Reasoning and Unsupervised Learning in a Fuzzy Cognitive Map

This paper presents a new model for unsupervised learning and reasoning on a special type of cognitive maps realized with Petri nets. The unsupervised learning process in the present context adapts the weights of the directed arcs from transitions to places in the Petri net. A Hebbian-type learning algorithm with a natural decay in weights is employed to study the dynamic behavior of the algorithm. The algorithm is conditionally stable for a suitable range of the mortality rate. After convergence of the learning algorithm, the network may be used for computing the beliefs of the desired propositions from the supplied beliefs of the axioms (places with no input arcs). Because of the conditional stability of the algorithm, it may be used in complex decision-making and learning such as automated car driving in an accident-prone environment. The paper also presents a new model for knowledge refinement by adaptation of weights in a fuzzy Petri net using a different form of Hebbian learning. This second model converges to stable points in both encoding and recall phases.