Journal of Neutrosophic and Fuzzy Systems

Data-stream drift is rarely one-dimensional: a changed stream may move in location, inflate in scale, alter its tail geometry, or differ globally even when no single moment changes decisively. This paper develops a fuzzy monitoring layer for a scalar stream zt ∈ R by comparing adjacent windows At and Bt through four robust evidences dj,t : median displacement, robust log-scale change, interquantile tail-shape change, and normalized one-dimensional transport. Stationary calibration maps each dj,t to a fuzzy grade uj,t ∈ [0,1]. A normalized 2-additive capacity then aggregates the evidence by qt = 4Σ j=1 mjuj,t +Σ j<k mjk min(uj,t ,uk,t ) ∈ [0,1], so pairwise reinforcement is modeled explicitly rather than hidden inside an arithmetic score. Persistence is separated from instantaneous evidence through At = [λAt−1 +qt −δ]+, and an alarm occurs when At ≥ h. The resulting Persistent Choquet Fuzzy Drift Monitor (PCFDM) also admits an exact component decomposition qt = Σj φj,t for drift attribution. A reproducible Monte Carlo study uses 120 independent stationary calibration streams and 220 test replications for each of seven scenarios. At matched stream-wise calibration, PCFDM detects mean, scale, mixed, and gradual drifts in 94.5%, 89.5%, 95.0%, and 92.3% of runs, with median delays 72, 88, 72, and 192 samples. Its transient-shock alarm rate is 40.5%, compared with 49.1% for fuzzy-mean evidence, 76.8% for maximum fuzzy evidence, and 65.9% for transport alone. Heavy-tail drift remains more difficult (48.2% detection), revealing a genuine trade-off between persistent multi-evidence confirmation and sensitivity to isolated shape changes. The contribution is therefore a mathematically decomposable fuzzy evidence mechanism for monitoring and explaining drift, not a claim of universal dominance over specialized change detectors.

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.