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Basics of Fuzzy Logic

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Fuzzy Logic for Image Processing

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Abstract

In this chapter, foundations of fuzzy logic are presented to introduce the necessary notations used throughout the following chapters. The chapter provides basic notions of fuzzy set theory and fuzzy systems, such as fuzzification, fuzzy rule base and inference engine, defuzzification, and fuzzy models.

Of all things that are certain, the most certain is doubt.

Bertolt Brecht

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Notes

  1. 1.

    Fuzzy sets can be defined in either discrete or continuous universes. Universes found in real-world applications are typically continuous, but in the area of digital image processing discrete universes are more often considered.

References

  1. Babuska, R.: Fuzzy modeling and Identication. Ph.D. thesis, Technische Universiteit Delft (1996)

    Google Scholar 

  2. Bersini, H., Bontempi, G.: Now comes the time to defuzzify neurofuzzy models. Fuzzy Sets Syst. 90, 161–169 (1997)

    Article  Google Scholar 

  3. Bertoli, M.: DotFuzzy. https://github.com/MicheleBertoli/DotFuzzy

  4. Brown, M., Harris, C.J.: Neurofuzzy Adaptive Modelling and Control. Prentice Hall, Hemel Hempstead (1994)

    Google Scholar 

  5. Castellano, G.: A neurofuzzy methodology for predictive modeling. Ph.D. thesis, University of Bari (2000)

    Google Scholar 

  6. Castro, J.: Fuzzy Logic Controllers are Universal Approximators. IEEE Trans. Syst., Man Cybern. 25(4), 629–635 (1995)

    Google Scholar 

  7. Castro, J., Delgado, M.: Fuzzy systems with defuzzication are universal approximators. IEEE Trans. Syst., Man Cybern. 26, 149–152 (1996)

    Google Scholar 

  8. Cingolani, P., Alcal-Fdez, J.: jFuzzyLogic: a java library to design fuzzy logic controllers according to the standard for fuzzy control programming. Int. J. Comput. Intell. Syst. 6, 6175 (2013)

    Article  Google Scholar 

  9. Funzy.: Having fun with fuzzy logic. https://code.google.com/p/funzy/

  10. Guillaume, S., Charnomordic, B.: Fuzzy inference systems: an integrated modeling environment for collaboration between expert knowledge and data using FisPro. Expert Syst. Appl. 39(10), 8744–8755 (2012)

    Article  Google Scholar 

  11. Guillaume, S., Charnomordic, B., Labl, J-L.: FisPro (Fuzzy inference system professional). https://www7.inra.fr/mia/M/fispro/

  12. Haykin, S.: Neural Networks: A Comprehensive Foundation. MacMillun College Publishing Company, New York (1994)

    MATH  Google Scholar 

  13. Jang, J-S.R.: ANFIS: Adaptive-network-based fuzzy inference system. IEEE Trans. Syst., Man Cybern. 23(3), 665–685 (1995)

    Google Scholar 

  14. Jang, J.-S.R., Sun, C.-T.: Neuro-fuzzy modelling and control. Proc. IEEE 83, 378–406 (1995)

    Article  Google Scholar 

  15. Lee, C.C.: Fuzzy logic in control systems: Fuzzy logic controller - part I and II. IEEE Trans. Syst., Man Cybern. 20(2), 404–435 (1990)

    Google Scholar 

  16. LibFuzzyEngine++. http://sourceforge.net/projects/libfuzzyengine/

  17. Lin, C., Lee, C.: Neural Fuzzy Systems: A Neural Fuzzy Synergism to Intelligent Systems. Prentice-Hall, Englewood Cliffs (1996)

    Google Scholar 

  18. Mamdani, E.H.: Advances in the linguistic synthesis of fuzzy controllers. Int. J. Man-Mach. Stud. 8, 669–678 (1976)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  20. Mouzouris, G.C., Mendel, M.J.: Dynamic non-singleton fuzzy logic systems for nonlinear modeling. IEEE Trans. Fuzzy Syst. 5(2), 199–208 (1997)

    Article  Google Scholar 

  21. Nauck, D.: Neuro-fuzzy systems: review and prospects. In: Proceedings of the Fifth European Congress on Intelligent Techniques and Soft Computing (EUFIT97), pp. 10441053 (1997)

    Google Scholar 

  22. NXTfuzzylogic. www.openhub.net/p/nxtfuzzylogic

  23. Omran, H.: JFuzzinator. http://sourceforge.net/projects/jfuzzinator/

  24. Pedrycz, W.: Fuzzy Control and Fuzzy Systems. Wiley, New York (1989)

    MATH  Google Scholar 

  25. Riza, L.S., Bergmeir, C., Herrera, F., Benitez, J.M.: FRBS - Fuzzy rule-based systems. http://dicits.ugr.es/software/FRBS/

  26. Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning representations by back-propagating errors. Nature 323, 533–536 (1986)

    Article  Google Scholar 

  27. Sugeno, M., Yasukawa, T.: A fuzzy-logic-based approach to qualitative modeling. IEEE Trans. Fuzzy Syst. 1, 7–31 (1993)

    Article  Google Scholar 

  28. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its application to modeling and control. IEEE Trans. Syst., Man Cybern. 15, 116–132 (1985)

    Google Scholar 

  29. Wang, L.: Adaptive Fuzzy Systems and Control. Prentice Hall, Englewood Clis (1994)

    Google Scholar 

  30. Wang, L., Mendel, J.M.: Fuzzy basis functions, universal approximation, and orthogonal least squares. IEEE Trans. Neural Netw. 3(5), 807–814 (1992)

    Article  Google Scholar 

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

    Google Scholar 

  32. Zimmermann, H.J.: Fuzzy Set Theory and its Applications. Kluwer, Norwell (1992)

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Bari Aldo Moro, Bari, Italy

    Laura Caponetti & Giovanna Castellano

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  1. Laura Caponetti
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  2. Giovanna Castellano
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Correspondence to Laura Caponetti .

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Caponetti, L., Castellano, G. (2017). Basics of Fuzzy Logic. In: Fuzzy Logic for Image Processing. SpringerBriefs in Electrical and Computer Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-44130-6_3

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  • DOI: https://doi.org/10.1007/978-3-319-44130-6_3

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-44130-6

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