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Adaptive Estimation of Fuzzy Cognitive Networks and Applications

  • T. L. Kottas
  • Y. S. Boutalis
  • M. A. Christodoulou
Chapter
Part of the Intelligent Systems, Control, and Automation: Science and Engineering book series (ISCA, volume 39)

Fuzzy Cognitive Networks (FCN) have been introduced by the authors as an operational extension of Fuzzy Cognitive Maps (FCM), which were initially introduced by Kosko to model complex behavioral systems in various scientific areas. 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 chapter, we present a study on the existence of solutions of FCMs equipped with continuous differentiable sigmoid functions having contractive or at least non-expansive properties. This is done by using an appropriately defined contraction mapping theorem and the non-expansive mapping theorem. It is proved that when the weight interconnections fulfill certain conditions the concept values will converge to a unique solution regardless the exact values of the initial concept values perturbations, or in some cases a solution exists that may not necessarily be unique. Otherwise the existence or the uniqueness of equilibrium cannot be assured. Based on these results an adaptive weight estimation algorithm is proposed which employs appropriate weight projection criteria to assure that the uniqueness of FCM solution is not compromised. Fuzzy Cognitive Networks are in the sequel invoked providing an application framework for the obtained results.

Keywords

Equilibrium Point Fuzzy System Sigmoid Function Input Node Maximum Power Point Tracker 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  • T. L. Kottas
    • 1
  • Y. S. Boutalis
    • 1
  • M. A. Christodoulou
    • 2
  1. 1.Laboratory of Automatic Control Systems & Robotics, Department of Electrical & Computer EngineeringDemocritus University of ThraceXanthiGreece
  2. 2.Department of Electrical & Electronic EngineeringTechnical University of CreteChaniaGreece

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