Fuzzy Graph Similarity with Uncertainty and Cross-Level Interactions

Document Type : Research Article

Authors

1 Department of General Science, BITS Pilani, Dubai Campus, Academic City, Dubai, UAE

2 Canadian Quantum Research Center, 106-46- Doyle Ave, Kelowna, British Columbia V1Y 0C2 Canada

3 Department of Mathematics, University of Mazandaran, Babolsar, Iran

4 Department of Physics, Sar. C., Islamic Azad University, Sari, Iran

Abstract

Real-world systems often exhibit relationships with inherent vagueness and imprecision, which fuzzy graphs effectively capture. Determining how similar two fuzzy graphs are remains essential for pattern recognition, social network analysis, and molecular biology applications where both edge strengths and node attributes carry uncertainty. Conventional approaches to measuring graph similarity struggle with the subtle uncertainties that characterize fuzzy graph structures. This paper presents FuzzyCLSim, a deep learning architecture for computing fuzzy graph similarity that integrates uncertainty quantification via fuzzy set theory. The proposed approach comprises three main innovations: a fuzzy graph convolutional network (F-GCN) propagating membership degrees together with features, a fuzzy weighted bilinear tensor network (F-WBTN) capturing directional fuzzy relationships between graphs, and a cross-level fuzzy feature extraction module combining node-level with graph-level fuzzy embeddings. Experimental results across three benchmark datasets demonstrate substantial improvements over existing methods, with average MSE reductions of 34\% and correlation gains of 7\%, validating our uncertainty-aware design choices.

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 10, Issue 1
December 2025
Pages 69-81

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History

  • Receive Date: 07 November 2025
  • Accept Date: 07 December 2025
  • Publish Date: 17 December 2025

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