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The Inevitability of Vagueness in Fuzzy Logic

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Fuzzy Logic and Technology, and Aggregation Operators (EUSFLAT 2023, AGOP 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14069))

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Abstract

Fuzzy Logic, in its fuzzy control incarnation, can be as well seen as an answer to the belated question on how can an algorithm take in account the subtle variations in a complex system – be it the simple and paradigmatic thermostat, the description of a traffic jam or the inner workings of a spaceship. Contrary to the best whodunit, the answer is given at the very start, and the history of the following years of fuzziness is a long demonstration of how, thanks to its explanatory power, a simple idea can be implemented in countless devices, and become the manifest for a technological society in which the logic discourse is based more on the human approach and on embracing the permanent state of flux and uncertainty that is the human experience than on the futile search for absolute truths and endless precision. If the control answer is somehow a given, so many other answers that concern foundations of Fuzzy Logic still beget proper questions. In this paper some of such foundational questions pertaining vagueness, its role in the definition of fuzziness and its many incarnations are set in their historical perspective, and some of the dots outlining the path from a rigid search for truth typical of the end of the nineteenth century to the more nuanced approach that has swept the twentieth century are connected.

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Notes

  1. 1.

    As an example, the definition of a fringe of a city center is often just in the eyes of a building’s owner: the author has been personally offered a rent in what was defined “a fringe” of the center, and the fastest train to the “real” center was in the best cases a 45 min trip.

  2. 2.

    There is a strange fixation with furniture in the history of fuzziness: probably the most egregious example, with his chair-that-transforms-into-stairs, is Bart Kosko [5].

  3. 3.

    In reality the debate will go on and on, and on, slowing only during the second world war. Notable more recent examples with a direct reference to the work of Black and Hempel are [6, 7]. While interesting in their own right, most of the more contemporary debate from the field of language seem to ignore the advancement made by Fuzzy Logic (and other non classical logics) in the field of dealing with vagueness. It is not known if this is due to a sort of bubble effect, to sheer lack of knowledge or to any other, more esoteric explanation.

References

  1. Bachmann, F.: Frege als konstruktiver Logizist. Das Problem der Begründung,Börger (1975)

    Google Scholar 

  2. Black, M.: Vagueness: an exercise in logical analysis. Philosophy Sci. 4(4), 427–455 (1937)

    Article  Google Scholar 

  3. Bradley, J., Seising, R.: The gap between scientific theory and application: Black and Zadeh - vagueness and fuzzy sets. In: NAFIPS 2006–2006 Annual Meeting of the North American Fuzzy Information Processing Society, pp. 408–413 (2006). https://doi.org/10.1109/NAFIPS.2006.365444

  4. Hempel, C.G.: Vagueness and logic. Philosophy Sci. 6(2), 163–180 (1939)

    Article  Google Scholar 

  5. Kosko, B., Toms, M.: Fuzzy Thinking: The New Science of Fuzzy Logic, vol. 288. Hyperion, New York (1993)

    Google Scholar 

  6. Rolf, B.: Black and Hempel on vagueness. Zeitschrift für allgemeine Wissenschaftstheorie/J. Gen. Philosophy Sci. 332–346 (1980)

    Google Scholar 

  7. Rolf, B.: A theory of vagueness. J. Philos. Logic, 315–325 (1980)

    Google Scholar 

  8. Russell, B.: Vagueness. Australas. J. Psychol. Philosophy 1(2), 84–92 (1923)

    Article  Google Scholar 

  9. Tabacchi, M.E.: Focusing Fuzzy Logic, Naturalia, vol. 6. UniPa Press (2021)

    Google Scholar 

  10. Tabacchi, M.E., Termini, S.: Varieties of vagueness, fuzziness and a few foundational (and ontological) questions. In: Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology, pp. 578–583. Atlantis Press (2011)

    Google Scholar 

  11. Tabacchi, M.E., Termini, S.: The fuzzy logic gambit as a paradigm of Lotfi’s proposals. In: Fullér, R., Giove, S., Masulli, F. (eds.) WILF 2018. LNCS (LNAI), vol. 11291, pp. 231–235. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-12544-8_18

    Chapter  Google Scholar 

  12. Van Heijenoort, J.: Ostension and vagueness. In: Selected Essays, pp. 71–74. Bibliopolis (1979)

    Google Scholar 

  13. Van Heijenoort, J.: Frege and vagueness. In: Selected Essays, pp. 85–98. Bibliopolis (1986)

    Google Scholar 

  14. Zadeh, L.: Fuzzy languages and their relation to human and machine intelligence. In: Man and Computer, pp. 130–165. Karger Publishers (1972)

    Google Scholar 

  15. Zadeh, L.: A fuzzy-algorithmic approach to the definition of complex or imprecise concepts. Int. J. Man-Mach. Stud. 8(3), 249–291 (1976). https://doi.org/10.1016/S0020-7373(76)80001-6

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  17. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-III. Inf. Sci. 9(1), 43–80 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-II. Inf. Sci. 8(4), 301–357 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zadeh, L.A.: Fuzzy sets and information granularity. Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers, pp. 433–448 (1979)

    Google Scholar 

  20. Zadeh, L.A.: Fuzzy logic= computing with words. Comput. Words Inf./Intell. Syst. 1: Found., 3–23 (1999)

    Google Scholar 

  21. Zadeh, L.A.: Is there a need for fuzzy logic? Inf. Sci. 178(13), 2751–2779 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8(3), 199–249 (1975)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Palermo, Italy

    Marco Elio Tabacchi

  2. Istituto Nazionale di Ricerche Demopolis, Palermo, Italy

    Marco Elio Tabacchi

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  1. Marco Elio Tabacchi
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Correspondence to Marco Elio Tabacchi .

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Editors and Affiliations

  1. University of the Balearic Islands, Palma, Spain

    Sebastia Massanet

  2. University of Oviedo, Gijón, Spain

    Susana Montes

  3. University of the Balearic Islands, Palma, Spain

    Daniel Ruiz-Aguilera

  4. University of the Balearic Islands, Palma, Spain

    Manuel González-Hidalgo

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Tabacchi, M.E. (2023). The Inevitability of Vagueness in Fuzzy Logic. In: Massanet, S., Montes, S., Ruiz-Aguilera, D., González-Hidalgo, M. (eds) Fuzzy Logic and Technology, and Aggregation Operators. EUSFLAT AGOP 2023 2023. Lecture Notes in Computer Science, vol 14069. Springer, Cham. https://doi.org/10.1007/978-3-031-39965-7_1

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  • DOI: https://doi.org/10.1007/978-3-031-39965-7_1

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