Renewable Energy Sources Selection Analysis with the Maximizing Deviation Method

Abstract

Multi-criteria decision-making (MCDM) methods offer powerful tools for decision-makers to identify the most suitable options in uncertain, complex, and contradictory situations. However, traditional fuzzy sets and Intuitionistic or Pythagorean fuzzy structures restrict the subjective judgment of experts due to mathematical constraints on the sum/sum of squares of membership and non-membership degrees, and are insufficient for modeling complex uncertainties. The main motivation of this research is to integrate the superior uncertainty-representation capability of Interval Fermatean Fuzzy Sets (IVFFS), which expands the flexibility limits of decision-makers with a cubic framework ($u^3 + v^3 \le 1$), into MCDM processes. Existing studies reveal a significant research gap: the lack of deviation-maximization mechanisms to objectively optimize criterion weights in an IVFFS environment. To fill this gap, this study develops a novel mathematical optimization model based on the Maximizing Deviation (MD) method for cases in which criterion-weighting information is completely or partially unknown. The biggest advantage of the proposed weighting model is that it objectively maximizes the discrepancies and deviations between expert decisions using Lagrangian multipliers, completely eliminating human bias and subjective errors. The developed IVFF-MD-based methodology was combined with the COPRAS ranking algorithm and applied to the selection of renewable energy sources, a critical step in mitigating global climate change and carbon emissions. v; robustness and sensitivity analyses demonstrated that the proposed framework is highly stable and robust to data fluctuations. This study contributes to the literature by introducing a theoretical weighting-optimization framework and offering a strategic decision-support mechanism for energy investments.