Volume 11 • Issue 2 • PP: 01 –08 • 2026
Dual-Scale Fuzzy Boundary Abstention for Selective Prototype Classification
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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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A classifier can be accurate on average and still be unreliable near regions in which competing classes overlap. We study this problem as selective fuzzy classification: for x ∈ Rd, the decision is either a label by(x) ∈ {1, . . . ,K} or abstention ⊥. The proposed dual-scale fuzzy boundary index (DFBI) decomposes local ambiguity into a distributed term Bmass(x) and an extremal term Bpress(x). The former quantifies similarity-weighted contradictory neighborhood mass, whereas the latter compares the strongest opposing and supporting fuzzy relations. Their geometric fusion qDFBI(x) = {Bmass(x)Bpress(x)}1/2 ∈ [0,1] induces the selective map gθc (x) = 1{qDFBI(x) ≤ θc}, where the empirical validation quantile θc targets coverage c. The analysis is entirely numerical rather than graphical and uses repeated stratified splits, selective accuracy, macro-F1, error capture, relative risk reduction, AURC, AUGRC, paired bootstrap intervals, ablation, neighborhood sensitivity, and a nonlinear stress test. At nominal c = 0.90, the mean selective-accuracy vector is ¯a = (0.9354,0.9882,0.9847,0.9744) for Iris, Wine, Breast Cancer, and Digits, while the corresponding error-capture vector is ¯e=(0.5726,0.7528,0.8093,0.7937). Relative to membership-margin uncertainty, Δa = (0.0211,0.0022,0.0194,0.0446). Thus the gain is not obtained by changing the base classifier f ; it follows from a local fuzzy acceptance policy ( f ,gθc ) whose uncertainty ordering is informed by boundary geometry.
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