The framework is applied to six crops (Cotton, Rice, Barley, Soybean, Wheat, and Maize) evaluated against four criteria: rainfall, temperature, days to harvest, and yield per hectare. Theoretical analysis establishes boundedness and flow conservation of the net outranking flow, Lipschitz stability of the ranking under data perturbation, consistency with Pareto dominance, and invariance under admissible rescaling of criteria and preference functions, providing formal guarantees rarely established for neutrosophic MCDM methods. Empirically, the framework identifies Rice as the top-ranked crop, followed by Maize, owing to Rice's dominant pairwise outranking performance. The resulting ranking is validated against six established MCDM benchmarks (TOPSIS, VIKOR, SAW, WPM, MARCOS, and MADM), yielding Spearman rank correlations of ρ ≥ 0.89 (up to ρ = 1.00) and concordant Kendall's τ statistics, confirming strong agreement. A comparison against six machine-learning surrogates (Random Forest, XGBoost, CatBoost, LightGBM, SVM, and a Deep Neural Network) under leave-one-out cross-validation shows that data-hungry learning models fail to reproduce the ranking reliably on this small-alternative-set problem, underscoring the practical advantage of the proposed deterministic, formally-grounded framework for real-world precision-agriculture decision support.