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Learning the optimal parameter of the Hamacher t-norm applied for fuzzy-rule-based model extraction

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Abstract

Mamdani-type inference systems with trapezoidal-shaped fuzzy membership functions play a crucial role in a wide variety of engineering systems, including real-time control, transportation and logistics, network management, etc. The automatic identification or construction of such fuzzy systems input output data is one of the key problems in modeling. In the past years, the authors have investigated several different fuzzy t-norms, among others, algebraic and trigonometric ones, and the Hamacher product by substituting the standard “min” t-norm operation, in order to achieve better model fitting. In the present paper, the focus is on examining the general parametric Hamacher t-norm, where the free parameter quite essentially influences the quality of modeling and the learning capability of the model identification system. Based on a wide scope of simulation experiments, a quasi-optimal interval for the value of the Hamacher operator is proposed.

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Acknowledgments

This work is partially supported by Óbuda University Grants, the project TÁMOP 421B; Széchenyi István University Main Research Direction Grant; and the National Scientific Research Fund Grants OTKA K 75711 and K 105529.

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Authors and Affiliations

  1. Faculty of Science, University of West Hungary, Szombathely, Hungary

    László Gál

  2. Institute of Microelectronics and Technology, Kandó Kálmán Faculty of Electrical Engineering, Óbuda University, Budapest, Hungary

    Rita Lovassy

  3. Institute of Intelligent Engineering Systems, John von Neumann Faculty of Informatics, Óbuda University, Budapest, Hungary

    Imre J. Rudas

  4. Department of Informatics, Faculty of Engineering Sciences, Széchenyi István University, Gyor, Hungary

    László T. Kóczy

  5. Department of Telecommunications and Media Informatics, Budapest University of Technology and Economics, Budapest, Hungary

    László T. Kóczy

Authors
  1. László Gál
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  2. Rita Lovassy
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  3. Imre J. Rudas
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  4. László T. Kóczy
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Corresponding author

Correspondence to Rita Lovassy.

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Gál, L., Lovassy, R., Rudas, I.J. et al. Learning the optimal parameter of the Hamacher t-norm applied for fuzzy-rule-based model extraction. Neural Comput & Applic 24, 133–142 (2014). https://doi.org/10.1007/s00521-013-1499-3

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  • DOI: https://doi.org/10.1007/s00521-013-1499-3

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