Skip to main content
SpringerLink
Log in

Rule Base Reduction and Genetic Tuning of Fuzzy Systems Based on the Linguistic 3-tuples Representation

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Recently, a new linguistic rule representation model was presented to perform a genetic lateral tuning of membership functions. It is based on the linguistic 2-tuples representation model, that allows the symbolic translation of a label considering an unique parameter. It involves a reduction of the search space that eases the derivation of optimal models. This work presents a new symbolic representation with three values (s, α, β), respectively representing a label, the lateral displacement and the amplitude variation of the support of this label. Based on this new representation we propose a new method for fine tuning of membership functions that is combined with a rule base reduction method in order to extract the most useful tuned rules. This approach makes use of a modified inference system that consider non-covered inputs in order to improve the final fuzzy model generalization ability, specially in highly non-linear problems with noise points. Additionally, we analyze the proposed approach showing its behavior in two real-world applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alcalá R, Herrera F (2004) Genetic tuning on fuzzy systems based on the linguistic 2-tuples representation. In: Proceedings of the 13th IEEE international conference on fuzzy systems, vol 1, pp 233–238

  2. Babuška R, Oosterhoff J, Oudshoorn A, Bruijn PM (2002) Fuzzy selftuning PI control of pH in fermentation, Eng Appl Artif Intell 15(1): 3–15

    Article  Google Scholar 

  3. Bastian A (1994) How to handle the flexibility of linguistic variables with applications. Int J Uncertain, Fuzziness Knowl-Based Syst 3(4): 463-484

    Article  MathSciNet  Google Scholar 

  4. Casillas J, Cordón O, Herrera F, Magdalena L (2005) Accuracy improvements in linguistic fuzzy modeling. Stud Fuzziness Soft Comput 129: 385

    Google Scholar 

  5. Casillas J, Cordón O, del Jesus MJ, Herrera F (2005) Genetic tuning of fuzzy rule deep structures preserving interpretability and its interaction with fuzzy rule set reduction. IEEE Trans Fuzzy Syst 13(1): 13–29

    Article  Google Scholar 

  6. Carmona P, Castro J, Zurita J (2004) Strategies to identify fuzzy rules directly from certainty degrees: a comparison and a proposal. IEEE Trans Fuzzy Sys 12(5): 631–640

    Article  Google Scholar 

  7. Cordón O, Herrera F (1997) A three-stage evolutionary process for learning descriptive and approximate fuzzy logic controller knowledge bases from examples. Int J Approx Reason 17(4): 369–407

    Article  MATH  Google Scholar 

  8. Cordón O, Herrera F, Peregrín A (1997) Applicability of the fuzzy operators in the design of fuzzy logic controllers. Fuzzy Sets Syst 86(1): 15–41

    Article  MATH  Google Scholar 

  9. Cordón O, del Jesus MJ, Herrera F (1998) Genetic learning of fuzzy rule-based classification systems cooperating with fuzzy reasoning methods. Int J Intell Syst 13: 1025–1053

    Article  Google Scholar 

  10. Cordón O, Herrera F, Sánchez L (1999) Solving electrical distribution problems using hybrid evolutionary data analysis techniques. Appl Intell 10: 5–24

    Article  Google Scholar 

  11. Cordón O, Herrera F (2000) A proposal for improving the accuracy of linguistic modeling. IEEE Trans Fuzzy Syst 8(3): 335–344

    Article  Google Scholar 

  12. Cordón O, Herrera F, Villar P (2001) Generating the knowledge base of a fuzzy rule-based system by the genetic learning of the data base. IEEE Trans Fuzzy Syst 9(4): 667–674

    Article  Google Scholar 

  13. Cordón O, Herrera F, Hoffmann F, Magdalena L (2001) Genetic fuzzy systems: Evolutionary tuning and learning of fuzzy knowledge bases World Scientific, Singapore, 488

  14. Cordón O, Gomide F, Herrera F, Hoffmann F, Magdalena L (2004) Ten years of genetic fuzzy systems: current framework and new trends. Fuzzy Sets Systems 41(1): 5–31

    Article  Google Scholar 

  15. Eshelman LJ (1991) The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic recombination. In: Foundations of genetic Algorithms 1, Rawlin G (Ed.) Morgan Kaufman, 265–283

  16. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, New York, P 372

    MATH  Google Scholar 

  17. Gómez-Skarmeta AF, Jiménez F (1999) Fuzzy modeling with hybrid systems. Fuzzy Sets Syste 104: 1991–208

    Google Scholar 

  18. González A, Pérez R (1999) A study about the inclusion of linguistic hedges in a fuzzy rule learning algorithm. Int J Uncertain Fuzziness Knowl-Based Syst 7(3): 257–266

    Article  Google Scholar 

  19. Gürocak HB (1999) A genetic-algorithm-based method for tuning fuzzy logic controllers. Fuzzy Sets Syst 108(1): 39–47

    Article  MATH  Google Scholar 

  20. Gürocak HB (2000) Tuning fuzzy logic controllers using response envelope method. Fuzzy Sets Syst 115(2): 287–304

    Article  Google Scholar 

  21. Herrera F, Lozano M, Verdegay JL (1995) Tuning fuzzy logic controllers by genetic algorithms. Int J Approx Reason 12: 299–315

    Article  MathSciNet  MATH  Google Scholar 

  22. Herrera F, Lozano M, Verdegay JL (1998) A learning process for fuzzy control rules using genetic algorithms. Fuzzy Sets Syst 100: 143–158

    Article  Google Scholar 

  23. Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6): 746–752

    Article  Google Scholar 

  24. Herrera F, Lozano M, Sánchez AM (2003) A taxonomy for the crossover operator for real-coded genetic algorithms: an experimental study. Int J Intell Syst 18: 309–338

