Fuzzy Graph Similarity with Uncertainty and Cross-Level Interactions

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 ۳۴\% and correlation gains of ۷\%, validating our uncertainty-aware design choices.

Keywords:

Fuzzy graph similarity , Graph neural networks , Uncertainty quantification , Fuzzy set theory , Deep Learning , Graph edit distance