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International Conference on Fuzzy Systems and Knowledge Discovery

FSKD 2006: Fuzzy Systems and Knowledge Discovery pp 276–285Cite as

Binary Relation Based Rough Sets

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4223))

Abstract

Rough set theory has been proposed by Pawlak as a tool for dealing with the vagueness and granularity in information systems. The core concepts of classical rough sets are lower and upper approximations based on equivalence relations. This paper studies arbitrary binary relation based generalized rough sets. In this setting, a binary relation can generate a lower approximation operation and an upper approximation operation. We prove that such a binary relation is unique, since two different binary relations will generate two different lower approximation operations and two different upper approximation operations. This paper also explores the relationships between the lower or upper approximation operation generated by the intersection of two binary relations and those generated by these two binary relations, respectively.

The first author is in part supported by the New Economy Research Fund of New Zealand and this work is also in part supported by two 973 projects (2004CB318103) and (2002CB312200) from the Ministry of Science and Technology of China.

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References

  1. Angiulli, F., Pizzuti, C.: Outlier mining in large high-dimensional data sets. IEEE Trans. on Knowledge and Data Engineering 17, 203–215 (2005)

    Article  Google Scholar 

  2. Bonikowski, Z., Bryniarski, E., Wybraniec-Skardowska, U.: Extensions and intentions in the rough set theory. Information Sciences 107, 149–167 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cattaneo, G., Ciucci, D.: Algebraic structures for rough sets. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds.) Transactions on Rough Sets II. LNCS, vol. 3135, pp. 208–252. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Dai, J.: 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. 141–147. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Dong, G., Han, J., Lam, J., Pei, J., Wang, K., Zou, W.: Mining constrained gradients in large databases. IEEE Trans. on Knowledge and Data Engineering 16, 922–938 (2004)

    Article  Google Scholar 

  6. Hall, M., Holmes, G.: Benchmarking attribute selection techniques for discrete class data mining. IEEE Trans. on Knowledge and Data Engineering 15, 1437–1447 (2003)

    Article  Google Scholar 

  7. Hu, F., Wang, G., Huang, H., et al.: Incremental attribute reduction based on elementary sets. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 185–193. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Jensen, R., Shen, Q.: Semantics-preserving dimensionality reduction: Rough and fuzzy-rough-based approaches. IEEE Trans. on Knowledge and Data Engineerin 16, 1457–1471 (2004)

    Article  Google Scholar 

  9. Kondo, M.: On the structure of generalized rough sets. Information Sciences 176, 589–600 (2005)

    Article  MathSciNet  Google Scholar 

  10. Kryszkiewicza, M.: Rough set approach to incomplte information systems. Information Sciences 112, 39–49 (1998)

    Article  MathSciNet  Google Scholar 

  11. Kryszkiewicza, M.: Rule in incomplte information systems. Information Sciences 113, 271–292 (1998)

    Article  Google Scholar 

  12. Leung, Y., Wu, W.Z., Zhang, W.X.: Knowledge acquisition in incomplete information systems: A rough set approach. European Journal of Operational Research 168, 164–180 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Li, D.G., Miao, D.Q., Yin, Y.Q.: Relation of relative reduct based on nested decision granularity. In: IEEE GrC 2006, pp. 397–400 (2006)

    Google Scholar 

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

    Google Scholar 

  15. Liu, Q.: Semantic analysis of rough logical formulas based on granular computing. In: IEEE GrC 2006, pp. 393–396 (2006)

    Google Scholar 

  16. Liu, G.: The transitive closures of matrices over distributive lattices. In: IEEE GrC 2006, pp. 63–66 (2006)

    Google Scholar 

  17. Pal, S., Mitra, P.: Case generation using rough sets with fuzzy representation. IEEE Trans. on Knowledge and Data Engineering 16, 292–300 (2004)

    Article  Google Scholar 

  18. Pawlak, Z.: Rough sets: Theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston (1991)

    MATH  Google Scholar 

  19. Polkowski, L., Skowron, A. (eds.): RSCTC 1998. LNCS (LNAI), vol. 1424. Springer, Heidelberg (1998)

    MATH  Google Scholar 

  20. Polkowski, L., Skowron, A. (eds.): Rough sets in knowledge discovery, vol. 1. Physica–Verlag, Heidelberg (1998)

    Google Scholar 

  21. Polkowski, L., Skowron, A. (eds.): Rough sets in knowledge discovery, vol. 2. Physica–Verlag, Heidelberg (1998)

    Google Scholar 

  22. Qin, K., Pei, Z., Du, W.: The relationship among several knowledge reduction approaches. In: Wang, L., Jin, Y. (eds.) FSKD 2005. LNCS (LNAI), vol. 3613, pp. 1232–1241. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Qin, K., Pei, Z.: On the topological properties of fuzzy rough sets. Fuzzy Sets and Systems 151, 601–613 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  24. Rajagopal, P., Masone, J.: Discrete Mathematics for Computer Science, Saunders College, Canada (1992)

    Google Scholar 

  25. Slowinski, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Trans. on Knowledge and Data Engineering 12, 331–336 (2000)