    Article  MATH  Google Scholar 

  25. Holland JH (1975) Adaptation in natural and systems. The University of Michigan Press, London, p 228

    Google Scholar 

  26. Hong TP, Lee CY (1999) Effect of merging order on performance of fuzzy induction. Intell Data Anal 3(2): 139–151

    Article  MATH  Google Scholar 

  27. Ishibuchi H, Nozaki K, Yamamoto N, Tanaka H (1995) Selecting fuzzy if-then rules for classification problems using genetic algorithms. IEEE Trans Fuzzy Syst (3)3: 260–270

    Article  Google Scholar 

  28. Nozaki K, Ishibuchi H, Tanaka H (1997) A simple but powerful heuristic method for generating fuzzy rules from numerical data. Fuzzy Sets Syst 86(3): 251–270

    Article  Google Scholar 

  29. Ishibuchi H, Murata T, Türksen IB (1997) Single-objective and two objective genetic algorithms for selecting linguistic rules for pattern classification problems. Fuzzy Sets Syst 89(2): 135–150

    Article  Google Scholar 

  30. Ishibuchi H, Yamamoto T (2003) Trade-off between the number of fuzzy rules and their classification performance. In: Accuracy improvements in linguistic fuzzy modeling, Casillas J, Cordón O, Herrera F, Magdalena L, (eds) Springer Heidelberg, Germany, pp 72–99

  31. Jang JSR (1993) ANFIS: adaptive network based fuzzy inference system. IEEE Trans Syst. Man Cyber 23(3): 665–684

    Article  MathSciNet  Google Scholar 

  32. Karr C (1991) Genetic algorithms for fuzzy controllers. AI Expert 6(2): 26–33

    Google Scholar 

  33. Klose A, Nurnberger A, Nauck D (1998) Some approaches to improve the interpretability of neuro-fuzzy classifiers. In: Proceeding of the 6th European congress on intelligent techniques and soft computing Vol 1, pp 629–633

  34. Krone A, Krause H, Slawinski T (2001) A new rule reduction method for finding interpretable and small rule bases in high dimensional search spaces. In: Proceeding of the 9th IEEE international conference on fuzzy syst, Vol 2, pp 693–699

  35. Krone A, Taeger H (2001) Data-based fuzzy rule test for fuzzy modelling. Fuzzy Sets Syst 123(3): 343–358

    Article  MathSciNet  MATH  Google Scholar 

  36. Liu BD, Chen CY, Tsao JY (2001) Design of adaptive fuzzy logic controller based on linguistic-hedge concepts and genetic algorithms. IEEE Trans Syst, Man Cybern. Part B: Cybern 31(1): 32–53

    Article  Google Scholar 

  37. Mamdani EH (1974) Application of fuzzy algorithms for control of simple dynamic plant. Proc. IEEE 121(12): 1585–1588

    Google Scholar 

  38. Mamdani EH, Assilian S (1975) An experiment in linguistic synthesis with a fuzzy logic controller. Int J Man-Mach Stud 7: 1–13

    Article  MATH  Google Scholar 

  39. Roubos JA, Setnes M (2001) Compact and transparent fuzzy models and classifiers through iterative complexity reduction. IEEE Trans on Fuzzy Syst 9(4): 516–524

    Article  Google Scholar 

  40. Setnes M, Babuška R, Kaymak U, van Nauta Lemke HR (1998) Similarity measures in fuzzy rule base simplification. IEEE Trans Syst, Man Cyber - Part B: Cybern 28(3): 376–386

    Article  Google Scholar 

  41. Setnes M, Roubos JA (2000) GA-fuzzy modeling and classification: complexity and performance. IEEE Trans Fuzzy Syst 8(5): 509–522

    Article  Google Scholar 

  42. Wang LX, Mendel JM (1992) Generating fuzzy rules by learning from examples. IEEE Trans Syst, Man Cybern 22:6, (1992) 1414–1427.

    Google Scholar 

  43. Yam Y, Baranyi P, Yang CT (1999) Reduction of fuzzy rule base via singular value decomposition. IEEE Trans Fuzzy Syst 7:120–132

    Article  Google Scholar 

  44. Yen J, Wang L (1999) Simplifying fuzzy rule-based models using orthogonal transformation methods. IEEE Transa Syst, Man Cybern Part B: Cybern 29: 13–24

    Article  Google Scholar 

  45. Zadeh LA (1965) Fuzzy sets. Info Control 8: 338–353

    Article  MathSciNet  MATH  Google Scholar 

  46. Zadeh LA (1973) Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans Syst, Man Cybern 3:28–44

    MathSciNet  MATH  Google Scholar 

  47. Zadeh LA (1975) The concept of a linguistic variable and its applications to approximate reasoning, parts I, II and III. Inf Sci 8:199–249, 301–357, 9:43–80

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Artificial Intelligence, University of Granada, 18071, Granada, Spain

    Rafael Alcalá, Jesús Alcalá-Fdez, María José Gacto & Francisco Herrera

Authors
  1. Rafael Alcalá
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jesús Alcalá-Fdez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. María José Gacto
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Francisco Herrera
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rafael Alcalá.

Additional information

Supported by the Spanish Ministry of Science and Technology under Projects TIC-2002-04036-C05-01 and TIN-2005-08386-C05-01.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alcalá, R., Alcalá-Fdez, J., Gacto, M.J. et al. Rule Base Reduction and Genetic Tuning of Fuzzy Systems Based on the Linguistic 3-tuples Representation. Soft Comput 11, 401–419 (2007). https://doi.org/10.1007/s00500-006-0106-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-006-0106-2

Keywords

Search

Navigation