Learning Fuzzy Automaton’s Event Transition Matrix When Post-Event State Is Unknown


When compared to other techniques for system modeling, the fuzzy discrete event systems (FDESs) methodology has the distinct advantage of being able to model a class of event-driven systems as fuzzy automata with ambiguous state and event-invoked state transition. This is not possible with any other system modeling technique. We developed algorithms for online-supervised learning of the event transition matrix of the fuzzy automaton in two papers that were published not too long ago. These algorithms make use of fuzzy states both before and after the occurrence of fuzzy events. It was hypothesized that the post-event state would be easily accessible, whereas the pre-event state would either be directly available or be able to be estimated through learning. In this article, the focus is on the development of an algorithm for learning the transition matrix in a different setting, specifically when the pre-event state is available but the post-event state is not. We make the assumption that the post-event state is characterized by a fuzzy set that is connected to a (physical) variable whose value can be obtained. When the fuzzy sets are of the Gaussian type, new algorithms based on stochastic gradient descent have been developed that can learn both the transition matrix and the parameters of the fuzzy sets. The results of the computer simulation are presented in order to validate the theoretical development.

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