hyfu-had-quantum-fuzzy - SKILL.md Agent Skill

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)