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A Multi-objective Evolutionary Algorithm for Tuning Type-2 Fuzzy Sets with Rule and Condition Selection on Fuzzy Rule-Based Classification System

  • Edward Hinojosa CárdenasEmail author
  • Heloisa A. Camargo
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)

Abstract

This paper presents a Multi-Objective Evolutionary Algorithm (MOEA) for tuning type-2 fuzzy sets and selecting rules and conditions on Fuzzy Rule-Based Classification Systems (FRBCS). Before the tuning and selection process, the Rule Base is learned by means of a modified Wang-Mendel algorithm that considers type-2 fuzzy sets in the rules antecedents and in the inference mechanism. The Multi-Objective Evolutionary Algorithm used in the tuning process has three objectives. The first objective reflects the accuracy where the correct classification rate of the FRBCS is optimized. The second objective reflects the interpretability of the system regarding complexity, by means of the quantity of rules and is to be minimized through selecting rules from the initial rule base. The third objective also reflects the interpretability as a matter of complexity and models the quantity of conditions in the Rule Base. Finally, we show how the FRBCS tuned by our proposed algorithm can achieve a considerably better classification accuracy and complexity, expressed by the quantity of fuzzy rules and conditions in the RB compared with the FRBCS before the tuning process.

Keywords

Fuzzy Rule-Based Classification System Type-2 fuzzy sets Multi-Objective Evolutionary Algorithm 

References

  1. 1.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8(3), 199–249 (1975). doi: 10.1016/0020-0255(75)90036-5
  2. 2.
    Karnik, N.N., Mendel, J.M., Liang, Q.: Type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 7(6), 643–658 (1999). doi: 10.1109/91.811231
  3. 3.
    Fazzolari, M., Alcala, R., Nojima, Y., Ishibuchi, H., Herrera, F.: A review of the application of multiobjective evolutionary fuzzy systems: current status and further directions. IEEE Trans. Fuzzy Syst. 21(1), 45–65 (2013). doi: 10.1109/TFUZZ.2012.2201338
  4. 4.
    Wang, L.X., Mendel, J.M.: Generating fuzzy rules by learning from examples. IEEE Trans. Syst. Man Cybern. 22(6), 1414–1427 (1992). doi: 10.1109/21.199466
  5. 5.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002). doi: 10.1109/4235.996017
  6. 6.
    Türk, S., John, R., Özcan, E.: Interval type-2 fuzzy sets in supplier selection. In: 14th UK Workshop on Computational Intelligence, pp. 1–7 (2014). doi: 10.1109/UKCI.2014.6930168
  7. 7.
    Hamza, M.F., Yap, H.J., Choudhury, I.: Advances on the use of Meta-Heuristic algorithms to optimize type-2 fuzzy logic systems for prediction, classification, clustering and pattern recognition. J. Comput. Theor. Nanosci. 13(1), 96–109 (2016). doi: 10.1166/jctn.2016.4774
  8. 8.
    Shukla, P.K., Tripathi, S.P.: A new approach for tuning interval type-2 fuzzy knowledge bases using genetic algorithms. J. Uncertainty Anal. Appl. 2(1), 4 (2014). doi: 10.1186/2195-5468-2-4
  9. 9.
    Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley, New York (2001)zbMATHGoogle Scholar
  10. 10.
    Alcalá-Fdez, J., Fernandez, A., Luengo, J., Derrac, J., García, S., Snchez, L., Herrera, F.: KEEL data-mining software tool: data set repository, integration of algorithms and experimental analysis framework. J. Multiple-Valued Logic Soft Comput. 17(2–3), 255–287 (2011)Google Scholar
  11. 11.
    Lichman, M.: UCI machine learning repository. School of Information and Computer Sciences, University of California, Irvine (2013). http://archive.ics.uci.edu/ml
  12. 12.
    Zhang, Q., Li, H.: MOEA/D: a multi-objective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)CrossRefGoogle Scholar
  13. 13.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm (2001)Google Scholar
  14. 14.
    Melin, P., Castillo, O.: A review on type-2 fuzzy logic applications in clustering, classification and pattern recognition. Appl. Soft Comput. 21, 568–577 (2014)CrossRefGoogle Scholar
  15. 15.
    Mendel, J.M.: On answering the question “Where do I start in order to solve a new problem involving type-2 fuzzy sets?” Inf. Sci. 179(19), 3418–3431 (2009)Google Scholar
  16. 16.
    Mendel, J.M.: General type-2 fuzzy logic systems made simple: a tutorial. IEEE Trans. Fuzzy Syst. 22(5), 1162–1182 (2014)CrossRefGoogle Scholar
  17. 17.
    Fernandez, A., Lopez, V., del Jesus, M.J., Herrera, F.: Revisiting evolutionary fuzzy systems: taxonomy, applications, new trends and challenges. Knowl. Based Syst. 80, 109–121 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Edward Hinojosa Cárdenas
    • 1
    Email author
  • Heloisa A. Camargo
    • 2
  1. 1.University of San AgustinArequipaPeru
  2. 2.Federal University of São CarlosSão CarlosBrazil

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