On the Temporal Granularity in Fuzzy Cognitive Maps

The theory of fuzzy cognitive maps (FCMs) is a powerful approach to modeling human knowledge that is based on causal reasoning. Taking advantage of fuzzy logic and cognitive map theories, FCMs enable system designers to model complex frameworks by defining degrees of causality between causal objects. They can be used to model and represent the behavior of simple and complex systems by capturing and emulating the human being to describe and present systems in terms of tolerance, imprecision, and granulation of information. However, FCMs lack the temporal concept that is crucial in many real-world applications, and they do not offer formal mechanisms to verify the behavior of systems being represented, which limit conventional FCMs in knowledge representation. In this paper, we present an extension to FCMs by exploiting a theory from formal languages, namely, the timed automata, which bridges the aforementioned inadequacies. Indeed, the theory of timed automata enables FCMs to effectively deal with a double-layered temporal granularity, extending the standard idea of B-time that characterizes the iterative nature of a cognitive inference engine and offering model checking techniques to test the cognitive and dynamic comportment of the framework being designed.