A fuzzy structure processing mechanism for graph grammar

Abstract

Abstract A strict graph-matching mechanism brings normativeness to graph grammar but leads to graph grammar insufficiency when processing fuzzy grammatical structures. To address this issue, the current paper proposes an improved formal framework for graph grammar that enables it to effectively specify the ambiguity of graph models while maintaining normativeness and intuition. First, the improved framework defines the connection probability for edges and classifies the edges based on the connection probability, which is used as the quantitative and qualitative description of the graph grammar structure’s ambiguity. Second, the concepts of credibility threshold, credible subgraphs and candidate subgraphs are defined, and the constraints on the redex are adjusted to increase the fault tolerance of the graph-matching process. Finally, the grammatical operation is redesigned, with a matching weight defined for each redex based on the connection probability and the credibility threshold, thereby providing a theoretical basis and practical guidance for the selection of multiple redexes.