From Fuzzy Cognitive Maps to Granular Cognitive Maps

Fuzzy cognitive maps (FCMs) form a class of graph-oriented fuzzy models describing causal relationships among concepts. In this study, we augment these models by introducing their generalization coming in the form of granular FCMs. In contrast with FCMs, in the granular FCMs, the connections between the nodes (states) are described in the form of information granules, especially intervals and fuzzy sets. Key scenarios in which granular models (and granular FCMs) arise are presented in order to offer a compelling rationale behind the formation of such models. In the context of system modeling, we show that information granularity emerges as an important design asset. We discuss detailed schemes of allocation of information granularity and quantify a performance of the resulting granular FCM in terms of a coverage criterion. For illustrative purposes, the detailed studies are completed for granular FCMs with interval-valued connections.