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On Type-Reduction Versus Direct Defuzzification for Type-2 Fuzzy Logic Systems

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Fifty Years of Fuzzy Logic and its Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 326))

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Abstract

This chapter examines type-reduction and direct defuzzification for interval type-2 fuzzy logic systems. It provides critiques of type-reduction as an end to itself as well as of direct defuzzification, and concludes that: (1) a good way to categorize type-reduction/direct defuzzification algorithm papers is as papers that either focus on algorithms that lead to a type-reduced set, or directly to a defuzzified value; (2) research on type-reduction as an end to itself has led to results that are arguably of very little value; and, (3) the practice of base-lining an IT2 FLS that uses direct defuzzification against one that uses type-reduction followed by defuzzification is unnecessary.

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References

  1. Biglarbegian, M., Melek, W.W., Mendel, J.M.: On the stability of interval type-2 TSK fuzzy logic control systems. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 40, 798–818 (2010)

    Google Scholar 

  2. Biglarbegian, M., Melek, W.W., Mendel, J.M.: On the robustness of type-1 and interval type-2 fuzzy logic systems in modeling. Inf. Sci. 181, 1325–1347 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  3. Coupland, S., John, R.I.: Geometric type-1 and type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 15(1), 3–15 (2007)

    Article  Google Scholar 

  4. Du, X., Ying, H.: Derivation and analysis of the analytical structures of the interval type-2 fuzzy-PI and PD controllers. IEEE Trans. Fuzzy Syst. 18(4), 802–814 (2010)

    Article  Google Scholar 

  5. Duran, K., Bernal, H., Melgarejo, M.: Improved iterative algorithm for computing the generalized centroid of an interval type-2 fuzzy set. In: Proceedings of NAFIPS Conference, New York, Paper 50056 (2008)

    Google Scholar 

  6. Dziech, A., Gorzalczany, M.B.: Decision making in signal transmission problems with interval-valued fuzzy sets. Fuzzy Sets Syst. 23, 191–203 (1987)

    Article  MathSciNet  Google Scholar 

  7. Gorzalczany, M.B.: Interval-valued fuzzy controller based on verbal model of object. Fuzzy Sets Syst. 28, 45–53 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  8. Greenfield, S., Chiclana, F.: Type-reduction of the discretised interval type-2 fuzzy set: what happens as discretisation becomes finer? In: Proceedings of IEEE Symposium on Advances in Type-2 Fuzzy Logic System, Paris, pp. 102–109,(2011)

    Google Scholar 

  9. Greenfield, S., Chiclana, F., Coupland, S., John, R.I.: The collapsing method for defuzzification of discretized interval type-2 fuzzy sets. Inf. Sci. 179, 2055–2069 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Greenfield, S., Chiclana, F., John, R.I.: The collapsing method: does the direction of collapse affect accuracy? In: Proceeding of IFSA-EUSFLAT, Lisbon, pp. 980–985 (2009)

    Google Scholar 

  11. Greenfield, S., Chiclana, F., John, R.I.: Type-reduction of the discretised interval type-2 fuzzy set. In: Proceedings of IEEE FUZZ Conference, JeJu Island, pp. 738–743 (2009)

    Google Scholar 

  12. Hu, H., Wang, Y., Cai, Y.: Advantages of the enhanced opposite direction searching algorithm for computing the centroid of an interval type-2 fuzzy set. Asian J. Control 14(6), 1–9 (2012)

    Google Scholar 

  13. Hu, H., Zhao, G., Yang, H.N.: Fast algorithm to calculate generalized centroid of interval type-2 fuzzy set. Control Decis. 25(4), 637–640 (2010)

    MathSciNet  Google Scholar 

  14. Karnik, N., Mendel, J.M.: Centroid of a type-2 fuzzy set. Inf. Sci. 132, 195–220 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Khosravi, A., Nahavandi, S., Khosravi, R.: A new neural network-based type reduction algorithm for interval type-2 fuzzy logic systems. In: Proceeding of IEEE FUZZ Conf., Hyderabad, Paper 1116, (2013)

    Google Scholar 

  16. Khosravi, A., Nahavandi, S.: Load forecasting using interval type-2 fuzzy logic systems: optimal type-reduction. IEEE Trans.Ind. Inf. 10(2), 1055–1063 (2014)

    Article  Google Scholar 

  17. Li, C., Yi, J., Zhao, D.: A novel type-reduction method for interval type-2 fuzzy logic systems. In: Proceedings 5th International Conference Fuzzy Systems Knowledge Discovery, Jinan, pp. 157–161 (2008)

    Google Scholar 

  18. Liang, Q., Mendel, J.M.: Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters. IEEE Trans. Fuzzy Syst. 8(5), 551–563 (2000)

    Article  Google Scholar 

  19. 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)

    Article  Google Scholar 

  20. Liu, X., Mendel, J.M., Wu, D.: Study on enhanced Karnik-Mendel algorithms: initialization explanations and computation improvements. Inf. Sci. 187, 75–91 (2012)

