An approach to incremental fuzzy modelling of dynamic behavior functions in complex systems

Modelling complex systems has been a main concern for many years and will likely persist for the future. Nevertheless, most of the researchers involved in this field agree that complex systems are formed through hierarchic evolution. As such, they can be described through hierarchic representations. These representations methods are mostly, binary logic based diagrams. They succeeded in providing means for logical representations of systems and the interactions between their components. However, they lack to model the time dependent behavior of the system (i.e., how the system or its parts acts or reacts to internal and external changes during its operating). We propose an approach to incremental fuzzy modelling of dependencies between different levels of hierarchy of a system. These dependencies might be static or time dependent. This fuzzy approach will allow a full scale representation of a system's behavior and not only snapshots as it the case with binary logic based paradigms. In the development of the model, we consider in a first step, systems with Single Input Single Output parameters. A clustering algorithm is built to organize the data of the system. From the organized data, we induce a fuzzy system that captures the functioning of the real system. Using simple facts, the approach proposes to optimize the existing approaches used in fuzzy control