Fuzzy systems (FSs) have enjoyed wide applications in various fields, including pattern recognition, intelligent control, data mining and bioinformatics, which is attributed to the strong interpretation and learning ability. In traditional application scenarios, FSs are mainly applied to model Euclidean space data and cannot be used to handle graph data of non-Euclidean structure in nature, such as social networks and traffic route maps. Therefore, development of FS modeling method that is suitable for graph data and can retain the advantages of traditional FSs is an important research. To meet this challenge, a new type of FS for graph data modeling called Graph Fuzzy System (GFS) is proposed in this paper, where the concepts, modeling framework and construction algorithms are systematically developed. First, GFS related concepts, including graph fuzzy rule base, graph fuzzy sets and graph consequent processing unit (GCPU), are defined. A GFS modeling framework is then constructed and the antecedents and consequents of the GFS are presented and analyzed. Finally, a learning framework of GFS is proposed, in which a kernel K-prototype graph clustering (K2PGC) is proposed to develop the construction algorithm for the GFS antecedent generation, and then based on graph neural network (GNNs), consequent parameters learning algorithm is proposed for GFS. Specifically, three different versions of the GFS implementation algorithm are developed for comprehensive evaluations with experiments on various benchmark graph classification datasets. The results demonstrate that the proposed GFS inherits the advantages of both existing mainstream GNNs methods and conventional FSs methods while achieving better performance than the counterparts.

本文提出了一种新型模糊系统 Graph Fuzzy System (GFS), 用于图数据建模，其中定义了与 GFS 相关概念，构建了 GFS 建模框架，并提出了学习 GFS 的算法，其中包括图神经网络和 K-原型图聚类。实验结果表明，该方法继承了现有主流图神经网络方法和传统模糊系统方法的优点并取得了更好的性能。

图模糊系统：概念、模型与算法