Bilinear Adaptive Parameter Estimation in Fuzzy Cognitive Networks

  • Authors:

  • Thodoris Kottas;Yiannis Boutalis;Manolis Christodoulou

  • Affiliations:

  • Democritus University of Thrace, Xanthi, Greece 67100;Democritus University of Thrace, Xanthi, Greece 67100 and Chair of Automatic Control, University of Erlangen-Nuremberg, Germany 91058;Technical University of Crete, Chania, Greece 73100

  • Venue:
  • ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
  • Year:
  • 2009

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Abstract

Fuzzy Cognitive Networks (FCN) have been introduced by the authors recently as an extension of Fuzzy Cognitive Maps (FCM). One important issue of their operation is the conditions under which they reach a certain equilibrium point after an initial perturbation. This is equivalent to studying the existence and uniqueness of solutions for their concept values. In this paper, we study the existence of solutions of FCNs equipped with continuous differentiable sigmoid functions. This is done by using an appropriately defined contraction mapping theorem. It is proved that when the weight interconnections and the chosen sigmoid function fulfill certain conditions the concept values will converge to a unique solution regardless the exact values of the initial concept values perturbations. Otherwise the existence or the uniqueness of equilibrium can not be assured. Assuming that these conditions are met, an adaptive bilinear weight estimation algorithm is proposed.