Advertisement

Interval Type-2 Fuzzy Systems: Design Methods and Applications

  • Jerry M. Mendel
Chapter

Abstract

This chapter is the IT2 version of Chap.  4. It focuses first on what exactly “design of an IT2 fuzzy system” means, and then provides a tabular way for making the choices that are needed in order to fully specify an IT2 fuzzy system. It introduces two approaches to design, the partially dependent approach and the totally independent approach, but this time for singleton, T1 non-singleton and IT2 non-singleton IT2 fuzzy systems. It then describes the extension of the six design methods that were covered for type-1 fuzzy systems in Chap.  4 to IT2 fuzzy systems, namely: IT2 WM, least squares, derivative-based, SVD-QR, derivative-free, and iterative. It continues the three Chap.  4 case studies (forecasting of time series, knowledge mining using surveys, and fuzzy logic control), and continues the Chap.  4 applications of forecasting of compressed video traffic using IT2 Mamdani and TSK fuzzy systems, and IT2 rule-based classification of video traffic. The application of equalization of time-varying nonlinear digital communication channels is also covered. Thirteen examples are used to illustrate the important concepts.

References

  1. Bargiela, A., and W. Pedrycz. 2003. Granular computing: An introduction. Dordrecht: Kluwer Academic Publishers.CrossRefzbMATHGoogle Scholar
  2. Cara, A.B., C. Wagner, H. Hagras, H. Pomares, and I. Rojas. 2013. Multiobjective optimization and comparison of nonsingleton type-1 and singleton interval type-2 fuzzy logic systems. IEEE Transcations on Fuzzy Systems 21: 459–476.CrossRefGoogle Scholar
  3. Castillo, O., and P. Melin. 2014. A review on interval type-2 fuzzy logic applications in intelligent control. Information Sciences 279: 615–631.MathSciNetCrossRefzbMATHGoogle Scholar
  4. Chen, S., B. Mulgrew, and S. McLaughlin. 1993a. A clustering technique for digital communications channel equalization using radial basis function network. IEEE Transaction on Neural Networks 4: 570–579.CrossRefGoogle Scholar
  5. Chen, S., B. Mulgrew, and S. McLaughlin. 1993b. Adaptive Bayesian equalizer with decision feedback. IEEE Transactions on Signal Processing 41: 2918–2927.CrossRefzbMATHGoogle Scholar
  6. Chen, S., S. McLaughlin, B. Mulgrew, and P.M. Grant. 1995. Adaptive Bayesian decision feedback equalizer for dispersive mobile radio channels. IEEE Transactions on Communications 43: 1937–1956.CrossRefGoogle Scholar
  7. Cowan, C.F.N., and S. Semnani. 1998. Time-variant equalization using a novel non-linear adaptive structure. International Journal of Adaptive Control and Signal Processing 12: 195–206.CrossRefzbMATHGoogle Scholar
  8. Dereli, T., A. Baykasoglu, K. Altun, A. Durmusoglu, and I. Burkhan Turksen. 2011. Industrial applications of type-2 fuzzy sets and systems: A concise review. Computers in Industry 62: 125–137.CrossRefGoogle Scholar
  9. Derrac, J., S. Garcia, D. Molina, and F. Herrera. 2011. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm and Evolutionary Computation 1: 3–18.CrossRefGoogle Scholar
  10. Du, X., and H. Ying. 2010. Derivation and analysis of the analytical structures of the interval type-2 fuzzy-PI and PD controllers. IEEE Transactions on Fuzzy Systems 18: 802–814.CrossRefGoogle Scholar
  11. Garcia, S., A. Fernandez, J. Luengo, and F. Herrera. 2010. Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power. Information Sciences 180: 2044–2064.CrossRefGoogle Scholar
  12. Hagras, H. 2007. Type-2 FLCs: A new generation of fuzzy controllers. IEEE Computational Intelligence Magazine 2: 30–43.CrossRefGoogle Scholar
