Multi-Valued Complex Fermatean Neutrosophic EDAS method for green investment portfolio ranking in uncertain ESG environments

Decision-making in real-world environments is frequently challenged by imprecise, multi-dimensional, and dynamically evolving information. Traditional approaches often struggle to effectively handle such complexity, particularly in multi-attribute group decision-making contexts involving diverse expert opinions. To address these limitations, this study introduces the Multi-Valued Complex Fermatean Neutrosophic Set (MVCFNS), an advanced fuzzy framework that integrates three key capabilities: (i) multi-valued representation of truth, indeterminacy, and falsity; (ii) complex-valued modeling to capture magnitude and periodic variations; and (iii) Fermatean constraints for enhanced uncertainty quantification. Building upon the MVCFNS structure, fundamental arithmetic operations for Multi-Valued Complex Fermatean Neutrosophic Numbers (MVCFNNs) are formulated, and two novel aggregation operators (MVCFNWA and MVCFNWG) are developed. Essential theoretical properties, including idempotency, boundedness, and monotonicity, are rigorously established. Furthermore, enhanced score and accuracy functions are proposed to facilitate improved comparison and ranking of alternatives. These components are systematically integrated into an MVCFNS-based EDAS (Evaluation based on Distance from Average Solution) decision-making framework. The practical applicability of the proposed method is validated using real-world sovereign-level ESG data from 2021–2023 to rank ten countries as potential green investment portfolio alternatives under uncertain ESG environments. The empirical results demonstrate that the MVCFNS-EDAS framework provides robust, transparent, and reliable decision support while effectively preserving multi-valued, complex, and indeterminate information inherent in ESG indicators.