Deciphering the Geometric Bonferroni Mean Operator in Pythagorean Neutrosophic Sets Framework

The Geometric Bonferroni Mean (GBM), is an extension of The Bonferroni mean (BM), that combines both BM and the geometric mean, allowing for the representation of correlations among the combined factors while acknowledging the inherent uncertainty within the decision-making process. Within the framework of Pythagorean neutrosophic set (PNS) that encompasses truth, indeterminacy, and falsity-membership degrees, each criterion can be integrated into a unified PNS value, portraying the overall evaluation of that criterion by employing the Geometric Bonferroni mean. This study aims to enhance decision-making in Pythagorean neutrosophic framework by introducing an aggregation operator to PNS using the Geometric Bonferroni Mean. Additionally, it proposes a normalized approach to resolve decision-making quandaries within the realm of PNS, striving for improved solutions. The novel Pythagorean Neutrosophic Normalized Weighted Geometric Bonferroni Mean (PNNWGBM) aggregating operator has been tested in a case of multi-criteria decision-making (MCDM) problem involving the selection of Halal products suppliers with several criteria. The result shows that this aggregating operator is offering dependable and pragmatic method for intricate decision-making challenges and able to effectively tackle uncertainty and ambiguity in MCDM problem.