Spherical Fermatean Neutrosophic Framework for Proposition‐Driven Multicriteria Decision‐Making Under Uncertainty

Source abstract

Multicriteria decision‐making (MCDM) problems in uncertain decision environments are made up of vagueness, indeterminacy, and disagreement among evaluators. The existing fuzzy and neutrosophic models, such as the intuitionistic, Pythagorean, and Fermatean models, are well suited to treat partial indeterminacy, but they are still limited in their ability to jointly describe indeterminacy, high degree of acceptance–rejection, and higher orders of uncertainty dispersion. To address these limitations, this paper presents a novel proposition‐oriented spherical Fermatean neutrosophic framework for uncertainty‐aware MCDM. The model expresses truth, indeterminacy, and falsity as a Fermatean admissible neutrosophic center in a three‐dimensional spherical space, and a radius parameter is added to represent the collective uncertainty coming from expert evaluations. On the basis of this structure, the weighted spherical Fermatean neutrosophic arithmetic averaging (WSFNAA) and weighted spherical Fermatean neutrosophic geometric averaging (WSFNGA) aggregation operators are proposed for robust decision aggregation. Furthermore, a proposition‐based scenario modeling mechanism is proposed to enable flexible, objective‐driven, and context‐specific evaluation by activating only relevant criteria. The applicability of the proposed framework is demonstrated by an agricultural crop selection case study with multiple expert assessments and entropy‐based objective weighting. The robustness, interpretability, and ranking stability of the proposed approach are confirmed by comparative analysis with benchmark neutrosophic MCDM methods, sensitivity analysis, and Monte Carlo validation, showing the effectiveness of the proposed approach as a practical decision support framework under uncertainty.