Skip to main content

Pawlak’s Landscaping with Rough Sets

  • Chapter
Transactions on Rough Sets VI

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 4374))

Abstract

This paper reviews, rather non-technically, Pawlak’s approach to vagueness through rough sets and looks for a foundation of rough sets in an early work of Obtułowicz. An extension of Obtułowicz’s proposal is suggested that in turn, hints at a unified approach to rough sets and fuzzy sets.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Banerjee, M.: A Categorial Approach to the Algebra and Logic of the Indiscernible. Ph.D Thesis, University of Calcutta (1993)

    Google Scholar 

  2. Banerjee, M., Chakraborty, M.K.: Rough sets through algebraic logic. Fundamenta Informaticae 28(3-4), 211–221 (1996)

    MATH  MathSciNet  Google Scholar 

  3. Banerjee, M., Chakraborty, M.K.: Foundations of vagueness: a category-theoretic approach. Electronic Notes in Theoretical Computer Science 82(4) (2003)

    Google Scholar 

  4. Chakraborty, M.K., Banerjee, M.: Rough consequence. Bulletin of the Polish Academy of Sciences (Mathematics) 41(4), 299–304 (1993)

    MATH  MathSciNet  Google Scholar 

  5. Chakraborty, M.K., Orłowska, E.: Substitutivity principles in some theories of uncertainty. Fundamenta Informaticae 32, 107–120 (1997)

    MATH  MathSciNet  Google Scholar 

  6. Chakraborty, M.K., Basu, S.: Graded consequence and some metalogical notions generalized. Fundamenta Informaticae 32, 299–311 (1997)

    MATH  MathSciNet  Google Scholar 

  7. Chakraborty, M.K., Basu, S.: Approximate reasoning methods in vagueness: graded and rough consequences. ICS Research Report 29, Warsaw University of Technology (1995)

    Google Scholar 

  8. Demri, S., Orłowska, E. (eds.): Incomplete Information: Structure, Inference, Complexity. Monographs in Theoretical Computer Science. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  9. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. In: Proc. International Conference on Fuzzy Sets in Informatics, Moscow, pp. 20–23 (1988)

    Google Scholar 

  10. Eytan, M.: Fuzzy sets: a topos-logical point of view. Fuzzy Sets and Systems 5, 47–67 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  11. Goguen, J.: Concept representation in natural and artificial languages: axioms, extensions and applications for fuzzy sets. International Journal for Man-Machine Studies 6, 513–561 (1975)

    Article  MathSciNet  Google Scholar 

  12. Higgs, D.: A categorical approach to Boolean-valued set theory. Preprint (1973)

    Google Scholar 

  13. Hyde, D.: From heaps and gaps to heaps of gluts. Mind 106, 440–460 (1997)

    Article  Google Scholar 

  14. Jacas, J.: On the generators of T-indistinguishability operator. Stochastica XIII, 49–63 (1988)

    MathSciNet  Google Scholar 

  15. Keefe, R.: Theories of Vagueness, Cambridge Studies in Philosophy, Cambridge, UK (2000)

    Google Scholar 

  16. Keefe, R., Smith, P. (eds.): Vagueness: A Reader. MIT Press, Cambridge (1997)

    Google Scholar 

  17. Keikeben, F. (2000), http://members.aol.com/kiekeben/theseus.html

  18. Obtułowicz, A.: Rough sets and Heyting algebra valued sets. Bulletin of the Polish Academy of Sciences (Mathematics) 13(9-10), 667–671 (1987)

    Google Scholar 

  19. Orłowska, E., Pawlak, Z.: Representation of non-deterministic information. Theoretical Computer Science 29, 27–39 (1984)

    Article  MathSciNet  Google Scholar 

  20. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  21. Pawlak, Z.: Some issues on rough sets. In: Peters, J.F., et al. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 1–58. Springer, Heidelberg (2004)

    Google Scholar 

  22. Pawlak, Z.: A treatise on rough sets. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets IV. LNCS, vol. 3700, pp. 1–17. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Pawlak, Z.: Rough sets and fuzzy sets. Fuzzy Sets and Systems 17, 99–102 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  24. Pawlak, Z.: Rough logic. Bulletin of the Polish Academy of Sciences (Technical Sciences) 35(5-6), 253–258 (1987)

    MATH  MathSciNet  Google Scholar 

  25. Pawlak, Z.: Hard and soft sets. ICS Research Report, 10/94, Warsaw University of Technology (1994)

    Google Scholar 

  26. Pawlak, Z.: Vagueness – a rough set view. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds.) Structures in Logic and Computer Science. LNCS, vol. 1261, pp. 106–117. Springer, Heidelberg (1997)

    Google Scholar 

  27. Pawlak, Z.: Vagueness and uncertainty: a rough set perspective. Computational Intelligence: An International Journal 11, 217–232 (1995)

    MathSciNet  Google Scholar 

  28. Pawlak, Z.: Rough sets, present state and further prospects. ICS Research Report, 15/19, Warsaw University of Technology (1995)

    Google Scholar 

  29. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Sciences, to appear.

    Google Scholar 

  30. Pawlak, Z., Skowron, A.: Rough sets: some extensions. Information Sciences, to appear.

    Google Scholar 

  31. Pawlak, Z., Skowron, A.: Rough sets and Boolean reasoning, Information Sciences, to appear.

    Google Scholar 

  32. Priest, G., Routley, R.: First historical introduction: a preliminary history of paraconsistent and dialethic approaches. In: Priest, G., Routley, R., Normann, J. (eds.) Paraconsistent Logic, Essays on the Inconsistent, pp. 1–75. Philosophia Verlag, München (1989)

    Google Scholar 

  33. Polkowski, L.: Rough Sets: Mathematical Foundations. Advances in Soft Computing. Physica Verlag, Heidelberg (2002)

    MATH  Google Scholar 

  34. Pultr, A.: Fuzziness and fuzzy equality. In: Skala, H.J., Termini, S., Trillas, E. (eds.) Aspects of Vagueness, pp. 119–135. D. Reidel Publishing Co., Dordrecht (1984)

    Google Scholar 

  35. Raju, P.T.: The principle of four-coloured negation in Indian philosophy. Review of Metaphysics 7, 694–713 (1953)

    Google Scholar 

  36. Rasiowa, H., Skowron, A.: Rough concepts logic in computation theory. In: Skowron, A. (ed.) Computation Theory. LNCS, vol. 208, pp. 288–297. Springer, Heidelberg (1985)

    Google Scholar 

  37. Russell, B.: Vagueness. Australian Journal of Philosophy 1, 84–92 (1923)

    Article  Google Scholar 

  38. Skowron, A.: The relationship between the rough set theory and evidence theory. Bulletin of the Polish Academy of Sciences (Technical Sciences) 37(1-2), 87–90 (1989)

    Google Scholar 

  39. Skowron, A.: Rough sets and vague concepts. Fundamenta Informaticae 64, 417–431 (2005)

    MATH  MathSciNet  Google Scholar 

  40. Skowron, A., Grzymała-Busse, J.W.: From rough set theory to evidence theory. In: Yager, R.R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer Theory of Evidence, pp. 193–236. John Wiley & Sons, New York (1994)

    Google Scholar 

  41. Trillas, E., Valverde, L.: An inquiry into indistinguishability operators. In: Skala, H.J., Termini, S., Trillas, E. (eds.) Aspects of Vagueness, pp. 231–256. D. Reidel Publishing Co., Dordrecht (1984)

    Google Scholar 

  42. Wang, H.: Beyond Analytic Philosophy. MIT Press, Cambridge (1986)

    Google Scholar 

  43. Wiggins, D.: Sameness and Substance, pp. 92–94. Blackwell, Oxford (1980)

    Google Scholar 

  44. Wygralak, M.: Some remarks on rough and fuzzy sets. BUSEFAL 21, 43–49 (1985)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

James F. Peters Andrzej Skowron Ivo Düntsch Jerzy Grzymała-Busse Ewa Orłowska Lech Polkowski

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this chapter

Cite this chapter

Chakraborty, M.K. (2007). Pawlak’s Landscaping with Rough Sets. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J., Orłowska, E., Polkowski, L. (eds) Transactions on Rough Sets VI. Lecture Notes in Computer Science, vol 4374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71200-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-71200-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71198-8

  • Online ISBN: 978-3-540-71200-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics