Abstract: This short note examines the mathematical relationship between the recently introduced
Neutral Set and the established Single-Valued Neutrosophic Set (SVNS). By means of a formal
comparison of definitions, notation, and admissibility conditions, we show that the Neutral Set is
mathematically equivalent to the SVNS, differing only in symbolic representation. Specifically, the
membership functions denoted by truth, indeterminacy, and falsity in the Neutral Set correspond
directly to the truth-membership, indeterminacy-membership, and falsity-membership functions of
the SVNS under a simple notational transformation. Furthermore, the informational regimes
identified for the Neutral Set—sub-ideal (incomplete information), intuitionistic (complete
information), and paraconsistent (contradictory information)—coincide with the interpretative
framework already established in neutrosophic set theory. We conclude that the Neutral Set should
be regarded as a reformulation or particular representation of the Single-Valued Neutrosophic Set
rather than a novel mathematical structure.
Keywords: Single-Valued Neutrosophic Set, Neutral Set, neutrosophic logic, neutrosophic set
theory, mathematical equivalence, indeterminacy, truth membership, falsity membership,
paraconsistent information, uncertainty modeling.
Publication Date: 2026-06-18