High-Speed Interval Type-2 Fuzzy System for Dynamic Crossover Parameter Adaptation in Differential Evolution and Its Application to Controller Optimization

  • Patricia Ochoa
  • Oscar CastilloEmail author
  • José Soria


The main contribution in this paper is the use of a new type-reduction method to improve the processing speed of Type-2 fuzzy systems for dynamic parameter adaptation in the Differential Evolution algorithm. The proposed type-reduction is an approximation to the Continuous Karnik–Mendel (CEK) method, which is the equivalent to using a traditional Interval Type-2 fuzzy system, but with lower computational cost. The motivation of this work is to verify that the proposed methodology is equivalent in performance to an Interval Type-2 fuzzy system. The first type-reduction method was proposed by Karnik and Mendel (KM), and then was followed by its enhanced version called EKM, and the continuous versions were called CKM and CEKM. In addition, there were variations of these and also other types of variations that eliminate the type-reduction process reducing the computational cost to a Type-1 defuzzification. The concept of approximation to the Continuous Karnik–Mendel (CEK) method is new in the area of metaheuristic algorithms and this is why it is in our interest to work with this methodology. We propose to use this methodology to achieve a dynamic crossover (CR) parameter adaptation in the Differential Evolution algorithm, and the objective is to use the type-reduction process and also provide a continuous solution to the defuzzification. This proposed methodology is applied to a set of mathematical functions and a control problem, for verifying the efficiency of the proposed methodology compared to the original algorithm and other existing methods in the literature.


Fuzzy system Differential Evolution algorithm Crossover parameter Dynamic parameter Interval Type-2 fuzzy logic 



Funding was provided by Consejo Nacional de Ciencia y Tecnología (Grant No. 122).


