A relational approach of fuzzy graph grammars

Abstract

Graph Grammars are a visual formal language for which there are several techniques of system specification and verification. This fact makes them an attractive option for describing complex systems. Fuzzy graph grammars generalize the concept of graph grammars, using fuzzy graphs. A fuzzy graph is composed of vertices and edges that have an associated membership value, which varies within a range of 0 to 1. Due to the lack of technique and analysis tools for fuzzy graph grammars, their use is still quite limited. One way to allow the analysis of fuzzy graphs grammars is using the extension of existing graph grammar approaches, including the concept of membership in the graph components. There is a relational approach of graph grammars that allows the use of theorem provers to perform property analysis of systems described in this language. This approach is the basis of a translation of graph grammars into the Event-B language, which enables the use of theorem provers of the Rodin tool. Therefore, the aim of this work is to extend this graph grammar approach, including fuzzy concepts, to allow the use of the theorem proving technique to analyze fuzzy graph grammars. In order to set this extension was first necessary to define the notion of typed fuzzy graph grammars.