Design of sigmoid activation functions for fuzzy cognitive maps via lyapunov stability analysis

Abstract

Fuzzy cognitive maps (FCMs) are used to support decision-making, and the decision processes are performed by inference of FCMs. The inference greatly depends on activation functions such as sigmoid function, hyperbolic tangent function, step function, and threshold linear function. However, the sigmoid functions widely used for decisionmaking processes have been designed by experts. Therefore, we propose a method for designing sigmoid functions through Lyapunov stability analysis. We show the usefulness of the proposed method through the experimental, results in inference of FCMs using the designed sigmoid functions. Copyright © 2010 The Institute of Electronics, Information and Communication Engineers.