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The Neutral Set as a Re-Notation of the Single-Valued Neutrosophic Set

Authors: Smarandache, Florentin;

The Neutral Set as a Re-Notation of the Single-Valued Neutrosophic Set

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.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green