Persistent Choquet Fuzzy Evidence for Detecting and Attributing

Distribution Drift in Data Streams

Rama Asad Nadweh1,*

1 Department of Science and Information Technology, Islamic Online University, Doha, Qatar

Received: November 01, 2025 Revised: January 05, 2026 Accepted: March 03, 2026 ⋆ Corresponding author

ABSTRACT

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.

Keywords: Fuzzy measure Choquet integral Concept drift Distribution drift Data streams Change detection

Evolving fuzzy systems Uncertainty aggregation

1. INTRODUCTION

Streaming environments violate the static-distribution assumption

whenever the law generating observations changes

with time. If Pt denotes the distribution at time t, drift is expressed

generically as Pt ̸= Pt+s for some s > 0; in supervised

learning this may involve Pt (X), Pt (Y), or the conditional

mechanism Pt (Y | X) [1–3]. The distinction matters. A detector

operating directly on an unlabeled signal zt identifies

distribution drift in that monitored quantity; if zt is a residual,

loss, score, or model diagnostic, such drift can become evidence

of model degradation without being logically identical