Skip to main content

Applications of Fuzzy-Rough Classifications to Logics

  • Chapter
Intelligent Decision Support

Part of the book series: Theory and Decision Library ((TDLD,volume 11))

Abstract

From a point of view of handling imperfect knowledge like uncertainty, vagueness, imprecision, etc., a concept of fuzzy-rough classifications is introduced. This is a notion defined as a kind of modification of the rough classifications. Two logics based on the fuzzy-rough classifications are proposed, and various properties are examined as compared with the indiscernibility relations. Also, decision procedures for the proposed logics are given in the tableau style which is useful in automated reasoning.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
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. D. Dubois and H. Prade: Rough fuzzy sets and fuzzy rough sets, Proc. of Internat. Conf. Fuzzy Sets in Informatics, Moscow, ( Sept. 1988 ), 20–23.

    Google Scholar 

  2. L. Farinas del Cerro and H. Prade: Rough sets, twofold fuzzy sets and modal logics. Fuzziness in indiscemibility and partial information, in: A.Di Nola and A.G. Ventre (ed.), The Math. of Fuzzy Systems, Verlag TÜV Rheinland, Köln, (1986), 103–120.

    Google Scholar 

  3. L. Farinas del Cerro and Andreas Herzig: A modal analysis of possibility theory, Lecture Notes in Computer Science,(Symbolic and Quantitative Approaches to Uncertainty), 548, 58–62.

    Google Scholar 

  4. G. Gargov: Two completeness theorems in the logic for data analysis ICS PAS Reports 581 Polish Academy of Sciences(1986)

    Google Scholar 

  5. G.E. Hughes and M. Cresswell: An introduction to modal logic, Methuen, London, 1968

    MATH  Google Scholar 

  6. M. Krynicki and H-P. Tuschik: An axiomatization of the logic with the rough quantifier J. of Symbolic Logic56, (1991), 608–617

    Google Scholar 

  7. A. Nakamura and J-M. Gao: A logic for fuzzy data analysis, Fuzzy Sets and Systems, 39, (1991), 127–132.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Nakamura: Topological soft algebra for the S5-modal fuzzy logic Proc. of the 21st ISMVL May 26–29 1991 Victoria80–84

    Google Scholar 

  9. A. Nakamura: A logic of imprecise monadic predicates and its relation to the S5-modal fuzzy logic, Lecture Notes in Computer Science,(Symbolic and Quantitative Approaches to Uncertainty), 548, 254–261.

    Google Scholar 

  10. E. Orlowska: Logic of indiscemibility relation Bulletin of the Polish Academy of Sciences Mathematics(1985), 475–485

    Google Scholar 

  11. Z. Pawlak: Rough sets International J. of Information and Computer Sciences 11(1982), 345–356

    Google Scholar 

  12. Z. Pawlak: Rough Sets, Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, 1991.

    MATH  Google Scholar 

  13. L.A. Zadeh: Fuzzy sets, Information and Control, 8, (1965), 338–353

    Article  MathSciNet  MATH  Google Scholar 

  14. L.A. Zadeh: Similarity relations and fuzzy orderings, Information Sciences, 3, (1971), 177–200.

    Article  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

© 1992 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Nakamura, A. (1992). Applications of Fuzzy-Rough Classifications to Logics. In: Słowiński, R. (eds) Intelligent Decision Support. Theory and Decision Library, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7975-9_15

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-7975-9_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4194-4

  • Online ISBN: 978-94-015-7975-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics