Introducing fuzzy reactive graphs: a simple application on biology

Abstract

In this paper, we propose a generalization for fuzzy graphs in order to model reactive systems with fuzziness. As we will show, the resulting fuzzy structure, called fuzzy reactive graphs (FRG), is able to model dynamical aspects of some entities which generally appear in: biology, computer science and some other fields. The dynamical aspect is captured by a transition function which updates the values of the graph after an edge has been crossed. The update process takes into account aggregation functions. The paper proposes a notion for bisimulation for such graphs and briefly shows how modal logic can be used to verify properties of systems modeled with FSGs. The paper closes with a toy example in the field of Biology.