Sulima Ahmed Mohammed Zubair - Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass ۵۲۵۷۱, Saudi Arabia.

This study introduces an approach for Multiple Attribute Decision-Making (MADM) that deals with the complexity of Single-Valued Neutrosophic Uncertain Linguistic Variables (SVNULVs). This method is engineered to grasp the interconnectedness of multiple inputs and to meet the diverse requirements for semantic transformations. Due to the shortcomings of existing operational rules in terms of closeness and flexibility, this paper proposes a novel set of operational rules and a ranking process for SVNULVs, integrating the concept of a Linguistic Scale Function (LSF). We propose an innovative operator along with its weighted counterpart to amalgamate SVNULVs, thereby characterizing the dynamics among various inputs through these new operations. Concurrently, we scrutinize and discuss the unique cases and favorable properties of these proposed operators. Building upon this new operator, the paper also unveils a fresh MADM methodology leveraging SVNULVs. To validate the effectiveness of this proposed methodology, an illustrative example is employed, demonstrating the precision of the method and its advantages over existing MADM techniques.

multiple attribute decision-making, Hamy mean operator, neutrosophic uncertain linguistic set, linguistic scale function, neutrosophic set