Volume 11 • Issue 1 • PP: 17–24 • 2026
Hesitation-Gated Fuzzy–Neutrosophic Prototype Learning under Asymmetric Label Noise
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© 2026 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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Label corruption is difficult for prototype classifiers because a mislabeled observation does two things at once: it perturbs the prototype vyi associated with the supplied label and obscures whether the observation is genuinely ambiguous or simply inconsistent with its assigned class. This paper develops an adaptive fuzzy–neutrosophic prototype learning algorithm that separates these effects. For each training observation, the membership vector ui = (ui1, . . . ,uiK) ∈ ΔK−1 induced by the current prototypes is converted into the evidence state zi = (Ti, Ii,Fi) ∈ [0,1]3: truth is the membership assigned to the observed class, falsity is the strongest competing membership, and indeterminacy is the normalized membership entropy. These quantities drive three coupled mechanisms: a contradiction margin ci = [Fi −Ti]+ that attenuates unreliable labels, an entropy-dependent fuzzy exponent mi ∈ [mmin,mmax] that adapts membership weighting near class overlap, and a conservative soft-label correction activated only when Fi > Ti and the hesitation Ii is sufficiently small. The resulting Adaptive Fuzzy–Neutrosophic Prototype Learning (AFNPL) algorithm remains a lightweight prototype method with linear cost in the number of observations, classes and features per iteration. A reproducible three-class study evaluates 0–40% cyclic asymmetric label corruption under low, medium and high class overlap. At medium overlap and 40% corruption, AFNPL obtains 91.54% test accuracy and 91.55% macro-F1, compared with 72.52%/72.37% for noisy class means and 80.23%/80.17% for trimmed class means. Its internal contradiction score also detects corrupted labels with mean AUC between 0.959 and 0.971 across the contaminated settings. The contribution is therefore not only a robust prototype update, but a fuzzy learning mechanism in which neutrosophic truth, indeterminacy and falsity have explicit algorithmic roles in label reliability and adaptive fuzzy weighting.
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