Parameterization and concept optimization of FCM models

Fuzzy Cognitive Maps (FCM) are widely used to model and analyze the behavior of complex multicomponent systems. The application of FCM might be non-trivial in some specific context, however. Two rather general problems of the application of FCM and respective solutions are described in this paper. The first problem is as follows: In some cases the concept values obtained at the end of an FCM simulation are very similar. If this occurs, the order of concepts, thus their relative importance cannot well defined. The second problem is to select the appropriate concepts and to define their number. The concepts are given by human experts, but the selection of the appropriate concepts which help to reach the required accuracy of the model, while keeping the model as simple as possible is a difficult task. This paper deals with these two (connected) problems and proposes solutions for them. The proposed solution for the first problem is to choose the optimal λ parameter value in the threshold function, the one for the second is to apply a “state reduction method” based on fuzzy tolerance relations presented in the paper.