Comparison of Fuzzy Controller Optimization with Dynamic Parameter Adjustment Based on of Type-1 and Type-2 Fuzzy Logic

  • Marylu L. Lagunes
  • Oscar CastilloEmail author
  • Fevrier Valdez
  • Jose Soria
Part of the Studies in Computational Intelligence book series (SCI, volume 827)


This paper presents the comparison of fuzzy controller optimization results using dynamic parameter adjustment Type-1 (T1) and Interval Type-2 (T2) fuzzy logic to the Firefly Algorithm (FA). The FA is used for optimizations parameters of the membership functions in the fuzzy controllers. The dynamic adjustment is applied to the randomness parameter of the search space, which represents the exploration of the method, avoiding stagnation or premature convergence. The FA generates the values that the parameters of the membership functions take for optimization use in the fuzzy systems for control. The control plants have one or more input variables that are processed and result in one or more output variables, it would be very difficult to model the human reasoning in equations to achieve a machine acquires the knowledge acquired by humans. For that reason the fuzzy logic that generates that insertity is used as if it were human reasoning.


Type-1 fuzzy logic Interval type-2 fuzzy logic FA Dynamic adjustment 


  1. 1.
    X.S. Yang, X. He, Firefly algorithm: recent advances and applications. Int. J. Swarm Intell. 1(1), 36 (2013)CrossRefGoogle Scholar
  2. 2.
    X.-S. Yang, Nature-Inspired Metaheuristic Algorithms. (Luniver Press, 2010)Google Scholar
  3. 3.
    L. Amador-Angulo, O. Castillo, Comparative analysis of designing differents types of membership functions using bee colony optimization in the stabilization of fuzzy controllers, in Nature Inspired Design of Hybrid Intelligent Systems, vol. 667 (Springer, Berlin, 2017), pp. 551–571Google Scholar
  4. 4.
    M.L. Lagunes, O. Castillo, J. Soria, Methodology for the optimization of a fuzzy controller using a bio-inspired algorithm. Fuzzy Log. Intell. Syst. Des. 648, 131–137 (2017). SpringerCrossRefGoogle Scholar
  5. 5.
    E. Bernal, O. Castillo, J. Soria, Imperialist competitive algorithm with dynamic parameter adaptation applied to the optimization of mathematical functions. Nat. Inspired Des. Hybrid Intell. Syst. 667, 329–341 (2017). SpringerCrossRefGoogle Scholar
  6. 6.
    L. Rodríguez, O. Castillo, J. Soria, A study of parameters of the grey wolf optimizer algorithm for dynamic adaptation with fuzzy logic. Nat. Inspired Des. Hybrid Intell. Syst. 667, 371–390 (2017). SpringerCrossRefGoogle Scholar
  7. 7.
    C. Peraza, F. Valdez, O. Castillo, Improved method based on type-2 fuzzy logic for the adaptive harmony search algorithm. Fuzzy Log. Augment. Neural Optim. Algorithms 749, 29–37 (2018). SpringerGoogle Scholar
  8. 8.
    M.L. Lagunes, O. Castillo, F. Valdez, J. Soria, P. Melin, Parameter optimization for membership functions of type-2 fuzzy controllers for autonomous mobile robots using the firefly algorithm. Fuzzy Inf. Process. 831, 569–579 (2018). NAFIPSCrossRefGoogle Scholar
  9. 9.
    M.L. Lagunes, O. Castillo, J. Soria, Optimization of membership function parameters for fuzzy controllers of an autonomous mobile robot using the firefly algorithm. Fuzzy Log. Augment. Neural Optim. Algorithms 749, 199–206 (2018). SpringerGoogle Scholar
  10. 10.
    L.A. Zadeh, Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar
  11. 11.
    L.A. Zadeh, Fuzzy logic, Computer (Long. Beach. Calif), vol. 21, no. 4, pp. 83–93, (Apr. 1988)CrossRefGoogle Scholar
  12. 12.
    L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-III. Inf. Sci. (Ny) 9(1), 43–80 (1975)MathSciNetCrossRefGoogle Scholar
  13. 13.
    N.N. Karnik, J.M. Mendel, Q. Liang, Type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 7(6), 643–658 (1999)CrossRefGoogle Scholar