  13. Hagras, H., and C. Wagner. 2012. Towards the wide spread use of type-2 fuzzy logic systems in real world applications. IEEE Computational Intelligence Magazine 7 (3): 14–24.CrossRefGoogle Scholar
  14. Hao, M., and J.M. Mendel. 2015. Encoding words into normal interval type-2 fuzzy sets: HM method, accepted for publication in IEEE Transactions on Fuzzy Systems.Google Scholar
  15. Karnik, N.N., J.M. Mendel, and Q. Liang. 1999. Type-2 fuzzy logic systems. IEEE Transactions on Fuzzy Systems 7: 643–658.CrossRefGoogle Scholar
  16. Lee, K.Y. 1996. Complex fuzzy adaptive filters with lms algorithm. IEEE Transactions on Signal Processing 44: 424–429.CrossRefGoogle Scholar
  17. Liang, Q. and J.M. Mendel. 2000a. Decision feedback equalizer for nonlinear time-varying channels using type-2 fuzzy adaptive filters,” In Proceedings of FUZZ-IEEE’00, San Antonio, TX, May 2000a.Google Scholar
  18. Liang, Q., and J.M. Mendel. 2000b. Equalization of nonlinear time-varying channels using Type-2 fuzzy adaptive filters. IEEE Transactions on Fuzzy Systems 8: 551–563.CrossRefGoogle Scholar
  19. Liang, Q., and J.M. Mendel. 2000c. Designing interval type-2 fuzzy logic systems using an SVD–QR method: Rule reduction. Int’ernational Journal of Intelligent Systems 15: 939–957.CrossRefzbMATHGoogle Scholar
  20. Liang, Q. and J.M. Mendel. 2001. MPEG VBR video traffic modeling and classification using fuzzy techniques. IEEE Transactions on Fuzzy Systems, pp. 183–193, Feb. 2001.Google Scholar
  21. Liu, F., and J.M. Mendel. 2008. Encoding words into interval type-2 fuzzy sets using an Interval Approach. IEEE Transactions on Fuzzy Systems 16: 1503–1521.CrossRefGoogle Scholar
  22. Magdon-Ismail, M., A. Nicholson, and Y. Abu-Mostafa. 1998. Financial markets: Very noisy information processing. Proceedings of IEEE 86: 2184–2195.CrossRefGoogle Scholar
  23. Marín, L.G., F. Valencia and D. Sáez. 2016. Prediction interval based on type-2 fuzzy systems for wind power generation and loads in microgrid control design. In Proceedings FUZZ-IEEE 2016, Vancouver, Canada, July 2016.Google Scholar
  24. Mendel, J.M. 2000. Uncertainty, fuzzy logic, and signal processing. Signal Processing Journal 80: 913–933.CrossRefzbMATHGoogle Scholar
  25. Mendel, J.M. 2001. Introduction to rule-based fuzzy logic systems. Upper Saddle River, NJ: Prentice-Hall.zbMATHGoogle Scholar
  26. Mendel, J.M. 2003. Fuzzy sets for words: A new beginning. In Proceedings of 2003 IEEE int’ernational conference on fuzzy systems, St. Louis, MO, pp. 37–42, May 2003.Google Scholar
  27. Mendel, J.M. 2004. Computing derivatives in interval type-2 fuzzy logic systems. IEEE Transactions on Fuzzy Systems 12: 84–98.CrossRefGoogle Scholar
  28. Mendel, J.M. 2007a. Advances in type-2 fuzzy sets and systems. Information Sciences 177: 84–110.MathSciNetCrossRefzbMATHGoogle Scholar
  29. Mendel, J.M. 2007b. Computing with words and its relationships with fuzzistics. Information Sciences 177: 998–1006.MathSciNetGoogle Scholar
  30. Mendel, J.M. 2007c. Computing with words: Zadeh, Turing, Popper and Occam. IEEE Computational Intelligence Magazine 2: 10–17.CrossRefGoogle Scholar
  31. Mendel, J.M., H. Hagras, W.-W. Tan, W.W. Melek, and H. Ying. 2014. Introduction to type-2 fuzzy logic control. Hoboken, NJ: John Wiley and IEEE Press.CrossRefzbMATHGoogle Scholar
  32. Mendel, J.M., and R.I. John. 2002. Type-2 fuzzy sets made simple. IEEE Transactions on Fuzzy Systems 10: 117–127.CrossRefGoogle Scholar
  33. Mendel, J.M., and D. Wu. 2010. Perceptual computing: Aiding people in making subjective judgments. Hoboken, NJ: Wiley and IEEE Press.CrossRefGoogle Scholar
