Unveiling the Dynamic Behavior of Fuzzy Cognitive Maps

Fuzzy cognitive maps (FCMs) are recurrent neural networks comprised of well-defined concepts and causal relations. While the literature about real-world FCM applications is prolific, studies devoted to understanding foundations behind these rather scant. In this article, we introduce several definitions theorems that unveil dynamic behavior FCM-based models equipped with transfer F-functions. These analytical expressions allow estimating bounds for activation value each neuron analyzing covering proximity feasible spaces. The main theoretical findings suggest state space any model F-functions shrinks infinitely no guarantee converge a fixed point but its limit space. This result in conjunction values helps understand their poor performance when solving complex simulation problems.