Cognitive maps and fuzzy implications

A cognitive map is a collection of nodes linked by some arcs. Up to this point, there is unanimity in the literature about the previous definition. But if we look closer at the meaning of the nodes and links, we can see that there are crucial differences between the various authors. And these differences are not always explicit. In spite of this, it seems that many authors perform on the maps the same kind of analysis (strongly inspired by the book of Axelrod), even if these analyses are not consistent with their conception of a cognitive map. That is why it is important to clearly and formally define the kind of map used. In this paper, we propose a formal definition of a cognitive map relying on the concept of fuzzy implication. Thus in our frame work, a node is a logical proposition and a link is an implication. Starting from our definition, we show some properties of this kind of maps and some analysis techniques.