*B. Chaib-draa, J. Desharnais, Sylvain Lizotte*

It seems apparent that there is a variety of empirical structures in multiagent environments which may be represented by graph as for instance: the communication structure, the structure reflecting the degree of cooperation, the structure reflecting influences between agents, the structure reflecting commitments between agents, the authority structure, etc. In this context, graph theory and associated branches of mathematics, and particularly matrix algebra, provide techniques of computation and formulas for calculating certain quantitative and qualitative features of empirical structures. This paper presents a formal model which can serve as mathematical model of the structural properties of any empirical multiagent system consisting of relationships among pair of agents. Precisely, our work consists of a formal model based on binary relations and graphs. This model has a high computational value since it is essentially based on matrix algebra. In addition, this model takes into account fuzzy relations as for example: none, some, much and a lot. Finally, the proposed model provides a framework for the reasoning about others, the negotiation and communication between agents . We conclude by discussing our initial experiments about a crossroads in which interactions between cars are represented by a cognitive structure.

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