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

Author

Listed:
  • Themistoklis Koutsellis

    (National Technical University of Athens)

  • Georgios Xexakis

    (HOLISTIC P.C.)

  • Konstantinos Koasidis

    (National Technical University of Athens)

  • Alexandros Nikas

    (National Technical University of Athens)

  • Haris Doukas

    (National Technical University of Athens)

Abstract

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, $${\uplambda }$$ 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.

Suggested Citation

  • Themistoklis Koutsellis & Georgios Xexakis & Konstantinos Koasidis & Alexandros Nikas & Haris Doukas, 2022. "Parameter analysis for sigmoid and hyperbolic transfer functions of fuzzy cognitive maps," Operational Research, Springer, vol. 22(5), pages 5733-5763, November.
    • Handle: RePEc:spr:operea:v:22:y:2022:i:5:d:10.1007_s12351-022-00717-x
    DOI: 10.1007/s12351-022-00717-x
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    References listed on IDEAS

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    1. Alexandra S Penn & Christopher J K Knight & David J B Lloyd & Daniele Avitabile & Kasper Kok & Frank Schiller & Amy Woodward & Angela Druckman & Lauren Basson, 2013. "Participatory Development and Analysis of a Fuzzy Cognitive Map of the Establishment of a Bio-Based Economy in the Humber Region," PLOS ONE, Public Library of Science, vol. 8(11), pages 1-14, November.
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