On What I Still Hope from Fuzzy Logic

  • Enric TrillasEmail author
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 325)


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.


Membership Function Fuzzy Logic Boolean Algebra Primary Meaning Orthomodular Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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


  1. 1.
    Kauffman, A.: Introductionà la théorie des sous-ensembles flous à l’usage des ingenieurs. Masson, Paris (1973)Google Scholar
  2. 2.
    Menger, K.: Ensembles flous et fonctions aleatoires. C.R. Acad. Sci. de Paris. 232, 2001–2003 (1951)Google Scholar
  3. 3.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 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)CrossRefzbMATHGoogle Scholar
  5. 5.
    Russell, B.: Vagueness. Aus. J. Philos. Psychol. 1, 84–92 (1923)Google Scholar
  6. 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. 7.
    Boole, G.: An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities. Macmillan, London (1854)CrossRefGoogle Scholar
  8. 8.
    Menger, K.: Statistical metric spaces. Proc. Natl. Acad. Sci. USA 28(12), 535–537 (1942)Google Scholar
  9. 9.
    Wald, A.: On a statistical generalization of metric spaces. Proc. Natl. Acad. Sci. USA 29, 196–197 (1943)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Schweizer, B., Sklar, A.: Statistical metric spaces. Pac. J. Math. 10, 313–334 (1960)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Trillas, E.: Sobre funciones de negacién en la teoría de conjuntos difusos. Stochastica III(1), 47–60 (1979)MathSciNetGoogle Scholar
  12. 12.
    Trillas, E., Alsina, C., Renedo, E.: On some schemes of reasoning in fuzzy logic. New Math. Nat. Comput. 7(3), 433–451 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 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. 14.
    Zadeh, L.A.: Computing with Words. Principal Concepts and Ideas, Springer, New York (2012)CrossRefzbMATHGoogle Scholar
  15. 15.
    Watanabe, S.: Knowing and Guessing. Wiley, New York (1969)zbMATHGoogle Scholar
  16. 16.
    Wittgenstein, L.: Philosophical Investigations. Basil Blackwell, Oxford (1958)Google Scholar
  17. 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. 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. 19.
    Trillas, E.: On the genesis of fuzzy sets. Agora 27(1), 7–33 (2008)MathSciNetGoogle Scholar
  20. 20.
    Trillas, E., Guadarrama, S.: Fuzzy representations need a careful design. Int. J. Gen. Syst. 39(3), 329–346 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Trillas, E.; Moraga, C.: Reasons for a careful design of fuzzy sets. In: Proceedings EUSFLAT—Milano, pp. 140–145 (2013)Google Scholar
  22. 22.
    Trillas, E., Moraga, C., Termini, S.: A naïve look at fuzzy sets. Submitted to Fuzzy Sets Syst. (2014)Google Scholar
  23. 23.
    Medawar, P.: The Limits of Science. Harper, London (1984)Google Scholar
  24. 24.
    Trillas, E.: A model for ‘Crisp reasoning’ with fuzzy sets. Int. J. Intell. Syst. 27, 859–872 (2012)CrossRefGoogle Scholar
  25. 25.
    Trillas, E., Alsina, C.: Paradoxes of fuzzy logic revisited. Int. J. Approx. Reason. 26, 157–159 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  26. 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)CrossRefzbMATHMathSciNetGoogle Scholar
  27. 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)CrossRefGoogle Scholar
  28. 28.
    Trillas, E., Cubillo, S., Castiñeira, E.: On conjectures in ortholattices. Artif. Intell. 1(7), 255–275 (2000)CrossRefGoogle Scholar
  29. 29.
    Trillas, E.: Some uncertain reflections on uncertainty. Arch. Philos. Hist. Soft Comput. 1, 1–16 (2013)Google Scholar
  30. 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. 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

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.European Centre for Soft ComputingMieresSpain

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