  1. 1.
    Bäck, T., Fogel, D.B., Michalewicz, Z. (eds.): Evolutionary computation 1: Basic algorithms and operators. CRC Press, Bristol (2018)Google Scholar
  2. 2.
    Russell, S.J., Norvig, P.: Artificial intelligence: a modern approach. Pearson Education Limited, Malaysia (2016)zbMATHGoogle Scholar
  3. 3.
    Pinedo, M., Hadavi, K.: Scheduling: theory, algorithms and systems development. In: Operations Research Proceedings 1991, pp. 35–42. Springer, Berlin, Heidelberg (1992)Google Scholar
  4. 4.
    Such, F.P., Madhavan, V., Conti, E., Lehman, J., Stanley, K.O., Clune, J.: Deep neuroevolution: genetic algorithms are a competitive alternative for training deep neural networks for reinforcement learning. arXiv preprint arXiv:1712.06567. (2017)
  5. 5.
    Mirjalili, S.Z., Saremi, S., Mirjalili, S.M.: Designing evolutionary feedforward neural networks using social spider optimization algorithm. Neural Comput. Appl. 26(8), 1919–1928 (2015)CrossRefGoogle Scholar
  6. 6.
    Greiner, D., Galván, B., Périaux, J., Gauger, N., Giannakoglou, K., Winter, G. (eds.): Advances in evolutionary and deterministic methods for design, optimization and control in engineering and sciences. Springer International Publishing, Basel (2015)Google Scholar
  7. 7.
    Jain, L.C., Kandel, A., Teodorescu, H.N.L.: Fuzzy and neuro-fuzzy systems in medicine. CRC Press, Bristol (2017)Google Scholar
  8. 8.
    Miranda, G.H.B., Felipe, J.C.: Computer-aided diagnosis system based on fuzzy logic for breast cancer categorization. Comput. Biol. Med. 64, 334–346 (2015)CrossRefGoogle Scholar
  9. 9.
    Zadeh, L.A., Aliev, R.A.: Fuzzy logic theory and applications: part I and part II. World Scientific Publishing, New Jersey (2018)CrossRefGoogle Scholar
  10. 10.
    De Silva, C.W.: Intelligent control: fuzzy logic applications. CRC Press, Boca Raton (2018)Google Scholar
  11. 11.
    Díaz, I., Ralescu, A.L., Ralescu, D.A., Rodríguez-Muñiz, L.J.: Some results and applications using fuzzy logic in artificial intelligence. In: Gil, E., Gil, J., Gil, M.Á. (eds.) The Mathematics of the Uncertain, pp. 575–584. Springer, Cham (2018)CrossRefGoogle Scholar
  12. 12.
    Jalani, J., Jayaraman, S.: Design a fuzzy logic controller for a rotary flexible joint robotic arm. In: MATEC Web of Conferences, vol. 150, p. 01011. EDP Sciences (2018)Google Scholar
  13. 13.
    Chouhan, A.S., Parhi, D.R., Chhotray, A.: Control and balancing of two-wheeled mobile robots using Sugeno fuzzy logic in the domain of AI techniques. Emerging trends in Engineering, Science and Manufacturing, (ETESM-2018), IGIT, Sarang, India (2018)Google Scholar
  14. 14.
    Liu, X., Mendel, J.M.: Connect Karnik–Mendel algorithms to root-finding for computing the centroid of an interval type-2 fuzzy set. IEEE Trans. Fuzzy Syst. 19(4), 652–665 (2011)CrossRefGoogle Scholar
  15. 15.
    Zadeh, L.A.: Fuzzy logic—a personal perspective. Fuzzy Sets Syst. 281, 4–20 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Vaidyanathan, S., Azar, A.T.: Takagi–Sugeno fuzzy logic controller for Liu–Chen four-scroll chaotic system. Int. J. Intell. Eng. Informat. 4(2), 135–150 (2016)Google Scholar
  17. 17.
    Trillas, E., Eciolaza, L.: Fuzzy logic, vol. 10, p. 978. Springer International Publishing, Berlin (2015)Google Scholar
  18. 18.
    Bai, Y., Roth, Z.S.: Fuzzy logic control systems. In: Bai, Y., Roth, Z.S. (eds.) Classical and Modern Controls with Microcontrollers, pp. 437–511. Springer, Cham (2019)CrossRefGoogle Scholar
  19. 19.
    Castillo, O., Valdez, F., Soria, J., Amador-Angulo, L., Ochoa, P., Peraza, C.: Comparative study in fuzzy controller optimization using bee colony, differential evolution, and harmony search algorithms. Algorithms 12(1), 9 (2019)zbMATHCrossRefGoogle Scholar
  20. 20.
    Peraza, C., Valdez, F., Castillo, O.: Improved method based on type-2 fuzzy logic for the adaptive harmony search algorithm. In: Castillo, O., Melin, P., Kacprzyk, J. (eds.) Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications, pp. 29–37. Springer, Cham (2018)Google Scholar
  21. 21.
    Bernal, E., Castillo, O., Soria, J., Valdez, F., Melin, P.: A variant to the dynamic adaptation of parameters in galactic swarm optimization using a fuzzy logic augmentation. In: 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1–7. IEEE (2018)Google Scholar
  22. 22.
    Guzmán, J.C., Melin, P., Prado-Arechiga, G.: Fuzzy optimized classifier for the diagnosis of blood pressure using genetic algorithm. In: Castillo, O., Melin, P., Kacprzyk, J. (eds.) Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications, pp. 309–318. Springer, Cham (2018)Google Scholar
  23. 23.
    Miramontes, I., Guzman, J., Melin, P., Prado-Arechiga, G.: Optimal design of interval type-2 fuzzy heart rate level classification systems using the bird swarm algorithm. Algorithms 11(12), 206 (2018)zbMATHCrossRefGoogle Scholar
  24. 24.
    Barraza, J., Rodríguez, L., Castillo, O., Melin, P., Valdez, F.: A new hybridization approach between the fireworks algorithm and grey wolf optimizer algorithm. J Optim (2018). MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Sahoo, D.K., Sahu, R.K., Sekhar, G.C., Panda, S.: A novel modified differential evolution algorithm optimized fuzzy proportional integral derivative controller for load frequency control with thyristor controlled series compensator. J Electr Syst Inf Technol 5(3), 944–963 (2018)Google Scholar
