Skip to main content
SpringerLink
Log in

Rough Sets - Past, Present and Future: Some Notes

  • Conference paper
  • First Online:
Rough Sets and Knowledge Technology (RSKT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9436))

Included in the following conference series:

  • 1050 Accesses

Abstract

Some notes about the state-of-the-art of Rough Set Theory are discussed, and some future research topics are suggested as well.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Notes

  1. 1.

    In the examples there are some typos. I shall email the corrections upon request.

  2. 2.

    If \(R\subseteq W\times W'\) and \(Z\subseteq :U\times U'\), then \(R\longrightarrow Z=-(R^{\smile }\otimes -Z)\) (this operation is defined if \(|W|=|U|\)), and \(Z\longleftarrow R=-(-Z\otimes R^{\smile })\) (this operation is defined if \(|W^{\prime }|=|U^{\prime }|\)), where \(``-Z'' \) is the Boolean complement of Z and \(R^\smile \) is the reverse relation of R.

  3. 3.

    If \(R\subseteq X\times Y\) the right cylindrification of \(A\subseteq X\) is the relation \(A\times Y\). Notice that the relational formula of est is symmetric to the formula of (lZ). The reason is discussed in [21].

References

  1. Balbes, R., Dwinger, P.: Distributive Lattices. University of Missouri Press, Columbia (1974)

    MATH  Google Scholar 

  2. Carnielli, W.A., Marques, M.L.: Society semantics and multiple-valued logics. In: Carnielli W.A., D’Ottaviano, I. (Eds.): Contemporary Mathematics, vol. 235, pp. 149–163. American Mathematical Society (1999)

    Google Scholar 

  3. Ciucci, D., Dubois, D.: Three-valued logics, uncertainty management and rough sets. Trans. Rough Sets 17, 1–32 (2014)

    MATH  Google Scholar 

  4. Gabbay, D.M.: Labelled Deductive Systems. Oxford University Press, Oxford (1997)

    MATH  Google Scholar 

  5. Greco, S., Matarazzo, B., Slowinski, R.: Algebra and topology for dominance-based rough set approach. In: Ras, Z.W., Tsay, L.-S. (eds.) Advanced in Intelligent Information Systems. SCI, vol. 265, pp. 43–78. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  6. Iwinski, T.B.: Algebraic approach to rough sets. Bull. Pol. Acad. Sci. Math. 35(3–4), 673–683 (1987)

    MathSciNet  MATH  Google Scholar 

  7. Järvinen, J., Pagliani, P., Radeleczki, S.: Information completeness in Nelson algebras of rough sets induced by quasiorders. Stud. Logica 101(5), 1073–1092 (2013)

    Article  MathSciNet  Google Scholar 

  8. Järvinen, J., Radeleczki, S.: Representation of Nelson algebras by rough sets determined by quasiorders. Algebra Univers. 66, 163–179 (2011)

    Article  MathSciNet  Google Scholar 

  9. Khan, M.A., Banerjee, M.: A study of multiple-source approximation systems. In: Peters, J.F., Skowron, A., Słowiński, R., Lingras, P., Miao, D., Tsumoto, S. (eds.) Transactions on Rough Sets XII. LNCS, vol. 6190, pp. 46–75. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Lehmann, F., Wille, R.: A triadic approach to formal concept analysis. In: Ellis, G., Rich, W., Levinson, R., Sowa, J.F. (eds.) ICCS 1995. LNCS, vol. 954, pp. 32–43. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  11. Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: Formal concept analysis via multiadjoint concept lattices. Fuzzy Sets Syst. 160(2), 130–144 (2009)

    Article  Google Scholar 

  12. Miglioli, P.A., Moscato, U., Ornaghi, M., Usberti, U.: A constructivism based on classical truth. Notre Dame J. Formal logic 30(1), 67–90 (1989)

    Article  MathSciNet  Google Scholar 

  13. Nagarajan, E.K.R., Umadevi, D.: A method of representing rough sets system determined by quasi orders. Order 30(1), 313–337 (2013)

    Article  MathSciNet  Google Scholar 

  14. Orłowska, E.: Logic for nondeterministic information. Stud. Logica 44, 93–102 (1985)

    Article  MathSciNet  Google Scholar 

  15. Pagliani, P.: Remarks on special lattices and related constructive logics with strong negation. Notre Dame J. Formal Logic 31, 515–528 (1990)

    Article  MathSciNet  Google Scholar 

  16. Pagliani, P.: A pure logic-algebraic analysis on rough top and rough bottom equalities. In: Ziarko, W.P. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery. Workshops in Computing, pp. 225–236. Springer, Heidelberg (1994)

    Google Scholar 

  17. Pagliani, P.: A modal relation algebra for generalized approximation spaces. In: Tsumoto, S., Kobayashi, S., Yokomori, T., Tanaka, H., Nakamura, A. (eds.) Proceedings of the 4th International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery. The University of Tokyo, Japan, Invited Section “Logic and Algebra”, pp. 89–96, 6–8 November 1996

    Google Scholar 

  18. Pagliani, P.: From information gaps to communication needs: a new semantic foundation for some non-classical logics. J. Logic Lang. Inf. 6(1), 63–99 (1997)

    Article  MathSciNet  Google Scholar 

  19. Pagliani, P.: Rough set systems and logic-algebraic structures. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis. STUDFUZZ, vol. 13, pp. 109–190. Physica-Verlag, Heidelberg (1997)

    Chapter  Google Scholar 

  20. Pagliani, P.: A practical introduction to the modal relational approach to approximation spaces. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1, pp. 209–232. Physica-Verlag, Heidelberg (1998)

