Interrogating the structure of fuzzy cognitive maps

Causal algebra in fuzzy cognitive maps (FCMs) plays a critical role in the analysis and design of FCMs. Improving causal algebra in FCMs to model complicated situations has been one of the major research topics in this area. In this paper we propose a dynamic causal algebra in FCMs which can improve FCMs' inference and representation capability. The dynamic causal algebra shows that the indirect, strongest, weakest and total effects a vertex influences another in the FCM not only depend on the weights along all directed paths between the two vertices but also the states of the vertices on the directed paths. Therefore, these effects are nonlinear dynamic processes determined by initial conditions and propagated in the FCM to reach a static or cyclic pattern. We test our theory with a simple example.