  26. 26.
    Hong, H., Panahi, M., Shirzadi, A., Ma, T., Liu, J., Zhu, A.X., Ochoa, P., Castillo, O., Soria, J., Kazakis, N.: Flood susceptibility assessment in Hengfeng area coupling adaptive neuro-fuzzy inference system with genetic algorithm and differential evolution. Sci. Total Environ. 621, 1124–1141 (2018)CrossRefGoogle Scholar
  27. 27.
    Ochoa, P., Castillo, O., Soria, J.: Differential evolution algorithm with interval type-2 fuzzy logic for the optimization of the mutation parameter. In: Castillo, O., Melin, P., Kacprzyk, J. (eds.) Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications, pp. 55–65. Springer, Cham (2018)Google Scholar
  28. 28.
    Juang, C.F., Chen, Y.H., Jhan, Y.H.: Wall-following control of a hexapod robot using a data-driven fuzzy controller learned through differential evolution. IEEE Trans. Ind. Electron. 62(1), 611–619 (2015)CrossRefGoogle Scholar
  29. 29.
    Bui, D.T., Nguyen, Q.P., Hoang, N.D., Klempe, H.: A novel fuzzy K-nearest neighbor inference model with differential evolution for spatial prediction of rainfall-induced shallow landslides in a tropical hilly area using GIS. Landslides 14(1), 1–17 (2017)CrossRefGoogle Scholar
  30. 30.
    Chen, W., Panahi, M., Pourghasemi, H.R.: Performance evaluation of GIS-based new ensemble data mining techniques of adaptive neuro-fuzzy inference system (ANFIS) with genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO) for landslide spatial modelling. Catena 157, 310–324 (2017)CrossRefGoogle Scholar
  31. 31.
    Marinaki, M., Marinakis, Y., Stavroulakis, G.E.: Fuzzy control optimized by a multi-objective differential evolution algorithm for vibration suppression of smart structures. Comput. Struct. 147, 126–137 (2015)zbMATHCrossRefGoogle Scholar
  32. 32.
    Ontiveros-Robles, E., Melin, P., Castillo, O.: New methodology to approximate type-reduction based on a continuous root-finding Karnik–Mendel algorithm. Algorithms 10(3), 77 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    Mendel, J.M., Liu, X.: Simplified interval type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 21(6), 1056–1069 (2013)CrossRefGoogle Scholar
  34. 34.
    Mendel, J.M.: General type-2 fuzzy logic systems made simple: a tutorial. IEEE Trans. Fuzzy Syst. 22(5), 1162–1182 (2014)CrossRefGoogle Scholar
  35. 35.
    Liu, X.: A survey of continuous Karnik–Mendel algorithms and their generalizations. In: Sadeghian, A., Mendel, J.M., Tahayori, H. (eds.) Advances in Type-2 Fuzzy Sets and Systems, pp. 19–31. Springer, New York (2013)CrossRefGoogle Scholar
  36. 36.
    Price, K., Storn, R.M., Lampinen, J.A.: Differential evolution: a practical approach to global optimization. Springer Science & Business Media, Cham (2006)zbMATHGoogle Scholar
  37. 37.
    Stanovov, V., Akhmedova, S., Semenkin, E.: LSHADE algorithm with rank-based selective pressure strategy for solving CEC 2017 benchmark problems. In: 2018 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE, Rio de Janeiro, Brazil (2018)Google Scholar
  38. 38.
    Ochoa, P., Castillo, O., Soria, J., Cortes-Antonio, P.: Differential evolution algorithm using a dynamic crossover parameter with high-speed interval type 2 fuzzy system. In: Mexican International Conference on Artificial Intelligence, pp. 369–378. Springer, Cham, Guadalajara, Mexico (2018)Google Scholar
  39. 39.
    Kadavy, T., Pluhacek, M., Viktorin, A., Senkerik, R.: Comparing boundary control methods for firefly algorithm. In: International Conference on Bioinspired Methods and Their Applications, pp. 163–173. Springer, Cham, Rio de Janeiro, Brazil (2018)Google Scholar
  40. 40.
    Kumar, A., Misra, R. K., & Singh, D.: Improving the local search capability of effective butterfly optimizer using covariance matrix adapted retreat phase. In: Evolutionary Computation (CEC), 2017 IEEE Congress on pp. 1835–1842. IEEE (2017)Google Scholar
  41. 41.
    Castillo, O., Melin, P., Kacprzyk, J., Pedrycz, W.: Type-2 fuzzy logic: theory and applications. In: Granular Computing, 2007. GRC 2007. IEEE International Conference on, p. 145. IEEE (2007)Google Scholar
  42. 42.
    Hernández-Guzmán, V. M., Silva-Ortigoza, R. Control of a ball and beam system. In: Automatic Control with Experiments, pp. 825–867. Springer, Cham (2019)Google Scholar
  43. 43.
    Castillo, O., Lizárraga, E., Soria, J., Melin, P., Valdez, F.: New approach using ant colony optimization with ant set partition for fuzzy control design applied to the ball and beam system. Inf. Sci. 294, 203–215 (2015)MathSciNetCrossRefGoogle Scholar
  44. 44.
    Peraza, C., Valdez, F., Castro, J.R., Castillo, O.: Fuzzy dynamic parameter adaptation in the harmony search algorithm for the optimization of the ball and beam controller. Adv. Oper. Res. (2018). CrossRefGoogle Scholar
  45. 45.
    Castillo, O., Amador-Angulo, L., Castro, J.R., Garcia-Valdez, M.: A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems. Inf. Sci. 354, 257–274 (2016)CrossRefGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association 2019

Authors and Affiliations

  1. 1.Division of Graduate StudiesTijuana Institute of TechnologyTijuanaMexico

Personalised recommendations