Comparative Study of Type-1 and Interval Type-2 Fuzzy Systems in the Fuzzy Harmony Search Algorithm Applied to Benchmark Functions

  • Cinthia Peraza
  • Fevrier ValdezEmail author
  • Oscar Castillo
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 643)


At present the use of fuzzy systems applied to problem solving is very common, since the use of linguistic variables is less complex when solving a problem. This article presents a study of the use of type-1 and interval type-2 fuzzy system applied to the solution of problems of optimization using metaheuristic algorithms. There are many types of algorithms that mimic social, biological, etc. behaviors. In this case the work focuses on the metaheuristic algorithms in specific the fuzzy harmony search algorithm (FHS), the metaheuristic algorithms use a technique to obtain a suitable exploration in a definite space to finish with an exploitation around the best position found, with this it is possible to obtain a good solution of the problem. In particular, it was applied to 11 mathematical reference functions using different numbers of dimensions.


Metaheuristic algorithms Harmony search Type-1 fuzzy logic Type-2 fuzzy logic Dynamic parameter adaptation 


  1. 1.
    Arias, N.B., et al.: Metaheuristic optimization algorithms for the optimal coordination of plug-in electric vehicle charging in distribution systems with distributed generation. Electr. Power Syst. Res. 142, 351–361 (2017)CrossRefGoogle Scholar
  2. 2.
    Askarzadeh, A.: A novel metaheuristic method for solving constrained engineering optimization problems: crow search algorithm. Comput. Struct. 169, 1–12 (2016)CrossRefGoogle Scholar
  3. 3.
    Assad, A., Deep, K.: Applications of harmony search algorithm in data mining: a survey. In: Proceedings of Fifth International Conference on Soft Computing for Problem Solving. Springer Singapore (2016)Google Scholar
  4. 4.
    Geem, Z.W., Kim, J.H., Loganathan, G.V.: A new heuristic optimization algorithm: harmony search. Simulation 76(2), 60–68 (2001)CrossRefGoogle Scholar
  5. 5.
    Kar, P., Swain, S.C.: A harmony search-firefly algorithm based controller for damping power oscillations. In: 2016 Second International Conference on Computational Intelligence & Communication Technology (CICT). IEEE (2016)Google Scholar
  6. 6.
    Lee, A., Geem, Z.W., Suh, K.-D.: Determination of optimal initial weights of an artificial neural network by using the harmony search algorithm: application to breakwater armor stones. Appl. Sci. 6(6), 164 (2016)CrossRefGoogle Scholar
  7. 7.
    Mendel, J.: Type-2 fuzzy sets and systems: an overview [corrected reprint]. IEEE Comput. Intell. Mag. 2(2), 20–29 (2007)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Mendel, J.: Type-2 Fuzzy sets and systems: How to learn about them. IEEE SMC eNewsletter 27 (2009)Google Scholar
  9. 9.
    Mendel, J., John, R.I.B.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10(2), 117–127 (2002)CrossRefGoogle Scholar
  10. 10.
    Mendel, J., John, R.I., Liu, F.: Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst. 14(6), 808–821 (2006)CrossRefGoogle Scholar
  11. 11.
    Molina-Moreno, F., et al.: Optimization of buttressed earth-retaining walls using hybrid harmony search algorithms. Eng. Struct. 134, 205–216 (2017)CrossRefGoogle Scholar
  12. 12.
    Nigdeli, S.M., Bekdaş, G., Yang, X.-S.: Optimum tuning of mass dampers by using a hybrid method using harmony search and flower pollination algorithm. In: International Conference on Harmony Search Algorithm. Springer, Singapore (2017)Google Scholar
  13. 13.
    Peraza, C., et al.: A new fuzzy harmony search algorithm using fuzzy logic for dynamic parameter adaptation. Algorithms 9(4), 69 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Peraza, C., Valdez, F., Castillo, O.: Interval type-2 fuzzy logic for dynamic parameter adaptation in the Harmony search algorithm. In: 2016 IEEE 8th International Conference on Intelligent Systems (IS). IEEE (2016)Google Scholar
  15. 15.
    Shaddiq, S., et al.: Optimal capacity and placement of distributed generation using metaheuristic optimization algorithm to reduce power losses in Bantul distribution system, Yogyakarta. In: 2016 8th International Conference on Information Technology and Electrical Engineering (ICITEE). IEEE (2016)Google Scholar
  16. 16.
    Terano, T., Asai, K., Sugeno, M.: Fuzzy systems theory and its applications. Academic Press Professional Inc, New York (1992)zbMATHGoogle Scholar
  17. 17.
    Thanh, L.T., et al.: A computational study of hybrid approaches of metaheuristic algorithms for the cell formation problem. J. Oper. Res. Soc. 67(1), 20–36 (2016)CrossRefGoogle Scholar
  18. 18.
    Wang, G.-G., et al.: A new metaheuristic optimisation algorithm motivated by elephant herding behaviour. Int. J. Bio-Inspir. Comput. 8(6), 394–409 (2016)CrossRefGoogle Scholar
  19. 19.
    Zadeh, L.A.: Fuzzy sets. Inform. Control 8(3), 338–353 (1965)CrossRefzbMATHGoogle Scholar
  20. 20.
    Zadeh, L.A.: Fuzzy sets and applications: selected papers (1987)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Cinthia Peraza
    • 1
  • Fevrier Valdez
    • 1
    Email author
  • Oscar Castillo
    • 1
  1. 1.Tijuana Institute of TechnologyTijuanaMexico

Personalised recommendations