Normalising the Output of Fuzzy Cognitive Maps

Fuzzy cognitive maps (FCMs) constitute a quasi-quantitative modelling tool with the inherent ability to reduce the computational and data complexity of a represented system, as well as engage experts in the process to introduce human cognition in terms of how a system behaves. However, despite being constructed with and for experts, aiming to assist them into better understanding system dynamics, the interpretation of the semi-quantitative outputs of FCMs has been found challenging. The use of transfer functions in the FCM iterations has led to the distortion of the output values, hampering the qualitative interpretation of the results, and making it difficult for experts to understand the link with the fuzzy input they provided. For this reason, this study introduces a normalisation procedure, following an optimal selection of the $\lambda$ parameter of the sigmoid and hyperbolic tangent functions, to enable operating the transfer functions in the “almost linear” area, and then map the output domain into the input domain by a means of a linear transformation. Based on a case study in the energy field, we find that the proposed procedure reduces the distortion caused by the transfer functions, compresses the results and avoids the risk of exaggerating the differences in the output values, and thus builds towards enhancing FCMs’ ability to provide qualitatively interpretable results.