  14. 14.
    Q. Liang, J.M. Mendel, Interval type-2 fuzzy logic systems: theory and design. IEEE Trans. Fuzzy Syst. 8(5), 535–550 (2000)CrossRefGoogle Scholar
  15. 15.
    O. Castillo, P. Melin, J. Kacprzyk, W. Pedrycz, Type-2 fuzzy logic: theory and applications, in 2007 IEEE International Conference on Granular Computing (GRC 2007), (2007), pp. 145–145Google Scholar
  16. 16.
    J. Pérez, F. Valdez, O. Castillo, Modification of the bat algorithm using type-2 fuzzy logic for dynamical parameter adaptation. Nat. Inspired Des. Hybrid Intell. Syst. 667, 343–355 (2017). SpringerCrossRefGoogle Scholar
  17. 17.
    C. Soto, F. Valdez, O. Castillo, A review of dynamic parameter adaptation methods for the firefly algorithm. Nat. Inspired Des. Hybrid Intell. Syst. 667, 285–295 (2017). SpringerCrossRefGoogle Scholar
  18. 18.
    C. Solano-Aragón, O. Castillo, Optimization of benchmark mathematical functions using the firefly algorithm. Recent. Adv. Hybrid Approaches Des. Intell. Syst. 547, 177–189 (2014). SpringerCrossRefGoogle Scholar
  19. 19.
    P. Ochoa, O. Castillo, J. Soria, Fuzzy differential evolution method with dynamic parameter adaptation using type-2 fuzzy logic, in Intelligent Systems, 8th International Conference on, IEEE, (2016), pp. 113–118Google Scholar
  20. 20.
    Water Level Control in a Tank—MATLAB & Simulink Example—MathWorks America Latina. [Online]. Available: Accessed 04 Jul 2018
  21. 21.
    Temperature Control in a Shower—MATLAB & Simulink—MathWorks America Latina. [Online]. Available: Accessed 04 Jul 2018
  22. 22.
    P. Melin, C.I. González, J.R. Castro, O. Mendoza, O. Castillo, Edge-detection method for image processing based on generalized type-2 fuzzy logic. IEEE Trans. Fuzzy Syst. 22(6), 1515–1525 (2014)CrossRefGoogle Scholar
  23. 23.
    C.I. González, P. Melin, J.R. Castro, O. Castillo, O. Mendoza, Optimization of interval type-2 fuzzy systems for image edge detection. Appl. Soft Comput. 47, 631–643 (2016)CrossRefGoogle Scholar
  24. 24.
    C.I. González, P. Melin, J.R. Castro, O. Mendoza, O. Castillo, An improved sobel edge detection method based on generalized type-2 fuzzy logic. Soft. Comput. 20(2), 773–784 (2016)CrossRefGoogle Scholar
  25. 25.
    E. Ontiveros, P. Melin, O. Castillo, High order α-planes integration: a new approach to computational cost reduction of general Type-2 fuzzy systems. Eng. Appl. AI 74, 186–197 (2018)CrossRefGoogle Scholar
  26. 26.
    C. Leal Ramírez, O. Castillo, P. Melin, A. Rodríguez Díaz, Simulation of the bird age-structured population growth based on an interval type-2 fuzzy cellular structure. Inf. Sci. 181(3), 519–535 (2011)MathSciNetCrossRefGoogle Scholar
  27. 27.
    N.R. Cázarez-Castro, L.T. Aguilar, O. Castillo, Designing type-1 and type-2 fuzzy logic controllers via fuzzy lyapunov synthesis for nonsmooth mechanical systems. Eng. Appl. of AI 25(5), 971–979 (2012)CrossRefGoogle Scholar
  28. 28.
    O. Castillo, P. Melin, Intelligent systems with interval type-2 fuzzy logic. Int. J. Innov. Comput. Inf. Control 4(4), 771–783 (2008)Google Scholar
  29. 29.
    G.M. Mendez, O. Castillo, Interval type-2 TSK fuzzy logic systems using hybrid learning algorithm, Fuzzy Systems, 2005, in The 14th IEEE International Conference on FUZZ’05, 230–235Google Scholar
  30. 30.
    P. Melin, O. Castillo, Intelligent control of complex electrochemical systems with a neuro-fuzzy-genetic approach. IEEE Trans. Ind. Electr. 48(5), 951–955CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Marylu L. Lagunes
    • 1
  • Oscar Castillo
    • 1
    Email author
  • Fevrier Valdez
    • 1
  • Jose Soria
    • 1
  1. 1.Tijuana Institute of TechnologyTijuanaMexico

Personalised recommendations