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International Conference on Rough Sets and Knowledge Technology

RSKT 2006: Rough Sets and Knowledge Technology pp 200–207Cite as

Rough Sets and Brouwer-Zadeh Lattices

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4062))

Abstract

Many researchers study rough sets from the point of view of description of the rough set pairs (a rough set pair is also called a rough set), i.e. <lower approximation set, upper approximation set>. In this paper, it is showed that the collection of all the rough sets in an approximation space can be made into a distributive Brouwer-Zadeh lattice. The induced Brouwer-Zadeh lattice from an approximation space is called the rough Brouwer-Zadeh lattice. The rough top equation and rough bottom equation problem is studied in the framework of rough Brouwer-Zadeh lattices.

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References

  1. Pawlak, Z.: Rough Sets-Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  2. Lin, T.Y., Liu, Q.: Rough approximate operators: axiomatic rough set theory. In: Ziarko, W.P. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, pp. 256–260. Springer, Heidelberg (1994)

    Google Scholar 

  3. Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. Information Sciences 109, 21–47 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Zhu, W., Wang, F.Y.: Reduction and axiomization of covering generalized rough sets. Information Sciences 152, 217–230 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Düntsch, I.: Rough relation algebras. Fundamenta Informace 21, 321–331 (1994)

    MATH  Google Scholar 

  6. Düntsch, I.: Rough sets and algebra of relations. In: Orlowska, E. (ed.) Incomplete Information: Rough Set Analysis, pp. 95–108. Physica-Verlag, Herdelberg (1998)

    Google Scholar 

  7. Cattaneo, G., Giuntini, R., Pilla, R.: BZMVdM algebras and stonian MV-algebras. Fuzzy Sets and Systems 108, 201–222 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Cattaneo, G., Ciucci, D.: Heyting Wajsberg algebras as an abstract enviroment linking fuzzy and rough sets. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 77–84. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  9. Jarvinen, J.: On the structure of rough approximations. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 123–130. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Dai, J.H.: Structure of rough approximations based on molecular lattices. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 69–77. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  11. Iwiński, T.B.: Algebraic approach to rough sets. Bulletin of the Polish Academy of Sciences: Mathematics 35, 673–683 (1987)

    MATH  MathSciNet  Google Scholar 

  12. Pomykala, J., Pomykala, J.A.: The Stone algebra of rough sets. Bulletin of the Polish Academy of Sciences: Mathematics 36, 495–508 (1988)

    MATH  MathSciNet  Google Scholar 

  13. Gehrke, M., Walker, E.: On the structure of rough sets. Bulletin of the Polish Academy of Sciences: Mathematics 40, 235–255 (1992)

    MATH  MathSciNet  Google Scholar 

  14. Comer, S.: On connections between information systems, rough sets and algebraic logic. In: Rauszer, C. (ed.) Algebraic Methods in Logic and Computer Science, pp. 117–124. Banach Center Publications, Warsaw (1993)

    Google Scholar 

  15. Pagliani, P.: Rough sets and Nelson algebras. Fundamenta Informaticae 27, 205–219 (1996)

    MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  17. Iturrioz, L.: Rough sets and 3-valued structures. In: Orlowska, E. (ed.) Logic at Work, pp. 596–603. Springer, Heidelberg (1998)

    Google Scholar 

  18. Pagliani, P.: Rough set theory and logic-algebraic structures. In: Orlowska, E. (ed.) Incomplete Information: Rough Set Analysis, pp. 109–190. Physica-Verlag, Herdberg (1998)

    Google Scholar 

  19. Dai, J.H., Pan, Y.H.: On rough algebras (in Chinese). Journal of Software 16, 1197–1204 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  20. Dai, J.H.: Logic for rough sets with rough double Stone algebraic semantics. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 141–148. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Artificial Intelligence, Zhejiang University, Hangzhou, 310027, P.R. China

    Jianhua Dai, Weidong Chen & Yunhe Pan

Authors
  1. Jianhua Dai
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  2. Weidong Chen
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  3. Yunhe Pan
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Editor information

Editors and Affiliations

  1. College of Computer Science and Technology, Chongqing, University of Posts and Telecommunication, 400065, Chongqing, P.R. China

    Guo-Ying Wang

  2. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

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

    Andrzej Skowron

  4. Department of Computer Science, University of Regina, Regina,, S4S 0A2, Saskatchewan, Canada

    Yiyu Yao

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© 2006 Springer-Verlag Berlin Heidelberg

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Dai, J., Chen, W., Pan, Y. (2006). Rough Sets and Brouwer-Zadeh Lattices. In: Wang, GY., Peters, J.F., Skowron, A., Yao, Y. (eds) Rough Sets and Knowledge Technology. RSKT 2006. Lecture Notes in Computer Science(), vol 4062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11795131_29

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  • DOI: https://doi.org/10.1007/11795131_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36297-5

  • Online ISBN: 978-3-540-36299-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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