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A Characterization of Rough Separability

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Rough Sets and Knowledge Technology (RSKT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7414))

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Abstract

Rough separability in topology is discussed by its connections with pseudometric spaces and rough sets. Pseudometric spaces are presented from the point of view of their connections with approximation spaces. A special way of determining equivalence relations by pseudometric spaces is considered and open sets in pseudometric spaces are studied. Investigations focus on the class of pseudometric spaces which are lower bounded in each point since open sets in these spaces coincide with definable sets of some prescribed approximation spaces. It is also shown that all equivalence and non transitive tolerance relations can be determined by pseudometric spaces in specified ways.

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References

  1. Bazan, J.: Hierarchical Classifiers for Complex Spatio-temporal Concepts. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 474–750. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. Demri, S., Orłowska, E.: Incomplete Information: Structures, Inference, Complexity. Springer (2002)

    Google Scholar 

  3. Engelking, R.: General Topology. PWN (1977)

    Google Scholar 

  4. Jankowski, J., Skowron, A.: Wisdom Technology: A Rough-Granular Approach. In: Marciniak, M., Mykowiecka, A. (eds.) Bolc Festschrift. LNCS, vol. 5070, pp. 3–41. Springer, Heidelberg (2009)

    Google Scholar 

  5. Kopelberg, S.: General theory of Boolean algebras. In: Monk, J.D., Bonnet, R. (eds.) Handbook of Boolean Algebras. North Holland (1989)

    Google Scholar 

  6. Kuratowski, K.: Wstęp do teorii mnogości i topologii. PWN (1980)

    Google Scholar 

  7. Orłowska, E., Pawlak, Z.: Representation of nondeterministic information. Theoretical Computer Science 29, 27–39 (1984)

    Article  MathSciNet  Google Scholar 

  8. Pawlak, Z.: Information Systems – theoretical foundation. Information Systems 6, 205–218 (1981)

    Article  MATH  Google Scholar 

  9. Pawlak, Z.: Rough sets. International Journal of Computing and Information Sciences 18, 341–356 (1982)

    Article  MathSciNet  Google Scholar 

  10. Pawlak, Z.: Rough sets. Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers (1991)

    Google Scholar 

  11. Pawlak, Z.: Some Issues on Rough Sets. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 1–58. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Science 177, 3–27 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Peters, J.F.: Near sets. Special theory about nearness of objects. Fundamenta Informaticae 73, 1–27 (2006)

    MathSciNet  Google Scholar 

  14. Peters, J.F., Wasilewski, P.: Foundations of near sets. Elsevier Science 179(18), 3091–3109 (2009)

    MathSciNet  MATH  Google Scholar 

  15. Polkowski, L.: Rough Sets: Mathematical Foundations. Physica-Verlag (2002)

    Google Scholar 

  16. Skowron, A.: Rough sets and vague concepts. Fundamenta Informaticae 64(1-4), 417–431 (2005)

    MathSciNet  MATH  Google Scholar 

  17. Skowron, A., Wasilewski, P.: An Introduction to Perception Based Computing. In: Kim, T.-H., Lee, Y.-H., Kang, B.-H., Ślęzak, D. (eds.) FGIT 2010. LNCS, vol. 6485, pp. 12–25. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  18. Skowron, A., Wasilewski, P.: Information systems in modeling interactive computations on granules. Theoretical Computer Science 412(42), 5939–5959 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Skowron, A., Wasilewski, P.: Toward interactive rough–granular computing. Control & Cybernetics 40(2), 1–23 (2011)

    Google Scholar 

  20. Ślęzak, D., Wasilewski, P.: Granular Sets – Foundations and Case Study of Tolerance Spaces. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 435–442. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  21. Wasilewski, P.: Dependency and supervenience. In: Proc. of the Concurrency, Specification and Programming, CS & P 2003. Warsaw Univerity (2003)

    Google Scholar 

  22. Wasilewski, P.: On selected similarity relations and their applications into cognitive science. Unpublished doctoral dissertation, Jagiellonian University: Department of Logic, Cracow, Poland (2004) (in Polish)

    Google Scholar 

  23. Wasilewski, P.: Concept Lattices vs. Approximation Spaces. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005, Part I. LNCS (LNAI), vol. 3641, pp. 114–123. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  24. Wasilewski, P.: Indiscernibility relations (in preparation)

    Google Scholar 

  25. Wasilewski, P., Peters, J., Ramanna, S.: Perceptual Tolerance Intersection. In: Peters, J.F., Skowron, A., Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) Transactions on Rough Sets XIII. LNCS, vol. 6499, pp. 159–174. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  26. Wasilewski, P.: Pseudometric Spaces from Rough Sets Perspective. In: Skowron, A., Suraj, Z. (eds.) Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam. ISRL, vol. 43, pp. 581–604. Springer, Heidelberg (2012)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Informatics, The University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Piotr Wasilewski

  2. Institute of Mathematics, The University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

Authors
  1. Piotr Wasilewski
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  2. Andrzej Skowron
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Editor information

Editors and Affiliations

  1. School of Information Science and Technology, Southwest Jiaotong University, 610031, Chengdu, P.R. China

    Tianrui Li

  2. Institute of Mathematics, The University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland

    Hung Son Nguyen

  3. Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, 400065, Chongqing, China

    Guoyin Wang

  4. Department of Electrical Engineering and Computer Science, University of Kansas, 66045 - 7621, Lawrence, KS, USA

    Jerzy Grzymala-Busse

  5. Department of Computing and Software, McMaster University, L8S 4K1, Hamilton, Ontario, Canada

    Ryszard Janicki

  6. Faculty of Computers and Information, Cairo University, Cairo, Egypt

    Aboul Ella Hassanien

  7. Software School, Dalian University of Technology, Dalian, China

    Hong Yu

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© 2012 Springer-Verlag Berlin Heidelberg

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Wasilewski, P., Skowron, A. (2012). A Characterization of Rough Separability. In: Li, T., et al. Rough Sets and Knowledge Technology. RSKT 2012. Lecture Notes in Computer Science(), vol 7414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31900-6_1

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  • DOI: https://doi.org/10.1007/978-3-642-31900-6_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31899-3

  • Online ISBN: 978-3-642-31900-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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