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A Reflection on Fuzzy Conditionals

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Combining Experimentation and Theory

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 271))

Abstract

This chapter is just a reflection on some theoretical aspects dealing with the representation in fuzzy terms of imprecise linguistic rules. Namely, it deals with the functions able to represent ‘rules’, or fuzzy conditionals, whose election at each case not only depends on the problem’s context, but on the kind of reasoning intended for its use. Some results on the suitability of Mamdani-Larsen type conditionals are presented.

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References

  1. Mamdani, E., Trillas, E.: Correspondence between an experimentalist and a theoretician (2010)

    Google Scholar 

  2. Delval, J., Rivière, A., llueve, S., Sombrero, E.l.: Una investigación psicológica sobre la tabla de verdad del condicional. Revista de Psicología General y Aplicada 30, 825–850 (1975) (in Spanish)

    Google Scholar 

  3. Trillas, E., Guadarrama, S.: Fuzzy representations need a careful design. International Journal of General Systems 39(3), 329–346 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  4. Trillas, E.: Why do fuzzy representations need a careful design? In: Computational Intelligence in Decision and Control: Proceedings of the 8th International Conference FLINS, pp. 189–197 (2008)

    Google Scholar 

  5. Birkhoff, G., von Neumann, J.: The logic of quantum mechanics. Annals of Mathematics 37(4), 823–843 (1936)

    Article  MathSciNet  Google Scholar 

  6. Trillas, E., Alsina, C.: Mamdani-Larsen conditionals and the synthesis of rules, Tech. Rep. FSC-2010-6, European Centre for Soft Computing (2010) (in this book)

    Google Scholar 

  7. Klir, G.J., Yuan, B.: Fuzzy sets and fuzzy logic. Prentice Hall PTR, Upper Saddle River (1995)

    MATH  Google Scholar 

  8. Trillas, E., Alsina, C., Pradera, A.: On a class of Fuzzy Set Theories. In: Proc. FUZZ-IEEE 2007, London, pp. 1–5 (2007)

    Google Scholar 

  9. Nguyen, H., Walker, E.: A First Course in Fuzzy Logic. Chapman & Hall/CRC (2000)

    Google Scholar 

  10. Pradera, A., Trillas, E., Guadarrama, S., Renedo, E.: On fuzzy set theories. In: Wang, P., Ruan, D., Kerre, E. (eds.) Fuzzy Logic. A Spectrum of Theoretical and Practical Issues. Studies in Fuzziness and Soft Computing, vol. 215, pp. 15–47. Springer, Heidelberg (2007)

    Google Scholar 

  11. Trillas, E., Renedo, E., Alsina, C.: A short note on lattices allowing disjunctive reasoning. Mathware and Soft Computing 13(2), 135–137 (2006)

    MATH  MathSciNet  Google Scholar 

  12. Türksen, I., Kreinovich, V., Yager, R.: A new class of fuzzy implications. Axioms of Fuzzy Implication Revisited, Fuzzy Sets and Systems 100(1-3), 267–272 (1998)

    MATH  Google Scholar 

  13. Trillas, E., Valverde, L.: On implication and indistinguisability in the setting of fuzzy logic. In: Kacprzyk, J., Yager, R. (eds.) Management Decision Support Sysstems Using Fuzzy Sets and Possibility Theory, pp. 198–212. Verlag TÜV-Rheinland, Köln (1985)

    Google Scholar 

  14. Alsina, C., Castro, J., Trillas, E.: On the characterization of S and R implications. In: Proceedings 6th Int. Fuzzy Systems Assoc. World Cong., Brazil, vol. I, pp. 317–319 (1995)

    Google Scholar 

  15. Del Campo, C., Trillas, E.: On Mamdani-Larsen’s type fuzzy implications. In: Proc. Int. Conf. on Information Processing and Management of Uncertainty in Knowlegge-based Systems, IPMU 2000, Madrid, vol. 2, pp. 712–716 (2000)

    Google Scholar 

  16. Alsina, C., Trillas, E., García-Honrado, I.: On the coincidence of conditional functions. In: Proceedings NAFIPS 2010, Toronto, Canada (2010); 978-1-4244-7858-6/10

    Google Scholar 

  17. Moraga, C., Trillas, E., Guadarrama, S.: Multiple-valued logic and artificial intelligence: Fundamentals of fuzzy control revisited. Artif. Intell. Rev. 20(3-4), 169–197 (2003)

    Article  MATH  Google Scholar 

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Trillas, E., García-Honrado, I. (2012). A Reflection on Fuzzy Conditionals. In: Trillas, E., Bonissone, P., Magdalena, L., Kacprzyk, J. (eds) Combining Experimentation and Theory. Studies in Fuzziness and Soft Computing, vol 271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24666-1_26

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  • DOI: https://doi.org/10.1007/978-3-642-24666-1_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24665-4

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