Rough Sets - Past, Present and Future: Some Notes

  • Piero PaglianiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9436)


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


  1. 1.
    Balbes, R., Dwinger, P.: Distributive Lattices. University of Missouri Press, Columbia (1974)zbMATHGoogle Scholar
  2. 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. 3.
    Ciucci, D., Dubois, D.: Three-valued logics, uncertainty management and rough sets. Trans. Rough Sets 17, 1–32 (2014)zbMATHGoogle Scholar
  4. 4.
    Gabbay, D.M.: Labelled Deductive Systems. Oxford University Press, Oxford (1997)zbMATHGoogle Scholar
  5. 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)CrossRefGoogle Scholar
  6. 6.
    Iwinski, T.B.: Algebraic approach to rough sets. Bull. Pol. Acad. Sci. Math. 35(3–4), 673–683 (1987)MathSciNetzbMATHGoogle Scholar
  7. 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)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Järvinen, J., Radeleczki, S.: Representation of Nelson algebras by rough sets determined by quasiorders. Algebra Univers. 66, 163–179 (2011)MathSciNetCrossRefGoogle Scholar
  9. 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) CrossRefGoogle Scholar
  10. 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) CrossRefGoogle Scholar
  11. 11.
    Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: Formal concept analysis via multiadjoint concept lattices. Fuzzy Sets Syst. 160(2), 130–144 (2009)CrossRefGoogle Scholar
  12. 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)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Nagarajan, E.K.R., Umadevi, D.: A method of representing rough sets system determined by quasi orders. Order 30(1), 313–337 (2013)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Orłowska, E.: Logic for nondeterministic information. Stud. Logica 44, 93–102 (1985)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Pagliani, P.: Remarks on special lattices and related constructive logics with strong negation. Notre Dame J. Formal Logic 31, 515–528 (1990)MathSciNetCrossRefGoogle Scholar
  16. 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. 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 1996Google Scholar
  18. 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)MathSciNetCrossRefGoogle Scholar
  19. 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)CrossRefGoogle Scholar
  20. 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. 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 1998Google Scholar
  22. 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. 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. 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)CrossRefGoogle Scholar
  25. 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. 26.
    Pagliani P.: Covering-based rough sets and formal topology. A uniform approach (To appear in Transactions of Rough Sets) (2014)Google Scholar
  27. 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 2005Google Scholar
  28. 28.
    Pagliani, P., Chakraborty, M.: A geometry of approximation. Trends in Logic. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  29. 29.
    Qian, Y., Liang, J., Yao, Y., Dang, C.: MGRS: a multi-granulation rough set. Inf. Sci. 180(6), 949–970 (2010)MathSciNetCrossRefGoogle Scholar
  30. 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) CrossRefGoogle Scholar
  31. 31.
    Reyes, G.E., Zolfaghari, N.: Bi-Heyting algebras, toposes and modalities. J. Philos. Logic 25, 25–43 (1996)MathSciNetCrossRefGoogle Scholar
  32. 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. 33.
    Sendlewski, A.: Nelson algebras through Heyting ones: I. Stud. Logica 49(1), 105–126 (1990)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Sette, A.M.: On the propositional calculus \(P^1\). Math. Japonicae 18, 173–180 (1973)MathSciNetzbMATHGoogle Scholar
  35. 35.
    Sette, A.M., Carnielli, W.A.: Maximal weakly-intuitionistic logics. Stud. Logica 55, 181–203 (1995)MathSciNetCrossRefGoogle Scholar
  36. 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)CrossRefGoogle Scholar
  37. 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)MathSciNetzbMATHGoogle Scholar
  38. 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. 39.
    Wansing, H.: The Logic of Information Structures. Springer, Berlin (1993)CrossRefGoogle Scholar
  40. 40.
    Wille, R.: Restructuring lattice theory. In: Rival, I. (ed.) Ordered Sets. NATO ASI Series 83, Reidel, pp. 445–470 (1982)Google Scholar
  41. 41.
    Yao, Y.Y.: The two sides of the theory of rough sets. Knowl.-Based Syst. 80, 67–77 (2015)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.RomeItaly

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