Abstract EN:

The scientific environment of this work is complex systems, self-organized systems and their informatics implementation. The purpose of these implementations is funded on agent-based modelling which allows designing interacting networks of communicating entities that composed these systems. To try to make automatic treatments of the self-organisation between these agents, we have to use something which allows some efficient operators. So the algebraic tools proposed here the tables proposed here are generalizations of k-sets of Eilenberg. These tools are efficient algebraic data structures and allow modeling some specificity of the complexity of the systems considered. This work ends with an important part concerning practical applications. The applications mainly concern economical aspects. Two kinds of developments are made: the first is the use of automata in game theory. In these important economic modelling activities, we propose an original representation of probabilistic automata which evolve with genetic algorithms and can produce models for adaptive strategies. These strategies are kind of more general models which mixed cooperative and competitive aspects. So the model proposed is versatile and give the base of a generic framework for modelling many kind of interacting agents in various systems. With this first kind of development for economical model, we show how to use many simple automata and how they are able to generate by interaction, a kind of self-organization. The second kind of development use a more sophisticated model based on cognitive sciences. (Francisco Varela is a good entry for understand the "cognitive sciences" we talk about. . . ). The aim is to build a framework for decision support system which models a complex system where knowledge database interact with decision process and where emotional aspects interact also. This model is original and can be also used for educational process modelling. This work describes some basis for operators for complex system modelling and sketches some innovative methods for various applications which deal with self-organization and complexity of description for natural and artificial systems.