  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.
