MCDM using normalized weighted Bonferroni mean operator in Pythagorean neutrosophic environment

Abstract

Intuitionistic Fuzzy Set (IFS) adds a hesitation degree to classical fuzzy units, which accounts for uncertainty. Pythagorean Fuzzy Set (PFS) extends IFS by means of the usage of the Pythagorean theorem, allowing greater flexibility in assigning membership and non-membership degrees, especially useful when handling higher stages of uncertainty. Neutrosophic Fuzzy Set (NFS) introduces a three-dimensional structure where reality, indeterminacy, and falsity are independently defined, allowing for extra complicated modeling of uncertainty. 

Pythagorean Neutrosophic Fuzzy Set (PNFS) is a specialized extension of the Neutrosophic Fuzzy Set that includes the standards of Pythagorean fuzzy units. This idea is mainly useful for managing decision-making situations wherein uncertainty and hesitation are prominent. The Bonferroni mean (BM) operator is an extension of the traditional arithmetic mean and is a powerful aggregation operator utilized in multi-criteria decision making (MCDM), as it is able to capture the relationships between pairs of criteria. 

In this paper, the Pythagorean neutrosophic normalized weighted Bonferroni mean operator (PNNWBM) is presented, and its properties are reviewed. The Pythagorean Neutrosophic Numbers (PNN) are aggregated through PNNWBM, and the alternatives are ranked via the Pythagorean Neutrosophic score function in the selection of mobile networks based on diverse criteria. Through comparative analysis with various existing approaches and the obtained results, the effectiveness of the proposed operator is confirmed.