Neutrosophic Selective Separability

Giorgio Nordo; Lorenzo Aff`; Florentin Smarandache

Authors

Giorgio Nordo MIFT Department– Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, 98166 Sant’Agata, Messina, Italy;
Lorenzo Aff` MIFT Department– Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, 98166 Sant’Agata, Messina, Italy;
Florentin Smarandache Emeritus Professor, Mathematics, Physical and Natural Sciences Division, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA;

Abstract

We develop a confidence-sensitive neutrosophic framework for selective separability. Single-valued
neutrosophic sets are evaluated through an admissible aggregation operator Φ(T,1 − I,1 − F), so that the
conservative minimum is only one possible choice. We first study uncertain dense data over an ordinary
topology and prove operator-independent transfer results for M-, H-, R-, and S-separability, while showing
that the admissible witnesses remain genuinely confidence-sensitive. We then pass to single-valued neutrosophic
topological spaces and distinguish strong intrinsic density, which reaches the full confidence height of every
effective open set, from weak intrinsic density, which only requires positive confidence overlap. The weak and
strong notions differ for individual neutrosophic sets, although both recover the expected classical space classes
on crisp-induced topologies. To keep countable network weight meaningful, we introduce countably calibrated
neutrosophic networks based on a dense rational set of point profiles. We also formulate both trace-based and
genuinely graded selection principles controlled by single-valued neutrosophic filters on the index set. Finally, we
compare the minimum and product confidence aggregators, discuss numerical resolution thresholds for intrinsic
selection, and derive consequences for Fr´echet–Urysohn and function spaces

DOI 10.5281/zenodo.21981659