Single valued Refined Neutrosophic Relations

Background Cantor’s classical definition of a set assumes that its elements are distinct with no repetition. However, this assumption may be inadequate when the information contains repeated, indeterminate, or contradictory elements. Single valued refined neutrosophic sets (SVRNSs) have been developed to address such situations by allowing multiple degrees of indeterminacy and contradiction. A simpler and more applicable form known as the single-valued refined neutrosophic set (SVRNS) was subsequently introduced. Methods In this study, the concept of a refined intuitionistic fuzzy relation is extended to a single-valued refined neutrosophic relation (SVRNR). Results We defined the single-valued refined neutrosophic set relation (SVRNR) and investigated its fundamental properties, including composition, reflexivity, symmetry, and transitivity. Several related studies have been reported. Conclusion This study develops a theory of single-valued refined neutrosophic relations and systematically examines their fundamental properties. Illustrative examples were provided to demonstrate the applicability of the proposed concepts.