Symmetry (Jul 2023)

Fuzzy Model Parameter and Structure Optimization Using Analytic, Numerical and Heuristic Approaches

  • Joel Artemio Morales-Viscaya,
  • Adán Antonio Alonso-Ramírez,
  • Marco Antonio Castro-Liera,
  • Juan Carlos Gómez-Cortés,
  • David Lazaro-Mata,
  • José Eleazar Peralta-López,
  • Carlos A. Coello Coello,
  • José Enrique Botello-Álvarez,
  • Alejandro Israel Barranco-Gutiérrez

DOI
https://doi.org/10.3390/sym15071417
Journal volume & issue
Vol. 15, no. 7
p. 1417

Abstract

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Fuzzy systems are widely used in most fields of science and engineering, mainly because the models they produce are robust, accurate, easy to evaluate and capture real-world uncertainty better than do the classical alternatives. We propose a new methodology for structure and parameter tuning of Takagi–Sugeno–Kang fuzzy models using several optimization techniques. The output parameters are determined analytically, by finding the minimum of the root-mean-square error (RMSE) for a properly defined error function. The membership functions are simplified by considering symmetry and equispacing, to reduce the optimization problem of finding their parameters, and allow it to be carried out using the numerical method of gradient descent. Both algorithms are fast enough to finally implement a strategy based on the hill climbing approach to finding the optimal structure (number and type of membership functions) of the fuzzy system. The effectiveness of the proposed strategy is shown by comparing its performance, using four case studies found in current relevant works, to the popular adaptive network-based fuzzy inference system (ANFIS), and to other recently published strategies based on evolutionary fuzzy models. In terms of the RMSE, performance was at least 28% better in all case studies.

Keywords