    Article  Google Scholar 

  21. Liu, X., Qin, Y., Wu, L.: Fast and direct Karnik-Mendel algorithm computation for the centroid of an interval type-2 fuzzy set. In: Proceedings IEEE FUZZ Conference, Brisbane, pp. 1058–1065 (2012)

    Google Scholar 

  22. Melgarejo, M.C.A.: A fast recursive method to compute the generalized centroid of an interval type-2 fuzzy set. In: Proceedings of NAFIPS Conference, San Diego, pp. 190–194 (2007)

    Google Scholar 

  23. Mendel, J.M.: Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Prentice-Hall, Upper Saddle River (2001)

    Google Scholar 

  24. Mendel, J.M.: On KM algorithms for solving type-2 fuzzy set problems. IEEE Trans. Fuzzy Syst. 21(3), 426–446 (2013)

    Article  Google Scholar 

  25. Mendel, J.M.: Type-2 fuzzy sets and beyond. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds.) On Fuzziness: A Homage to Lotfi A. Zadeh, vol. 2. Ch. 34. Springer (2013)

    Google Scholar 

  26. Mendel, J.M., Hagras, H., Tan, W.-W., Melek, W.M., Ying, H.: Introduction to Type-2 Fuzzy Logic Control. IEEE Press and Wiley, Hoboken (2014)

    Book  Google Scholar 

  27. Mendel, J.M., Liu, X.: New closed-form solutions for Karnik-Mendel algorithm+defuzzification of an interval type-2 fuzzy set. In: Proceedings IEEE FUZZ Conference, Brisbane, pp. 1610–1617 (2012)

    Google Scholar 

  28. Mendel, J.M., Liu, X.: Simplified interval type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 21(6), 1056–1069 (2013)

    Article  Google Scholar 

  29. Nie, M., Tan, W.W.: Towards an efficient type-reduction method for interval type-2 fuzzy logic systems. In: Proceeding of IEEE FUZZ Conference, Hong Kong, Paper FS0339 (2008)

    Google Scholar 

  30. Niewiadomski, A., Ochelska, J., Szczepaniak, P.S.: Interval-valued linguistic summaries of databases. Control Cybern. 35(2), 415–444 (2006)

    MATH  Google Scholar 

  31. Tau, C.W., Taur, J.S., Chang, C.-W., Chang, Y.-H.: Simplified type-2 fuzzy sliding controller for wing rock system. Fuzzy Sets Syst. 207, 111–129 (2012)

    Article  Google Scholar 

  32. Ulu, C., Guzelkaya, M., Eskin, I.: A closed form type-reduction method for piecewise linear interval type-2 fuzzy sets. Int. J. Approx. Reason. 54(9), 1421–1433 (2013)

    Article  Google Scholar 

  33. Wu, D.: Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: overview and comparisons. IEEE Trans. Fuzzy Syst. 21(1), 80–99 (2013)

    Article  Google Scholar 

  34. Wu, D., Mendel, J.M.: Enhanced Karnik-Mendel algorithms. IEEE Trans. Fuzzy Syst. 17(4), 923–934 (2009)

    Article  Google Scholar 

  35. Wu, D. and Nie, M.: Comparison and practical implementations of type-reduction algorithms for type-2 fuzzy sets and systems. In: Proceedings of IEEE FUZZ Conference, Taipei, pp. 2131–2138 (2011)

    Google Scholar 

  36. Wu, D., Tan, W.W.: Computationally efficient type-reduction strategies for a type-2 fuzzy logic controller. In: Proceedings of IEEE FUZZ Conference, Reno, pp. 353–358, (2005)

    Google Scholar 

  37. Wu, H., Mendel, J.M.: Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 10(5), 622–639 (2002)

    Article  Google Scholar 

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Authors and Affiliations

  1. Ming Hsieh Department of Electrical Engineering, Signal & Image Processing Institute, University of Southern California, Los Angeles, CA, 90089-2564, USA

    Jerry M. Mendel

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  1. Jerry M. Mendel
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Correspondence to Jerry M. Mendel .

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Editors and Affiliations

  1. Department of Computer Science, Texas State University, San Marcos, Texas, USA

    Dan E. Tamir

  2. School of Computing and Information Sciences, Florida International University, Miami, Florida, USA

    Naphtali D. Rishe

  3. School of Computing and Information Sciences, The University of South Florida, Tampa, Florida, USA, and Florida International University, Miami, Florida, USA

    Abraham Kandel

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Mendel, J.M. (2015). On Type-Reduction Versus Direct Defuzzification for Type-2 Fuzzy Logic Systems. In: Tamir, D., Rishe, N., Kandel, A. (eds) Fifty Years of Fuzzy Logic and its Applications. Studies in Fuzziness and Soft Computing, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-319-19683-1_20

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  • DOI: https://doi.org/10.1007/978-3-319-19683-1_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19682-4

  • Online ISBN: 978-3-319-19683-1

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