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Lattice Structure of Variable Precision Rough Sets

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Thriving Rough Sets

Part of the book series: Studies in Computational Intelligence ((SCI,volume 708))

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Abstract

The main purpose of this chapter is to study the lattice structure of variable precision rough sets. The notion of variation in precision of rough sets have been further extended to variable precision rough set with variable classification error and its algebraic properties are also studied.

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References

  1. Pawłak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11(5), 341–356 (1982)

    Article  MATH  Google Scholar 

  2. Pawłak, Z.: Rough classification. Int. J. Man-Mach. Stud. 20(5), 469–483 (1984)

    Article  Google Scholar 

  3. Basu, S.: Rough finite-state machine. Cybern. Syst. 36, 107–124 (2005)

    Article  MATH  Google Scholar 

  4. Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27(2–3), 245–253 (1996)

    MathSciNet  MATH  Google Scholar 

  5. Slowinski, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Trans. Knowl. Data Eng. 12(2), 331–336 (2000)

    Article  Google Scholar 

  6. Yao, Y.Y.: On generalizing Pawłak approximation operators. In: Rough Sets and Current Trends in Computing. Lecture Notes in Computer Science, vol. 1424, pp. 298–307. Springer, Berlin, Germany (1998)

    Google Scholar 

  7. Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Inf. Sci. 111(14), 239–259 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  8. Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. Inf. Sci. 109(14), 21–47 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhu, W., Wang, F.: A new type of covering rough sets. In: Proceedings of the IEEE International Conference on Intelligent Systems, pp. 444–449. London, UK, Sept 2006

    Google Scholar 

  10. Zhu, W.: Basic concepts in covering-based rough sets. In: Proceedings of the 3rd International Conference on Natural Computation (ICNC 07), pp. 283–286, Aug 2007

    Google Scholar 

  11. Wang, S., Zhu, P., Zhu, W.: Structure of covering-based rough sets. Int. J. Math. Comput. Sci. 6, 147–150 (2010)

    Google Scholar 

  12. Zhu, W.: Relationship among basic concepts in covering-based rough sets. Inf. Sci. 179(14), 2478–2486 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ziarko, W.: Variable precision rough set model. J. Comput. Syst. Sci. 46(1), 39–59 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhu, Y., Zhu, W.: A variable precision covering-based rough set model based on functions. Hindawi Publishing Corporation. Sci. World J. 2014, Article ID 210129, 5 pages

    Google Scholar 

  15. Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Inf. Sci. 179(3), 210–225 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang, C., Chen, D., Sun, B., Hu, Q.: Communication between information systems with covering based rough sets. Inf. Sci. 216, 17–33 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Banerjee, M., Chakraborty, M.K.: Rough sets through algebraic logic. Fundam. Inform. 28(3–4), 211–221 (1996)

    MathSciNet  MATH  Google Scholar 

  18. Pomykala, J., Pomykala, J.A.: The stone algebra of rough sets. Bull. Polish Acad. Sci. Math. 36(7–8), 495–508 (1988)

    MathSciNet  MATH  Google Scholar 

  19. Banerjee, M., Chakraborty, M.K.: Algebras from rough sets. In: Pal, S.K., Polkowski, L., Skowron, A. (eds.) Rough-Neural Computing—Techniques for Computing with Words. Springer, Heidelberg (preprint)

    Google Scholar 

  20. Cattaneo, G., Ciucci, D.: Lattices with interior and closure operators and abstract approximation spaces. In: Peters, J.F., Skowron, A., Wolski, M., Chakraborty, M.K., Wu, W.-Z. (eds.) Transactions on Rough Sets X. LNCS, vol. 5656, pp. 67–116. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Jarvinen, J.: Lattice theory for rough sets. In: Transactions on Rough Sets VI. Series Lecture Notes in Computer Science, vol. 4374, pp. 400–498

    Google Scholar 

  22. Samanta, P., Chakraborty, M.K.: Generalized rough sets and implication lattice. In: Transactions on Rough Sets XIV, pp. 183–201

    Google Scholar 

  23. Katzberg, J., Ziarko, W.: Variable precision rough sets with asymmetric bounds. In: Rough Sets, Fuzzy Sets and Knowledge Discovery, pp. 167–177. Springer (1994)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Bethune College, 181, Bidhan Sarani, Kolkata, 700006, India

    Sumita Basu

Authors
  1. Sumita Basu
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Correspondence to Sumita Basu .

Editor information

Editors and Affiliations

  1. Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

  2. Institute of Mathematics, University of Warsaw Institute of Mathematics, Warsaw, Poland

    Andrzej Skowron

  3. University of Regina, Department of Computer Science University of Regina, Regina, Saskatchewan, Canada

    Yiyu Yao

  4. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. Polish-Japanese Academy IT , Warsaw, Poland

    Lech Polkowski

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Basu, S. (2017). Lattice Structure of Variable Precision Rough Sets. In: Wang, G., Skowron, A., Yao, Y., Ślęzak, D., Polkowski, L. (eds) Thriving Rough Sets. Studies in Computational Intelligence, vol 708. Springer, Cham. https://doi.org/10.1007/978-3-319-54966-8_17

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  • DOI: https://doi.org/10.1007/978-3-319-54966-8_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54965-1

  • Online ISBN: 978-3-319-54966-8

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