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

Sanjitha Radhakrishnan; Baiju Thankachan

Authors

Sanjitha Radhakrishnan Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India-576104;
Baiju Thankachan Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India-576104;

Keywords:

Single-valued neutrosophic set (SV NS), Single-valued neutrosophic multiple set (SV NMS), Multiple set, Similarity measure, Multicriteria decision-making

Abstract

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 SVNS, 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

DOI: 10.5281/zenodo.15468268