  34. Mendel, J.M. 2014. General type-2 fuzzy logic systems made simple: A tutorial. IEEE Transactions on Fuzzy Systems 22: 1162–1182.CrossRefGoogle Scholar
  35. Moon, J., and T. Jeon. 1998. Sequence detection for binary ISI channels using signal space partitioning. IEEE Transactions on Communications 46: 891–901.CrossRefGoogle Scholar
  36. Nie M., and W.W. Tan. 2010. Derivation of the analytical structure of symmetrical IT2 fuzzy PD and PI controllers. In Proceedings of 2010 IEEE int’ernationl conference on Fuzzy Systems, Barcelona, Spain, pp. 1–8, July 2010.Google Scholar
  37. Patra, S.K., and B. Mulgrew. 1998. Efficient architecture for Bayesian equalization using fuzzy filters. IEEE Transactions Circuits and Systems II: Analog and Digital Signal Processing 45: 812–820.CrossRefGoogle Scholar
  38. Proakis, J.G. 1989. Digital communications, 2nd ed. New York: McGraw-Hill.zbMATHGoogle Scholar
  39. Rickard, J.T., J. Aisbett, R. Yager and G. Gibbon. 2011. Linguistic weighted power means: Comparison with the linguistic weighted average. In Proceedings FUZZ-IEEE 2011, 2011 World Congress on Computational Intelligence, pp. 2185–2192, Taipei, Taiwan.Google Scholar
  40. Rickard, J.T., J. Aisbett, R.R. Yager, and G. Gibbon. 2013. Computing with words using weighted power mean aggregation operators. In Soft computing: State of the art theory and novel applications, ed. R.R. Yager, A.M. Abbasov, M.Z. Reformat, and S. Shahbazova, 145–160. New York: Springer.CrossRefGoogle Scholar
  41. Rutkowski, L. 2004. Flexible neuro-fuzzy systems: Structures, learning and performance evaluation. Boston: Kluwer.zbMATHGoogle Scholar
  42. Sarwal, P., and M.D. Srinath. 1995. A fuzzy logic system for channel equalization. IEEE Transactions Fuzzy Systems 3: 246–249.CrossRefGoogle Scholar
  43. Savazzi, P., L. Favalli, E. Costamagna, and A. Mecocci. 1998. A suboptimal approach to channel equalization based on the nearest neighbor rule. IEEE Journal Selected Areas in Communications 16: 1640–1648.CrossRefGoogle Scholar
  44. Tahayori, H., and A. Sadeghian. 2012. Median interval approach to model words with interval type-2 fuzzy sets. International Journal of Advanced Intelligence Paradigms 4 (3): 313–336.CrossRefGoogle Scholar
  45. Wang, L.-X., and J.M. Mendel. 1993. Fuzzy adaptive filters, with application to nonlinear channel equalization. IEEE Transactions Fuzzy Systems 1 (3): 161–170.CrossRefGoogle Scholar
  46. Wu, D., J.M. Mendel, and S. Coupland. 2012. Enhanced interval approach for encoding words into interval type-2 fuzzy sets and its convergence analysis. IEEE Transactions on Fuzzy Systems 20: 499–513.CrossRefGoogle Scholar
  47. Wu, D., and W.W. Tan. 2006. Genetic learning and performance evaluation of type-2 fuzzy logic controllers. Engineering Applications of Artificial Intelligence 19 (8): 829–841.CrossRefGoogle Scholar
  48. Wu, H., and J.M. Mendel. 2007. Classification of battlefield ground vehicles using acoustic features and fuzzy logic rule-based classifiers. IEEE Transactions on Fuzzy Systems 15: 56–72.CrossRefGoogle Scholar
  49. Zhou, H., and H. Ying. 2013. A method for deriving the analytical structure of a broad class of typical interval type-2 Mamdani fuzzy controllers. IEEE Transactions on Fuzzy Systems 21: 447–491.CrossRefGoogle Scholar
  50. Zhou, S.-M., J.M. Garibaldi, R.I. John, and F. Chiclana. 2009. On constructing parsimonious type-2 fuzzy logic systems via influential rule selection. IEEE Transactions on Fuzzy Systems 17: 654–667.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of Southern CaliforniaLos AngelesUSA

Personalised recommendations