Extensions of Fuzzy Cognitive Maps

Fuzzy Cognitive Maps (FCMs) are interpretable simulation models capable of representing complex systems; however, they have numerous limitations. They can only represent causal relationships, have a limited representation of uncertainty, and cannot capture nonlinear relationships, time delays/lags, or conditional relationships. Thus, several extensions of FCMs have been proposed. We organize various use cases, additional features, and added requirements of extensions of FCMs and identify candidates to support extension selection given a particular scenario. We examine how to build Interval-Valued FCMs (IVFCMs), Time-Interval FCMs (TI-FCMs), and Extended-FCMs (E-FCMs), how they operate, and the additional features they offer to introduce a subset of extensions. We comment on three trends of applying and developing extensions and suggest two skills for modelers to effectively use extensions. Finally, we provide exercises to solidify the readers’ understanding of extensions. After reading this chapter and completing its problems, readers should understand why we extend FCMs and be able to compare extensions and their additional capabilities. Moreover, they should be able to select and apply an extension for numerous distinct use cases.