Deciphering the Geometric Bonferroni Mean Operator in Pythagorean Neutrosophic Sets Framework

Mohammad Shafiq bin Mohammad Kamari; Zahari Bin Md. Rodzi; R.H. Al-Obaidi; Faisal Al-Sharq; Ashraf Al-Quran; Rawan A. shlaka

Authors

Mohammad Shafiq bin Mohammad Kamari College of Computing, Informatics and Mathematics Studies, MARA University of Technology Negeri Sembilan Branch, Seremban Campus, Seremban, Negeri Sembilan, 70300, Malaysia;
Zahari Bin Md. Rodzi College of Computing, Informatics and Mathematics Studies, MARA University of Technology Negeri Sembilan Branch, Seremban Campus, Seremban, Negeri Sembilan, 70300, Malaysia;
R.H. Al-Obaidi Fuel and Energy Techniques Engineering Department, College of Engineering and Technologies, Al-mustaqbal University, 51001, Babylon
Faisal Al-Sharq Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq,
Ashraf Al-Quran Department of Basic Sciences, Preparatory Year, King Faisal University, Al-Ahsa 31982, Saudi Arabia,
Rawan A. shlaka College of Pharmacy, National University of Science and Technology, Dhi Qar, Iraq,

Keywords:

aggregating operator; Bonferroni Mean (BM); Geometric Bonferroni Mean (GBM); Pythagorean neutrosophic set (PNS); multi-criteria decision-making (MCDM).

Abstract

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 multicriteria 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.

DOI: 10.5281/zenodo.13932052