Parameter analysis for sigmoid and hyperbolic transfer functions of fuzzy cognitive maps

Fuzzy cognitive maps (FCM) have recently gained ground in many engineering applications, mainly because they allow stakeholder engagement in reduced-form complex systems representation and modelling. They provide a pictorial form of systems, consisting of nodes (concepts) and node interconnections (weights), and perform system simulations for various input combinations. Due to their simplicity and quasi-quantitative nature, they can be easily used with and by non-experts. However, these features come with the price of ambiguity in output: recent literature indicates that changes in selected FCM parameters yield considerably different outcomes. Furthermore, it is not a priori known whether an FCM simulation would reach a fixed, unique final state (fixed point). There are cases where infinite, chaotic, or cyclic behaviour (non-convergence) hinders the inference process, and literature shows that the primary culprit lies in a parameter determining the steepness of the most common transfer functions, which determine the state vector of the system during FCM simulations. To address ambiguity in FCM outcomes, we propose a certain range for the value of this parameter, λ, which is dependent on the FCM layout, for the case of the log-sigmoid and hyperbolic tangent transfer functions. The analysis of this paper is illustrated through a novel software application, In-Cognitive, which allows non-experts to define the FCM layout via a Graphical User Interface and then perform FCM simulations given various inputs. The proposed methodology and developed software are validated against a real-world energy policy-related problem in Greece, drawn from the literature.