Skip to main content
SpringerLink
Log in

Fuzzy Logic as a Theory of Vagueness: 15 Conceptual Questions

  • Chapter
Views on Fuzzy Sets and Systems from Different Perspectives

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 243))

Introduction

Fuzzy logic has successfully established itself as an engineering tool. Though its purpose and validity in any context were highly controversial in the early years, this initial criticism was defused by the practical success of fuzzy set theory, to a large degree under the name of “fuzzy logic”. This began with Assilian’s and Mamdani’s steam engine in the 1970s [22] and has extended over an ever-expanding range of applications, from noodle cookers to washing machines, up to the present day. The history of fuzzy set theory’s birth, development and progression has been documented by Rudolf Seising in his book The Fuzzification of Systems [32].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Behounek, L.: An alternative justification of the axioms of fuzzy logics. The Bulletin of Symbolic Logic (to appear)

    Google Scholar 

  2. Bennett, A.D.C., Paris, J.B., Vencovská, A.: A new criteria for comparing fuzzy logics for uncertain reasoning. Journal of Logic, Language, and Information (9), 31–63 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bezdek, J.C.: Fuzzy Mathematics in Pattern Classification. Ph. D. Thesis, Center for Aplied Mathematics, Cornell University, Ithaca, New York (1973)

    Google Scholar 

  4. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)

    MATH  Google Scholar 

  5. Cignoli, R., D’Ottaviano, I.M.L., Mundici, D.: Algebraic Foundations of Many-valued Reasoning. In: Trends in Logic, vol. 7. Kluwer Academic Publishers, Dordrecht (1999)

    Google Scholar 

  6. Edgington, D.: Vagueness by Degrees. In: Keefe, R., Smith, P. (eds.) Vagueness: A Reader, pp. 294–316. MIT Press, Cambridge (1997)

    Google Scholar 

  7. Elkan, C.: The Paradoxical Success of Fuzzy Logic. In: Fikes, R., Lehnert, W. (eds.) Proceedings of the Eleventh National Conference on Artificial Intelligence, pp. 698–703. AAAI Press, Menlo Park (1993)

    Google Scholar 

  8. Fermüller, C.: Revisiting Giles: Connecting Bets, Dialogue Games, and Fuzzy Logics. In: Logic, Games and Philosophy: Foundational Perspectives. Logic, Epistemology and the Unity of Sciences. Springer, Berlin (to appear)

    Google Scholar 

  9. Fine, K.: Vagueness, Truth and Logic. Synthese (30), 265–300 (1975)

    Article  MATH  Google Scholar 

  10. Giles, R.: A non-classical logic for physics. Studia Logica 33(4), 399–417 (1974)

    Article  MathSciNet  Google Scholar 

  11. Giles, R.: A non-classical logic for physics. In: Wojcicki, R., Malinkowski, G. (eds.) Selected Papers on Łukasiewicz Sentential Calculi, pp. 13–51. Polish Academy of Sciences (1997)

    Google Scholar 

  12. Graff, D.: Shifting Sands: An Interest-Relative Theory of Vagueness. Philosophical Topics (28), 45–81 (2002)

    Google Scholar 

  13. Graff, D.: Phenomenal Continua and the Sorites. Mind (110), 905–935 (2001)

    Article  Google Scholar 

  14. Graff, D.: Gap Principles, Penumbral Consequence, and Infinitely Higher-Order Vagueness. In: Beall, J.C. (ed.) Liars and Heaps: New Essays on Paradox, pp. 195–221. Oxford University Press, Oxford (2003)

    Google Scholar 

  15. Heisenberg, W.: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik (43), 172–198 (1927)

    Article  Google Scholar 

  16. Keefe, R.: Theories of Vagueness. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  17. Klement, E.P., Mesiar, R., Pap, E.: Bausteine der Fuzzy Logic: T-Normen – Eigenschaften und Darstellungssätze. In: Seising, R. (ed.) Fuzzy Theorie und Statistik – Modelle und Anwendungen in der Diskussion (Computational Intelligence), pp. 127–225. Vieweg, Braunschweig (1999)

    Google Scholar 

  18. Lakoff, G.: Hedges: A Study in Meaning Criteria and the Logic of Fuzzy Concepts. Journal of Philosophical Logic (2), 458–508 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  19. Majer, O., Behounek, L., Cintula, P.: Uncertainty: Reasoning about probability and vagueness (2006), http://www.flu.cas.cz/Logica/Aconf/col2006.html

