Skip to main content

A Fuzzy Generalisation of Information Relations

  • Chapter

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 114))

Abstract

In this paper we consider a fuzzy generalisation of some information relations. Basic properties of these relations are provided. We give characterisations of these relations formalised by means of fuzzy information operators. For particular classes of fuzzy information relations the corresponding classes of fuzzy information logics are defined and briefly discussed.

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. Balbiani, P., Orlowska, E.: A hierarchy of modal logics with relative accessibility relations. Journal of Applied Non-Classical Logics 9, no 2–3 (1999) 303–348

    Article  MathSciNet  MATH  Google Scholar 

  2. De Baets, B., Mesiar, R.: Pseudo-metrics and T—equivalences. Journal of Fuzzy Mathematics 5 (2) (1997) 471–481

    MathSciNet  MATH  Google Scholar 

  3. Demri, S., Orlowska, E., Vakarelov, D.: Indiscernibility and complementarity relations in information systems. J. Gerbrandy, M. Marx, M. de Rijke and Y. Venema (eds) JFAK, Essays Dedicated to Johan van Benthem on the Occasion of his 50th Birthday. Amsterdam University Press (1999)

    Google Scholar 

  4. Demri, S. and Orlowska, E. Incomplete Information: Structure, Inference, Complexity. EATCS Monographs in Theoretical Computer Science, Springer (2002)

    Book  MATH  Google Scholar 

  5. Dubois, D., Prade, H.: Putting fuzzy sets and rough sets together. Intelligent Decision Support, Slowinski, R. ( ed. ), Kluwer Academic (1992) 203–232

    Google Scholar 

  6. Düntsch, I., Orlowska, E.: Beyond modalities: Sufficiency and Mixed Algebras. Relational Methods for Computer Science Applications, Orlowska, E. and Szalas, A. (eds), Physica—Verlag, Heidelberg (2000) 263–283

    Google Scholar 

  7. Düntsch, I. and Orlowska, E.: Logics of complementarity in information systems. Mathematical Logic Quarterly 46 (2000) 267–288

    Article  MATH  Google Scholar 

  8. Godo, L., Rodriquez, R.O.: Fuzzy Modal Logic for Similarity Reasoning Kluwer Academic Publishers 6 (1999) 33–48

    Google Scholar 

  9. Hâjek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)

    Book  MATH  Google Scholar 

  10. Humberstone, I.: Inaccessible words. Notre Dame Journal of Formal Logic 24 (1983) 346–352

    Article  MathSciNet  MATH  Google Scholar 

  11. Kerre, E.E. (ed.): Introduction to the Basic Principles of Fuzzy Set Theory and Some of Its Applications, Communication Cognition, Gent (1993)

    Google Scholar 

  12. Klir, G.J., Yuan, B.: Fuzzy Logic: Theory and Applications. Prentice—Hall, Englewood Cliffs, NJ (1995)

    MATH  Google Scholar 

  13. Konikowska, B.: A logic for reasoning about relative similarity. Studia Logica 58 (1997) 185–226

    Article  MathSciNet  MATH  Google Scholar 

  14. Orlowska, E.: Kripke models with relative accessibility and their applications to inference from incomplete information. Mathematical Problems in Computation Theory, Mirkowska, G. Rasiowa, H. (eds.), Banach Center Publications 21 (1988) 329–339

    Google Scholar 

  15. Orlowska, E.: Many—valudness and uncertainty. Proceedings of the 27th International Symposium on Multiple-Valued Logic ISMVL-97, Antigonish, Canada (1997) 153–160. Also in Multiple Valued Logics 4 (1999) 207–227

    MathSciNet  MATH  Google Scholar 

  16. Orlowska, E. (ed.): Incomplete Information — Rough Set Analysis. Studies in Fuzziness and Soft Computing, Springer—Verlag (1998)

    Book  Google Scholar 

  17. Orlowska, E.: Studying incompleteness of information: a class of information logics. in Kijania—Placek, K. and Wolernski, J. (eds.), The Lvov—Warsaw School and Contempotary Philosophy, Kluwer Academic Press (1998) 283–300

    Google Scholar 

  18. Radzikowska, A.M., Kerre, E.E.: Fuzzy rough sets revisited. Proceedings of European Congress of Intelligent Techniques and Soft Computing EUFIT-99, Aachen, Germany. Published on CD-ROM (1999)

    Google Scholar 

  19. Radzikowska, A.M., Kerre, E.E.: On some classes of fuzzy information relations. Proceedings of the 31st International Symposium of Multiple Valued Logics ISMVL-2001, Warsaw, Poland (2001) 75–80

    Google Scholar 

  20. Radzikowska, A.M., Kerre, E.E.: Towards studying of fuzzy information relations. Proceedings of International Conference in Fuzzy Logic and Technology EUSFLAT-2001, Leicester, UK (2001) 365–368

    Google Scholar 

  21. Radzikowska, A.M., Kerre, E.E.: A comparative study on fuzzy rough sets. Fuzzy Sets and Systems 126 (2) (2002) 137–155

    Article  MathSciNet  MATH  Google Scholar 

  22. Radzikowska, A.M., Kerre, E.E.: A general calculus of fuzzy rough sets. Submitted (2002)

    Google Scholar 

  23. Radzikowska, A.M., Kerre, E.E.: Fuzzy rough sets based on residuated lattices. Submitted (2002)

    Google Scholar 

  24. Radzikowska, A.M., Kerre, E.E.: Characterisations of main classes of fuzzy relations using information operators. Submitted (2002)

    Google Scholar 

  25. Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North Holland, Amsterdam (1983)

    Google Scholar 

  26. Thiele, H.: Fuzzy Rough Sets versus Rough Fuzzy Sets — An Interpretation and a Comparative Study using Concepts of Modal Logics. Proceedings of European Congress of Intelligent Techniques and Soft Computing EUFIT-97, Aachen, Germany (1997) 159–167

    Google Scholar 

  27. Turunen, E.: Mathematics Behind Fuzzy Logics. Physica—Verlag (1999)

    Google Scholar 

  28. Vakarelov, D.: A modal logic for similarity relations in Pawlak knowledge representation systems. Fundamenta Informaticae 15 (1991) 61–79

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Radzikowska, A.M., Kerre, E.E. (2003). A Fuzzy Generalisation of Information Relations. In: Fitting, M., Orłowska, E. (eds) Beyond Two: Theory and Applications of Multiple-Valued Logic. Studies in Fuzziness and Soft Computing, vol 114. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1769-0_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-1769-0_13

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2522-0

  • Online ISBN: 978-3-7908-1769-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics