Skip to main content

Mediative Fuzzy Logic: A Novel Approach for Handling Contradictory Knowledge

  • Chapter
  • 793 Accesses

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 208))

Abstract

In this paper we are proposing a novel fuzzy method that can handle imperfect knowledge in a broader way than Intuitionistic fuzzy logic does (IFL). This fuzzy method can manage non-contradictory, doubtful, and contradictory information provided by experts, providing a mediated solution, so we called it Mediative Fuzzy Logic (MFL). We are comparing results of MFL, with IFL and traditional Fuzzy logic (FL).

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. George J. Klir, Bo Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Ed. Prentice Hall, USA, 1995.

    MATH  Google Scholar 

  2. L. A. Zadeh, “Fuzzy Sets”, Information and Control, Vol. 8, p.p. 338–353, 1965.

    Article  MATH  Google Scholar 

  3. Jerry M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems, Introduction and new directions, Ed. Prentice Hall, USA, 2000.

    Google Scholar 

  4. O. Montiel, O. Castillo, P. Melin, A. Rodríguez Días, R. Sepúlveda, ICAI-2005.

    Google Scholar 

  5. Donald A. Bal, Wendell H. McCulloch, JR., “International Business. Introduction and Essentials”, Fifth Edition, pp. 138–140, 225, USA, 1993.

    Google Scholar 

  6. Horwitz R. I.: Complexity and contradiction in clinical trial research. Am. J. Med., 82: 498–510, 1987.

    Article  Google Scholar 

  7. J. Scott Armstrong, “Principles of Forecasting. A Handbook for researchers and Practitioners”, Edited by J. Scott Armstrong, University of University of Pennsylvania, Wharton School, Philadelphia, PA., USA, 2001.

    Google Scholar 

  8. Aristotle, The Basic Works of Aristotle, Modern Library Classics, Richard McKeon Ed., 2001.

    Google Scholar 

  9. Robin Smith, Aristotle's logic, Stanford Encyclopedia of Philosophy, 2004, http://plato.stanford.edu/entries/aristotle-logic/.

    Google Scholar 

  10. Dirk Baltzly, Stanford Encyclopedia of Philosophy, 2004, http://plato.stanford. edu/entries/stoicism/

    Google Scholar 

  11. J J O'Connor and E F Robertson, Augustus DeMorgan, MacTutor History of Mathematics: Indexes of Biographies (University of St. Andrews), 2004, http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/ De_Morgan.html

    Google Scholar 

  12. George Boole, The Calculus of Logic, Cambridge and Dublin Mathematical Journal, Vol. III (1848), 1848, pp. 183–98

    Google Scholar 

  13. J J O'Connor and E F Robertson, George Boole, MacTutor History of Mathematics: Indexes of Biographies (University of St. Andrews), 2004, http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Boole.html

    Google Scholar 

  14. J J O'Connor and E F Robertson, Friedrich Ludwig Gottlob Frege, MacTutor History of Mathematics: Indexes of Biographies (University of St. Andrews), http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Frege.html

    Google Scholar 

  15. J J O'Connor and E F Robertson, Luitzen Egbertus Jan Brouwer, MacTutor History of Mathematics: Indexes of Biographies (University of St. Andrews), http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/ Brouwer.html

    Google Scholar 

  16. J J O'Connor and E F Robertson, Arend Heyting, MacTutor History of Mathematics: Indexes of Biographies (University of St. Andrews), 2004, http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Heyting.html

    Google Scholar 

  17. J J O'Connor and E F Robertson, Gerhard Gentzen, MacTutor History of Mathematics: Indexes of Biographies (University of St. Andrews), 2004, http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Gentzen.html

    Google Scholar 

  18. J J O'Connor and E F Robertson, Jan Lukasiewicz, MacTutor History of Mathematics: Indexes of Biographies (University of St. Andrews), 2004, http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Lukasiewicz.html

    Google Scholar 

  19. Wikipedia the free encyclopedia, vailable from the web page: http://en.wikipedia.org/wiki/Jan_Lukasiewicz

    Google Scholar 

  20. Wikipedia the free encyclopedia, available from the webpage: http://en.wikipedia.org/wiki/Newton_da_Costa

    Google Scholar 

  21. How to build your own paraconsistent logic: an introduction to the Logics of Formal (In)Consistency. W. A. Carnielli. In: J. Marcos, D. Batens, and W. A. Carnielli, organizers, Proceedings of the Workshop on Paraconsistent Logic (WoPaLo), held in Trento, Italy, 5–9 August 2002, as part of the 14th European Summer School on Logic, Language and Information (ESSLLI 2002), pp. 58–72.

    Google Scholar 

  22. Jerry M. Mendel and Robert I. Bob John, Type-2 Fuzzy Sets Made Simple, IEEE Transactions on Fuzzy Systems, Vol. 10, No. 2, April 2002.

    Google Scholar 

  23. Atanassov, K., “Intuitionistic Fuzzy Sets: Theory and Applications”, Springer-Verlag, Heidelberg, Germany, 1999.

    MATH  Google Scholar 

  24. Mariana Nikilova, Nikolai Nikolov, Chris Cornelis, Grad Deschrijver, “Survey of the Research on Intuitionistic Fuzzy Sets”, In: Advanced Studies in Contemporary Mathematics 4(2), 2002, p. 127–157.

    MATH  Google Scholar 

  25. O. Castillo, P. Melin, A New Method for Fuzzy Inference in Intuitionistic Fuzzy Systems, Proceedings of the International Conference NAFIPS 2003, IEEE Press, Chicago, Illinois, USA, Julio 2003, pp. 20–25.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer

About this chapter

Cite this chapter

Montiel, O., Castillo, O. (2007). Mediative Fuzzy Logic: A Novel Approach for Handling Contradictory Knowledge. In: Castillo, O., Melin, P., Kacprzyk, J., Pedrycz, W. (eds) Hybrid Intelligent Systems. Studies in Fuzziness and Soft Computing, vol 208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-37421-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-37421-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37419-0

  • Online ISBN: 978-3-540-37421-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics