GFS-Node: Graph Fuzzy Systems for Node Prediction

Graph data modeling is nontrivial due to the challenges to ensure model interpretability and handle data uncertainty. While methods derived from deep learning models, such as graph neural networks (GNNs), are able to handle graph data, the interpretability is limited. Graph fuzzy systems (GFSs) based on the fuzzy rules and fuzzy inference have been proposed to improve interpretability, but the existing methods are developed for whole graph prediction only and cannot deal with node prediction, which is a more common task in graph data modeling. To tackle the challenges, a novel GFS for node prediction (GFS-node) is investigated in this study. For this purpose, the concepts, framework, and algorithms of GFS-node are systematically developed. First, several related concepts are defined, including the node fuzzy rule base, node fuzzy set, and node consequent processing module (NCPM). A general framework for GFS-node is then presented, where the construction of antecedents and the consequents of fuzzy rules are analyzed. Furthermore, a concrete implementation method of GFS-node is designed. In particular, the kernel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> virtual central nodes clustering (KVCN) algorithm is proposed to develop the algorithm for antecedent generation, and the linear message passing network (LMPN) is adopted to develop the algorithm for consequent generation and learning. Experiments are carried out on multiple benchmark datasets, and the results show that GFS-node combines the advantages of both traditional fuzzy systems and classical GNNs for node prediction.