hyfu-had-quantum-fuzzy

name

hyfu-had-quantum-fuzzy

description

HyFuHAD: Hybrid Quantum-Fuzzy Hyperspectral Anomaly Detection methodology. Combines Einstein fuzzy computing for classical inference with lightweight quantum defuzzifier for final detection. Uses multi-criteria decision framework with morphological, geometrical, and statistical membership functions. Use when: hyperspectral image anomaly detection, quantum neural network for remote sensing, fuzzy computing for image processing, Einstein fuzzy operations, or hybrid quantum-classical image analysis.

HyFuHAD: Hybrid Quantum-Fuzzy Anomaly Detection

Core Innovation

Combines classical Einstein fuzzy computing (smoother than min-max) with a lightweight quantum defuzzifier in a multi-criteria decision framework for hyperspectral anomaly detection.

Architecture

Phase 1: Multi-MF Fuzzification

Each pixel is fuzzified using multiple membership functions:

• Morphological MF: Based on spatial structure and texture
• Geometrical MF: Based on spectral shape and distance metrics
• Statistical MF: Based on statistical deviation from background

Phase 2: Einstein Fuzzy Inference

• Multi-fuzzy-rule system processes fuzzy degrees from all MFs
• Einstein sum: T-conorm providing smoother transitions than max
• Einstein product: T-norm providing smoother transitions than min
• Sub-second-level classical fuzzy detection output

Phase 3: Quantum Defuzzification

• Fuzzy features aggregated via proposed fuzzy feature aggregation network
• Lightweight quantum circuit processes aggregated features
• Quantum fuzzy detection fused with classical detection
• Final anomaly score from information fusion

Einstein Fuzzy Operations

Einstein Sum (T-conorm):
  S_E(a, b) = (a + b) / (1 + a*b)
  vs. max(a, b) — provides smoother "OR" transition

Einstein Product (T-norm):
  T_E(a, b) = (a * b) / (1 + (1-a)*(1-b))
  vs. min(a, b) — provides smoother "AND" transition

When to Use

• Hyperspectral remote sensing anomaly detection
• Multi-criteria decision with fuzzy logic
• Hybrid quantum-classical processing pipelines
• Need smoother fuzzy transitions than standard min/max

Key Advantages

• Einstein operations: smoother inference than min-max fuzzy logic
• Multi-MF approach: captures anomalies from multiple perspectives
• Quantum defuzzifier: leverages quantum feature processing
• Unsupervised: no labeled anomaly data required

References

• arXiv:2605.04388 "Hyperspectral Anomaly Detection Using Einstein Fuzzy Computing and Quantum Neural Network" (Lin et al., May 2026, accepted IEEE TGRS)