    Google Scholar 

  21. Pagliani P.: Modalizing relations by means of relations: a general framework for two basic approaches to knowledge discovery in database. In: Gevers, M. (ed.) Proceedings of the 7th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU ’98. Paris, France, pp. 1175–1182. Editions E.D.K., 6–10 July 1998

    Google Scholar 

  22. Pagliani, P.: Local classical behaviours in three-valued logics and connected systems. An information-oriented analysis. 1 and 2. Journal of Multiple-valued Logics 5, 6, pp. 327–347, 369–392 (2000, 2001)

    Google Scholar 

  23. Pagliani, P.: Pretopology and dynamic spaces. In: Proceedings of RSFSGRC’03, Chongqing, R.P. China, 2003. Extended version in Fundamenta Informaticae, vol. 59(2–3), pp. 221–239 (2004)

    Google Scholar 

  24. Pagliani, P.: Rough sets and other mathematics: ten research programs. In: Chakraborty, M.K., Skovron, A., Maiti, M., Kar, S. (eds.) Facets of Uncertainties and Applications. Springer Proceedings in Mathematics & Statistics, vol. 125, pp. 3–15. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  25. Pagliani, P.: The relational construction of conceptual patterns - tools, implementation and theory. In: Kryszkiewicz, M., Cornelis, C., Ciucci, D., Medina-Moreno, J., Motoda, H., Raś, Z.W. (eds.) RSEISP 2014. LNCS, vol. 8537, pp. 14–27. Springer, Heidelberg (2014)

    Google Scholar 

  26. Pagliani P.: Covering-based rough sets and formal topology. A uniform approach (To appear in Transactions of Rough Sets) (2014)

    Google Scholar 

  27. Pagliani P., Chakraborty M.K.: Information quanta and approximation spaces. I: Non-classical approximation operators. In: Proceedings of the IEEE International Conference on Granular Computing, Beijing, R.P. China, Vol. 2, pp. 605–610. IEEE Los Alamitos, 25–27 July 2005

    Google Scholar 

  28. Pagliani, P., Chakraborty, M.: A geometry of approximation. Trends in Logic. Springer, Heidelberg (2008)

    Book  Google Scholar 

  29. Qian, Y., Liang, J., Yao, Y., Dang, C.: MGRS: a multi-granulation rough set. Inf. Sci. 180(6), 949–970 (2010)

    Article  MathSciNet  Google Scholar 

  30. Rauszer, C.M.: Rough logic for multi-agent systems. In: Masuch, M., Polos, L. (eds.) Logic at Work 1992. LNCS, vol. 808, pp. 161–181. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  31. Reyes, G.E., Zolfaghari, N.: Bi-Heyting algebras, toposes and modalities. J. Philos. Logic 25, 25–43 (1996)

    Article  MathSciNet  Google Scholar 

  32. Sambin, G.: Intuitionistic formal spaces and their neighbourhood. In: Ferro, R., Bonotto, C., Valentini, S., Zanardo, A. (eds.) Logic Colloquium ’88, pp. 261–285. North-Holland, Elsevier (1989)

    Google Scholar 

  33. Sendlewski, A.: Nelson algebras through Heyting ones: I. Stud. Logica 49(1), 105–126 (1990)

    Article  MathSciNet  Google Scholar 

  34. Sette, A.M.: On the propositional calculus \(P^1\). Math. Japonicae 18, 173–180 (1973)

    MathSciNet  MATH  Google Scholar 

  35. Sette, A.M., Carnielli, W.A.: Maximal weakly-intuitionistic logics. Stud. Logica 55, 181–203 (1995)

    Article  MathSciNet  Google Scholar 

  36. Skowron, A., Stepaniuk, J.: Approximation of relations. In: Ziarko, W.P. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery. Workshops in Computing, pp. 161–166. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  37. Skowron, A., Stepaniuk, J., Peters, J.F.: Rough sets and infomorphisms: towards approximation of relations in distributed environments. Fundam. Informaticae 54, 263–277 (2003)

    MathSciNet  MATH  Google Scholar 

  38. Spinks, M., Veroff, R.: Constructive logic with strong negation is a substructural logic - I and II. Studia Logica 88, 89, 325–348, 401–425 (2008)

    Google Scholar 

  39. Wansing, H.: The Logic of Information Structures. Springer, Berlin (1993)

    Book  Google Scholar 

  40. Wille, R.: Restructuring lattice theory. In: Rival, I. (ed.) Ordered Sets. NATO ASI Series 83, Reidel, pp. 445–470 (1982)

    Google Scholar 

  41. Yao, Y.Y.: The two sides of the theory of rough sets. Knowl.-Based Syst. 80, 67–77 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rome, Italy

    Piero Pagliani

Authors
  1. Piero Pagliani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Piero Pagliani .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milano, Italy

    Davide Ciucci

  2. Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

  3. Indian Statistical Institute, Kolkata, India

    Sushmita Mitra

  4. Zhejiang Ocean University, Zhejiang, China

    Wei-Zhi Wu

Rights and permissions

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (http://creativecommons.org/licenses/by-nc/2.5/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Pagliani, P. (2015). Rough Sets - Past, Present and Future: Some Notes. In: Ciucci, D., Wang, G., Mitra, S., Wu, WZ. (eds) Rough Sets and Knowledge Technology. RSKT 2015. Lecture Notes in Computer Science(), vol 9436. Springer, Cham. https://doi.org/10.1007/978-3-319-25754-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25754-9_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25753-2

  • Online ISBN: 978-3-319-25754-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation