Operations on Neutrosophic N-Hypersoft Sets: A Novel Framework for Decision-Making

Abstract

The aims of this research are to combine the neutrosophic set with the N-hypersoft set framework to develop the Neutrosophic N-Hypersoft Set (NN-HSS), maintaining structural symmetry for the representation and analysis of binary and non-binary data. Furthermore, this study aims to propose a proper mathematical model to handle the uncertainty of multi-sub-attribute structures especially for rating-evaluation-based systems, for improving the accuracy and flexibility of decision making in uncertain and inconsistent environments.The proposed NN-HSS framework establishes fundamental set-theoretic operations, including top-weak and bottom-weak complements, the extended and restricted unions, and the intersections. These operations are formally defined and illustrated by a suitable example to demonstrate their applicability. Additionally, the NN-HSS framework proposes a weighted choice-values-based decision-making approach to evaluate and rank alternatives in uncertain multi-sub-attribute environments. A numerical example is presented to validate the effectiveness and applicability of the proposed approach. The results indicate that the suggested NN-HSS framework efficiently improves decision-making by precisely managing uncertainty in datasets with both binary and non-binary data. The study also emphasizes the usefulness of mathematical ideas in real-world decision-making, where ambiguity and imprecision are common. The suggested framework improves the modeling of intricate multi-sub-attribute structures and offers a reliable method for addressing real-world decision-making issues, especially in rating-based evaluation systems that are marked by inconsistency, uncertainty, and indeterminacy.