Single-Valued Neutrosophic Multiple sets and its Application in Multi-Criteria Decision-Making

Single-valued neutrosophic set (SV NS) is an advanced generalization of fuzzy sets and intuitionistic fuzzy sets, developed to better represent indeterminate and inconsistent information. In contrast, multiple sets are generalized fuzzy sets that can simultaneously represent several ambiguous attributes of an item in multiple ways. In this article, we introduce the concept of the single-valued neutrosophic multiple set (SV NMS), which extends both multiple sets and SV NS, offering a more effective tool for addressing complex multi-criteria decision-making (MCDM) problems. Additionally, we present the theory of similarity measures between single-valued neutrosophic multiple sets and establish a multiple-attribute decision-making method based on these similarity measures. We rank the options and select the best one by comparing each alternative to the ideal alternative using similarity measures. Finally, we provide a practical example to demonstrate the application and effectiveness of SV NMS in the multiple-attribute decision-making method.