Pythagorean Neutrosophic Method Based on the Removal Effects of Criteria (PNMEREC): An Innovative Approach for Establishing Objective Weights in Multi-Criteria Decision-Making Challenges

In the realm of multi-criteria decision-making (MCDM), the significance of criteria weights cannot be overstated. As a result, researchers have innovated and introduced various approaches aimed at precisely determining these weightings. This paper proposes a novel methodology that combines the Pythagorean neutrosophic set (PNS) with Method Based on the Removal Effects of Criteria (MEREC). This integrated method, PNMEREC seeks to offer a thorough and dependable method for evaluating criteria and establishing weightage in MCDM scenarios. PNS provides a more detailed way of handling uncertainty than traditional fuzzy sets or intuitionistic fuzzy sets by considering truth, indeterminacy, and falsity memberships values for each element, allowing for a wider range of uncertainties to be captured. This paper also introduces 5-point, 9-point, and 11-point PNS linguistic variables that can be utilized to represent evaluations from experts. The newly established linguistic variable scales enable decision-makers to express their criteria with clearer and heightened precision in PNS settings according to their preferences. A comparative analysis is conducted by comparing PNMEREC result with PN-Entropy and PN-Statistical Variance procedure to investigate the performance of the proposed method. The result of comparative analysis indicates that the weights produced by the PNMEREC method exhibit a high degree of reliability and stability, as demonstrated by the significant Pearson correlation coefficient values. Hence, the PNMEREC methodology possesses the capacity to thoroughly capture the determination of criterion weight via a more thorough and nuanced analysis. A sensitivity analysis is also conducted to compare the performance of the PNMEREC method using two distance techniques. The results reveal that the choice of distance technique impacts weight distribution and prioritization. Specifically, PN-Hamming emphasizes sharper distinctions, while PN-Euclidean offers a more balanced allocation.