aspg-24-4494-1791482501 20261008180141 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6430 2771-6449 2025 10 2 Suman Das Assistant Professor Grade II (Mathematics), Department of Education, National Institute of Technology Calicut, Kozhikode–673601, Kerala, India Ajoy Kanti Das Associate Professor, Department of Mathematics, Tripura University, Agartala–799022, Tripura, India A weak fuzzy assignment can mean two geometrically different things. A record may lie between otherwise legitimate clusters, so its membership vector ui = (ui1, . . . ,uiK) is genuinely ambiguous; or it may be remote from every prototype, in which case diffuse membership is a symptom of outlierness rather than a boundary. Treating both cases through one fuzziness scalar makes the prototype update unable to explain why a record should have reduced influence. This paper constructs Entropy–Remoteness Neutrosophic Fuzzy c-Means (ERN-FCM) from two separate quantities. Boundary indeterminacy is Ii = α[−Σk uik loguik]/logK, whereas robust remoteness is Fi = 1−exp(−τρi) with ρi = [(δi−q.90)/(q.90−q.50+ε)]+ and δi = mink ∥xi−vk∥2. Their conjunction gives truth Ti = (1−Ii)(1−Fi) and therefore Ti +Ii +Fi = 1+IiFi. Prototypes are updated by v+k = Σi Tium ikxi/Σi Tium ik, so remote or highly ambiguous records contribute less without being hard-deleted. The numerical study deliberately separates the two geometries. On Wine with 10% gross contamination, mean adjusted Rand index rises from 0.8665 for ordinary FCM to 0.8975 for ERN-FCM; on Breast Cancer the corresponding values are 0.7014 and 0.7074, whereas Iris remains a counterexample where FCM is slightly better (0.6328 versus 0.6179). The remoteness-aware uncertainty 1−Ti identifies gross outliers with AUC 0.9898–0.9956 at 10% contamination, and on a separate boundary benchmark Ii identifies bridge observations with AUC 0.9963. Paired bootstrap contrasts, component ablation, parameter sensitivity, and fixed-point diagnostics support a focused conclusion: ERN-FCM is most useful when cluster recovery and the type of uncertain observation must be distinguished, not as a universal replacement for FCM. 2025 10 15 4494 https://creativecommons.org/licenses/by/4.0/ 10.54216/JNFS.100202 https://www.americaspg.com/journal/24/article/4494 https://www.americaspg.com/storage/articles/manuscripts/01M0H1Y6792TJ9EX1D8GTD77K7.pdf