  20. Mamdani, E.H.: Twenty Years of Fuzzy Control: Experience Gained and Lessons Learnt. IEEE Transactions on Fuzzy Systems 1, 19–24 (1993)

    Google Scholar 

  21. Mamdani, E.H.: Advances in the Linguistic Synthesis of Fuzzy Controllers. International Journal of Man-Machine Studies 8, 669–678 (1976)

    Article  MATH  Google Scholar 

  22. Mamdani, E.H., Assilian, S.: An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller. International Journal of Man-Machine Studies 7(1), 1–13 (1975)

    Article  MATH  Google Scholar 

  23. Mendel, J.M., John, R.I.: Type-2 Fuzzy Sets Made Simple. IEEE Transactions on Fuzzy Systems 10(2), 117–127 (2002)

    Article  Google Scholar 

  24. Mendel, J.M.: Type-2 Fuzzy Sets: Some Questions and Answers, pp. 10–13. IEEE Computer Society Press, Los Alamitos (2003)

    Google Scholar 

  25. Novák, V.: Which Logic is the Real Fuzzy Logic? Fuzzy Sets and Systems (157), 635–641 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  26. Novák, V.: Are Fuzzy Sets a Reasonable Tool for Modeling Vague Phenomena? Fuzzy Sets and Systems (156), 635–641 (2005)

    Article  Google Scholar 

  27. Novák, V.: Fuzzy Sets as a Special Mathematical Model of Vagueness Phenomenon. In: Reusch, B. (ed.) Computational Intelligence, Theory and Applications, pp. 683–690. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  28. Paris, J.B.: A semantics for fuzzy logic. Soft Computing (1), 143–147 (1997)

    MathSciNet  Google Scholar 

  29. Raffman, D.: Vagueness and Context-Relativity. Philosophical Studies (81), 175–192 (1996)

    Article  Google Scholar 

  30. Raffman, D.: Is Perceptual Indiscriminability Nontransitive? Philosophical Topics (28), 153–176 (2002)

    Google Scholar 

  31. Ruspini, E.H.: On the semantics of fuzzy logic. International Journal of Approximate Reasoning (5), 45–88 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  32. Seising, R.: The Fuzzification of Systems. The Genesis of Fuzzy Set Theory and its Initial Applications – Developments up to the 1970s. Studies in Fuzziness and Soft Computing, vol. 216. Springer, Berlin (2007)

    MATH  Google Scholar 

  33. Seising, R., Bradley, J.: The Gap Between Scientific Theory and Application: Black and Zadeh: Vagueness and Fuzzy Sets. In: Demirli, K., Akgunduz, A. (eds.) Proceedings the 2006 Conference of the North American Fuzzy Information Processing Society (NAFIPS 2006, CD), Montreal (June 2006)

    Google Scholar 

  34. Seising, R., Bradley, J.: From vague or loose concepts to hazy and fuzzy sets – human understanding versus exact science. In: Gabrys, B., Howlett, R.J., Jain, L.C. (eds.) KES 2006. LNCS, vol. 4253, pp. 374–382. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  35. Seising, R., Bradley, J.: Are Soft Computing and Its Applications in Technology and Medicine Human-Friendly? In: Gabrys, B., Howlett, R.J., Jain, L.C. (eds.) KES 2006. LNCS (LNAI), vol. 4253. Springer, Heidelberg (2006)

    Google Scholar 

  36. Shapiro, S.: Vagueness in Context. Oxford University Press, New York (2006)

    Book  Google Scholar 

  37. Shapiro, S.: Vagueness and Converstion. In: Beall, J.C. (ed.) Liars and Heaps: New Essays on the Semantics of Paradox. Oxford University Press, Oxford (2003)

    Google Scholar 

  38. Sorensen, R.: Vagueness. In: Stanford Encyclopedia of Philosophy (2006), http://plato.stanford.edu/

  39. Trillas, E.: Menger’s Trace in Fuzzy Logic. Segunda Épocha 11(7), 89–96 (1996)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. No Affiliations,  

    Jeremy Bradley

Authors
  1. Jeremy Bradley
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Medical University of Vienna, Austria

    Rudolf Seising

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bradley, J. (2009). Fuzzy Logic as a Theory of Vagueness: 15 Conceptual Questions. In: Seising, R. (eds) Views on Fuzzy Sets and Systems from Different Perspectives. Studies in Fuzziness and Soft Computing, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93802-6_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-93802-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-93801-9

  • Online ISBN: 978-3-540-93802-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation