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Towards the Future of Fuzzy Logic pp 31–54Cite as

On What I Still Hope from Fuzzy Logic

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 325))

Abstract

This paper just tries to look towards a particular aspect of fuzzy logic’s future. Namely, that concerning to the form in which its theoretic evolution should be followed up to approach, in a scientific manner, one of the greats desiderata in the way to Zadeh’s Computing with Words: the renewal of the old thought of making interact Fuzzy Logic and Natural Language Common Sense Reasoning. For such a way, and from the perspective of its author, it is argued that fuzzy logic deserves to move towards a new experimental science of linguistic imprecision and non-random uncertainty. A goal for which a critical review of some still open questions should be done, but not only taking as models those of logic and mathematics. The author thinks that a better model is that of physics, joining observation, controlled experimentation and mathematical models in the ground of language and ordinary reasoning, with the extensive use of computational technology and its applications to practical problems.

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References

  1. Kauffman, A.: Introductionà la théorie des sous-ensembles flous à l’usage des ingenieurs. Masson, Paris (1973)

    Google Scholar 

  2. Menger, K.: Ensembles flous et fonctions aleatoires. C.R. Acad. Sci. de Paris. 232, 2001–2003 (1951)

    Google Scholar 

  3. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  4. de Luca, A., Termini, S.: A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Inf. Control 20, 301–312 (1972)

    Article  MATH  Google Scholar 

  5. Russell, B.: Vagueness. Aus. J. Philos. Psychol. 1, 84–92 (1923)

    Google Scholar 

  6. Boole, G.: The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning. Barclay and Macmillan, London (1847)

    Google Scholar 

  7. Boole, G.: An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities. Macmillan, London (1854)

    Book  Google Scholar 

  8. Menger, K.: Statistical metric spaces. Proc. Natl. Acad. Sci. USA 28(12), 535–537 (1942)

    Google Scholar 

  9. Wald, A.: On a statistical generalization of metric spaces. Proc. Natl. Acad. Sci. USA 29, 196–197 (1943)

    Article  MATH  MathSciNet  Google Scholar 

  10. Schweizer, B., Sklar, A.: Statistical metric spaces. Pac. J. Math. 10, 313–334 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  11. Trillas, E.: Sobre funciones de negacién en la teoría de conjuntos difusos. Stochastica III(1), 47–60 (1979)

    MathSciNet  Google Scholar 

  12. Trillas, E., Alsina, C., Renedo, E.: On some schemes of reasoning in fuzzy logic. New Math. Nat. Comput. 7(3), 433–451 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  13. Trillas, E.: Non-contradiction, excluded middle, and fuzzy sets. In: Di Gesú, V., Pal, S.K., Petrosino, A. (eds.), Proceedings of the 8th International Workshop on Fuzzy Logic and Applications (WILF 2009) Palermo, Italy, June 9–12, Fuzzy Logic and Applications. LNCS (LNAI), vol. 5571. pp. 1–11, Springer, Heidelberg (2009)

    Google Scholar 

  14. Zadeh, L.A.: Computing with Words. Principal Concepts and Ideas, Springer, New York (2012)

    Book  MATH  Google Scholar 

  15. Watanabe, S.: Knowing and Guessing. Wiley, New York (1969)

    MATH  Google Scholar 

  16. Wittgenstein, L.: Philosophical Investigations. Basil Blackwell, Oxford (1958)

    Google Scholar 

  17. Trillas, E.: Reflexions sobre ciència i magnitud. In: Levy, J. et al. (eds.) Festschrift en homenatge a Jaume Agustí, pp. 43–53, CSIC, Barcelona (2013)

    Google Scholar 

  18. Trillas, E., García Honrado, I.: A layperson reflection on sorites. In: Seising, R., Tabacchi, M.E. (eds.), Fuzziness and Medicine: Philosophical Reflections and Application Systems in Health Care, pp. 217–231, Springer, Berlin (2013)

    Google Scholar 

  19. Trillas, E.: On the genesis of fuzzy sets. Agora 27(1), 7–33 (2008)

    MathSciNet  Google Scholar 

  20. Trillas, E., Guadarrama, S.: Fuzzy representations need a careful design. Int. J. Gen. Syst. 39(3), 329–346 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  21. Trillas, E.; Moraga, C.: Reasons for a careful design of fuzzy sets. In: Proceedings EUSFLAT—Milano, pp. 140–145 (2013)

    Google Scholar 

  22. Trillas, E., Moraga, C., Termini, S.: A naïve look at fuzzy sets. Submitted to Fuzzy Sets Syst. (2014)

    Google Scholar 

  23. Medawar, P.: The Limits of Science. Harper, London (1984)

    Google Scholar 

  24. Trillas, E.: A model for ‘Crisp reasoning’ with fuzzy sets. Int. J. Intell. Syst. 27, 859–872 (2012)

    Article  Google Scholar 

  25. Trillas, E., Alsina, C.: Paradoxes of fuzzy logic revisited. Int. J. Approx. Reason. 26, 157–159 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  26. Trillas, E., Alsina, C.: Standard theories of fuzzy sets with the law \((a \cdot b^{\prime })^{\prime } = b + a^{\prime }\cdot b^{\prime }\). Int. J. Approx. Reason. 37(2), 87–92 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  27. Garmendia, L., Yager, R.R., Trillas, E., Salvador, A.: Measures of fuzzy sets under T-indistinguishabilities. IEEE Trans. Fuzzy Syst. 14(4), 568–572 (2006)

    Article  Google Scholar 

  28. Trillas, E., Cubillo, S., Castiñeira, E.: On conjectures in ortholattices. Artif. Intell. 1(7), 255–275 (2000)

    Article  Google Scholar 

  29. Trillas, E.: Some uncertain reflections on uncertainty. Arch. Philos. Hist. Soft Comput. 1, 1–16 (2013)

    Google Scholar 

  30. Mamdani, E.H., Trillas, E.: Correspondence between an experimentalist and a theoretician. In: Trillas, E, et al. (eds.) Combining Experimentation and Theory, pp. 1–18, Springer, Berlin (2012)

    Google Scholar 

  31. Mendel, J., Zadeh, L.A., Trillas, E., Yager, R.R., Lawry, J., Hagras, H., Guadarrama, S.: What computing with words means to me (Discussion Forum). IEEE Comput. Intell. Mag., 20–26 (2010)

    Google Scholar 

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Acknowledgments

This paper is partially funded by the Foundation for the Advancement of Soft Computing, and by the Spain’s Government project MICIIN/TIN \(2011-29827-C02-01\).

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Authors and Affiliations

  1. European Centre for Soft Computing, Calle Gonzalo Gutiérrez Quirós S/N, 33600, Mieres, Asturias, Spain

    Enric Trillas

Authors
  1. Enric Trillas
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Correspondence to Enric Trillas .

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Editors and Affiliations

  1. Institut für Geschichte der Medizin, Naturwissenschaft und Technik, Friedrich-Schiller-Universität Jena, Berggasse, Jena, Germany

    Rudolf Seising

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

    Enric Trillas

  3. Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland

    Janusz Kacprzyk

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Trillas, E. (2015). On What I Still Hope from Fuzzy Logic. In: Seising, R., Trillas, E., Kacprzyk, J. (eds) Towards the Future of Fuzzy Logic. Studies in Fuzziness and Soft Computing, vol 325. Springer, Cham. https://doi.org/10.1007/978-3-319-18750-1_3

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  • DOI: https://doi.org/10.1007/978-3-319-18750-1_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18749-5

  • Online ISBN: 978-3-319-18750-1

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