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Fuzzy Relational Equations and Universal Approximation

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A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 347))

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Abstract

This chapter presents the concepts of fuzzy relationships and fuzzy relational equations. These are applied to medical diagnosis and Bayesian inference. The notion of universal approximator with applications to dynamical systems, complete the chapter.

All Knowledge should be useful and be involve the pratical.

(Sophists – 5th Century BCE)

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References

  1. E. Esmi, P. Sussner, S. Sandri, Tunable equivalence fuzzy associative memories. Fuzzy Sets Syst. 292, 242–260 (2015)

    Google Scholar 

  2. P. Sussner, M.E. Valle, Implicative fuzzy associative memories. IEEE Trans. Fuzzy Syst. 14(6), 793–807 (2006)

    Article  Google Scholar 

  3. M.E. Valle, P. Sussner, A general framework for fuzzy morphological associative memories. Fuzzy Sets Syst. 159(7), 747–768 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. M.E. Valle, P. Sussner, Storage and recall capabilities of fuzzy morphological associative memories with adjunction-based learning. Neural Netw. 24(1), 75–90 (2011)

    Article  MATH  Google Scholar 

  5. G. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic Theory and Applications (Prentice-Hall, Englewood Cliffs, 1995)

    Google Scholar 

  6. R.C. Bassanezi, H.E. Roman, Relaciones Fuzzy: Optimizacion de Diagnostico Medico. Anais do Encontro Nacional de Ecologia (Rio de Janeiro), LNCC. (1989), pp. 115–124

    Google Scholar 

  7. J.C.R. Pereira, P.A. Tonelli, L.C. Barros, N.R.S. Ortega, Defuzzification in medical diagnosis. Adv. Log. Artif. Intell. Robot. 85, 202–207 (2002)

    Google Scholar 

  8. J.C.R. Pereira, P.A. Tonelli, L.C. Barros, N.R.S. Ortega, Clinical sings of pneumonia in children: association with and prediction od diagnosis by fuzzy sets theory. Braz. J. Med. Biol. Res. 37, 1–9 (2004)

    Article  Google Scholar 

  9. C.M. Bishop, Neural Networks for Pattern Recognition (Oxford University Press, Oxford, 1995)

    MATH  Google Scholar 

  10. P. Sussner, E. Esmi, Constructive Morphological Neural Networks: Some Theoretical Aspects and Experimental Results in Classification. Constructive Neural Networks (Springer, Berlin, 2009), pp. 123–144

    Google Scholar 

  11. W. Wangning, Fuzzy reasoning and fuzzy relational equations. Fuzzy Sets Syst. 20, 67–78 (1986)

    Article  MathSciNet  Google Scholar 

  12. W. Pedrycz, F. Gomide, An Introduction to Fuzzy Sets: Analysis and Design (The MIT Press, Cambridge, 1998)

    MATH  Google Scholar 

  13. E. Sanchez, Resolution of composite fuzzy relation equations. Inf. Control 30, 35–47 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Wergenknecht, K. Hartmann, On the construction of fuzzy eigen soluyions in given regions. Fuzzy Sets Syst. 20, 55–65 (1996)

    Article  Google Scholar 

  15. D.C. Montgomery, Forecasting and Time Series Analysis (St. Louis: McGraw-Hill, New York, 1976)

    MATH  Google Scholar 

  16. A. Min, C. Czado, Bayesian model selection for D-vine pair-copula constructions. Can. J. Stat. 39(2), 239–258 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. F. Bacani, Modelos de predição utilizando lógica fuzzy: uma abordagem inspirada na inferência bayesiana. Dissertação de Mestrado, IMECC-UNICAMP, Campinas, 2012

    Google Scholar 

  18. F. Bacani, L.C. Barros, Application of Prediction Models Using Fuzzy Sets: A Bayesian Inspired Approach (2016) (submitted for publication)

    Google Scholar 

  19. L.C. Barros, F. Bacani, E.E. Laureano, Equação relacional fuzzy e inferência bayesiana, in Proceedings of Second Brazilian Conference on Fuzzy Systems (Brazil, 2012)

    Google Scholar 

  20. H.T. Nguyen, E.A. Walker, A First Course of Fuzzy Logic (CRC Press, Boca Raton, 1997)

    MATH  Google Scholar 

  21. M.R.B. Dias, L.C. Barros, Differential equations based on fuzzy rules, in IFSA/EUSFLAT Conference (2009), pp. 240–246

    Google Scholar 

  22. J.D.M. Silva, Análise de estabilidade de sistemas dinâmicos p-fuzzy com aplicações em biomatemática. Tese de Doutorado, IMECC-UNICAMP, Campinas (2005)

    Google Scholar 

  23. H.T. Nguyen, M. Sugeno, R. Tang, R. Yager (eds.), Theoretical aspects of fuzzy control, in IEEE International Conference on Fuzzy Systems 1993 (Wiley, New York, 1995)

    Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidade Estadual de Campinas, São Paulo, Brazil

    Laécio Carvalho de Barros

  2. Centro de Matemática e Computação, Universidade Federal do ABC, Santo André, São Paulo, Brazil

    Rodney Carlos Bassanezi

  3. Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, Colorado, USA

    Weldon Alexander Lodwick

Authors
  1. Laécio Carvalho de Barros
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  2. Rodney Carlos Bassanezi
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  3. Weldon Alexander Lodwick
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Corresponding author

Correspondence to Laécio Carvalho de Barros .

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de Barros, L.C., Bassanezi, R.C., Lodwick, W.A. (2017). Fuzzy Relational Equations and Universal Approximation. In: A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics. Studies in Fuzziness and Soft Computing, vol 347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53324-6_6

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  • DOI: https://doi.org/10.1007/978-3-662-53324-6_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53322-2

  • Online ISBN: 978-3-662-53324-6

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