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On Fuzziness pp 441–448Cite as

Type-2 Fuzzy Sets and Beyond

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 299))

Abstract

This chapter explains why I started working on type-2 fuzzy sets and systems and the contributions made by my students, colleagues and myself to this field. It also predicts a very rosy outlook for this field.

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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 Transactions on Systems Man and Cybernetics, Part B-Cybernetics 40(3), 798–818 (2010)

    Article  Google Scholar 

  2. Dubois, D., Prade, H.: Operations in a Fuzzy-valued Logic. Information and Control 43, 224–240 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)

    MATH  Google Scholar 

  4. Gorzalczany, M.B.: A Method of Inference in Approximate Reasoning Based on Interval-valued Fuzzy ets. Fuzzy Sets and Systems 21, 1–17 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  5. Karnik, N.N., Mendel, J.M.: Introduction to Type-2 Fuzzy Logic Systems. In: Proceedings of the 1998 IEEE FUZZ Conference, Anchorage, AK, pp. 915–920 (May 1998)

    Google Scholar 

  6. Karnik, N.N., Mendel, J.M.: An Introduction to Type-2 Fuzzy Logic Systems. University of Southern California, Los Angeles (1998), http://sipi.usc.edu/~mendel/report

    Google Scholar 

  7. Karnik, N.N., Mendel, J.M.: Type-2 Fuzzy Logic Systems: Type-reduction. In: Proceedings of the IEEE Conference on Systems, Man and Cybernetics, San Diego CA, pp. 2046–2051 (October 1998)

    Google Scholar 

  8. Karnik, N.N., Mendel, J.M.: Operations on Type-2 Fuzzy Sets. Fuzzy Sets and Systems 122, 327–348 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Karnik, N.N., Mendel, J.M.: Centroid of a Type-2 Fuzzy Set. Information Sciences 132, 195–220 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Karnik, N.N., Mendel, J.M., Liang, Q.: Type-2 Fuzzy Logic Systems. IEEE Transactions on Fuzzy Systems 7, 643–658 (1999)

    Article  Google Scholar 

  11. Liang, Q., Mendel, J.M.: Interval Type-2 Fuzzy Logic Systems. In: Proceedings of the FUZZ-IEEE 2000, San Antonio, TX (May 2000)

    Google Scholar 

  12. Liu, F.: An Efficient Centroid Type-reduction Strategy for General Type-2 Fuzzy Logic System. Information Sciences 178, 2224–2236 (2008)

    Article  MathSciNet  Google Scholar 

  13. Liu, X., Mendel, J.M.: Connect Karnik-Mendel Algorithms to Root-Finding for Computing the Centroid of an Interval Type-2 Fuzzy Set. IEEE Transactions on Fuzzy Systems 19, 652–665 (2011)

    Article  Google Scholar 

  14. Martin, M.A., Mendel, J.M.: Flirtation, a Very Fuzzy Prospect: a Flirtation Advisor, USC Report (1995), http://sipi.usc.edu/~mendel

  15. Mendel, J.M.: Type-2 Fuzzy Sets: a Tribal Parody. IEEE Computational Intelligence Magazine 5, 24–27 (2010)

    Article  Google Scholar 

  16. Mendel, J.M., Liang, Q.: Pictorial Comparisons of Type-1 and Type-2 Fuzzy Logic Systems. In: Proceedings of the IASTED Int’l Conference on Intelligent Systems & Control, Santa Barbara, CA (October 1999)

    Google Scholar 

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

    MATH  Google Scholar 

  18. Mendel, J.M.: Reflections on Some Important Contributions Made by Lotfi A. Zadeh that Have Impacted my own Research. Scientia Iranica 18, 549–553 (2011)

    Article  Google Scholar 

  19. Mendel, J.M., John, R.I.: Type-2 Fuzzy Sets Made Simple. IEEE Transactions on Fuzzy Systems 10, 117–127 (2002)

    Article  Google Scholar 

  20. Mendel, J.M., Liu, F.: Super-Exponential Convergence of the Karnik-Mendel Algorithms for Computing the Centroid of an Interval Type-2 Fuzzy Set. IEEE Transactions on Fuzzy Systems 15, 309–320 (2007)

    Article  Google Scholar 

  21. Mendel, J.M., John, R.I., Liu, F.: Interval type-2 Fuzzy Logic Systems Made Simple. IEEE Transactions on Fuzzy Systems 14, 808–821 (2006)

    Article  Google Scholar 

  22. Mendel, J.M., Liu, F., Zhai, D.: Alpha-plane Representation for Type-2 Fuzzy Sets: Theory and Applications. IEEE Transactions on Fuzzy Systems 17, 1189–1207 (2009)

    Article  Google Scholar 

  23. Nie, M., Tan, W.W.: Towards an Efficient Type-reduction Method for Interval Type-2 Fuzzy Logic Systems. In: Proceedings of the IEEE International Conference on Fuzzy Systems, Hong Kong, China, pp. 1427–1434 (2008)

    Google Scholar 

  24. Wagner, C., Hagras, H.: Towards General Type-2 Fuzzy Logic Systems Based on zSlices. IEEE Transactions on Fuzzy Systems 18, 637–660 (2010)

    Article  Google Scholar 

  25. Zadeh, L.A.: Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Transactions on Systems, Man, and Cybernetics SMC-33, 28–44 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  26. Zadeh, L.A.: The Concept of a Linguistic Variable and its Application to Approximate Reasoning. Information Sciences 8, Part I, 199–249; 8, Part II, 301–357; 9, Part III, 43–80 (1975)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Signal and Image Processing Institute, Ming Hsieh Department of Electrical Engineering, Viterbi School of Engineering, University of Southern California, Los Angeles, CA, USA

    Jerry M. Mendel

Authors
  1. Jerry M. Mendel
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Editor information

Editors and Affiliations

  1. , Edificio de Investigación, European Centre for Soft Computing, C Gonzalo Gutiérrez Quirós S/N, Mieres, 33600, Spain

    Rudolf Seising

  2. Edificio de Investigación, 3ª Planta., European Centre for Soft Computing, C Gonzalo Gutiérrez Quirós S/N, Mieres, 33600, Asturias, Spain

    Enric Trillas

  3. Edificio de Investigación, 3ª Planta., European Centre for Soft Computing, Asturias, Mieres, 33600, Spain

    Claudio Moraga

  4. , Department of Mathematic and Informatics, Università di Palermo, Via Archirafi 34, Palermo, 90123, Italy

    Settimo Termini

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Mendel, J.M. (2013). Type-2 Fuzzy Sets and Beyond. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds) On Fuzziness. Studies in Fuzziness and Soft Computing, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35644-5_2

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  • DOI: https://doi.org/10.1007/978-3-642-35644-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35643-8

  • Online ISBN: 978-3-642-35644-5

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