    Article  Google Scholar 

  26. Su, C., Hsu, J.: An extended chi2 algorithm for discretization of real value attributes. IEEE Trans. on Knowledge and Data Engineering 17, 437–441 (2005)

    Article  Google Scholar 

  27. Wang, F.Y.: Outline of a computational theory for linguistic dynamic systems: Toward computing with words. International Journal of Intelligent Control and Systems 2, 211–224 (1998)

    Google Scholar 

  28. Wang, F.Y.: On the abstraction of conventional dynamic systems: from numerical analysis to linguistic analysis. Information Sciences 171, 233–259 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  29. Wang, G., Liu, F.: The inconsistency in rough set based rule generation. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 370–377. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  30. Wu, W.Z., Zhang, W.X.: Rough set approximations vs. measurable spaces. In: IEEE GrC 2006, pp. 329–332 (2006)

    Google Scholar 

  31. Wu, W.Z., Leung, Y., Mi, J.S.: On characterizations of (i, t) -fuzzy rough approximation operators. Fuzzy Sets and Systems 154, 76–102 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  32. Wu, W.Z., Zhang, W.X.: Constructive and axiomatic approaches of fuzzy approximation operator. Information Sciences 159, 233–254 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  33. Yang, X.P., Li, T.J.: The minimization of axiom sets characterizing generalized approximation operators. Information Sciences 176, 887–899 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  34. Yao, J., Liu, W.N.: The STP model for solving imprecise problems. In: IEEE GrC 2006, pp. 683–687 (2006)

    Google Scholar 

  35. Yao, Y.: A comparative study of fuzzy sets and rough sets. Information Sciences 109, 227–242 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  36. Yao, Y.: On generalizing pawlak approximation operators. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 298–307. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  37. Yao, Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 101, 239–259 (1998)

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  39. Yao, Y., Chen, Y.: Subsystem based generalizations of rough set approximations. In: Hacid, M.-S., Murray, N.V., Raś, Z.W., Tsumoto, S. (eds.) ISMIS 2005. LNCS (LNAI), vol. 3488, pp. 210–218. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  40. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  41. Zadeh, L.: The concept of a linguistic variable and its application to approximate reasoning – I. Information Sciences 8, 199–249 (1975)

    Article  MathSciNet  Google Scholar 

  42. Zadeh, L.: The concept of a linguistic variable and its application to approximate reasoning – II. Information Sciences 8, 301–357 (1975)

    Article  MathSciNet  Google Scholar 

  43. Zadeh, L.: The concept of a linguistic variable and its application to approximate reasoning – III. Information Sciences 9, 43–80 (1975)

    Article  MathSciNet  Google Scholar 

  44. Zadeh, L.: Fuzzy logic = computing with words. IEEE Transactions on Fuzzy Systems 4, 103–111 (1996)

    Article  Google Scholar 

  45. Zhong, N., Yao, Y., Ohshima, M.: Peculiarity oriented multidatabase mining. IEEE Trans. on Knowledge and Data Engineering 15, 952–960 (2003)

    Article  Google Scholar 

  46. Zhu, F., He, H.C.: The axiomization of the rough set. Chinese Journal of Computers 23, 330–333 (2000)

    MathSciNet  Google Scholar 

  47. Zhu, F., He, H.C.: Logical properties of rough sets. In: Proc. of the Fourth International Conference on High Performance Computing in the Asia-Pacific Region, vol. 2, pp. 670–671. IEEE Press, Los Alamitos (2000)

    Chapter  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  49. Zhu, W., Wang, F.Y.: A new type of covering rough sets. In: IEEE IS 2006, September 4-6 (to appear, 2006)

    Google Scholar 

  50. Zhu, W., Wang, F.Y.: Relationships among three types of covering rough sets. In: IEEE GrC 2006, pp. 43–48 (2006)

    Google Scholar 

  51. Zhu, W., Wang, F.Y.: Axiomatic systems of generalized rough sets. In: Wang, G.-Y., Peters, J.F., Skowron, A., Yao, Y. (eds.) RSKT 2006. LNCS (LNAI), vol. 4062, pp. 216–221. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  52. Zhu, W., Wang, F.Y.: Covering based granular computing for conflict analysis. In: Mehrotra, S., Zeng, D.D., Chen, H., Thuraisingham, B., Wang, F.-Y. (eds.) ISI 2006. LNCS, vol. 3975, pp. 566–571. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. The Key Laboratory of Complex Systems and Intelligent Science, Institute of Automation, The Chinese Academy of Sciences, Beijing, 100080, China

    William Zhu & Fei-Yue Wang

  2. Department of Computer Science, University of Auckland, Auckland, New Zealand

    William Zhu

  3. Computer Information Engineering College, Jiangxi Normal University, China

    William Zhu

  4. Systems and Industrial Engineering Department, The University of Arizona, Tucson, AZ, 85721, USA

    Fei-Yue Wang

Authors
  1. William Zhu
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  2. Fei-Yue Wang
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Editor information

Editors and Affiliations

  1. School of Electrical and Electronic Engineering, Nanyang Technological University,, Block S1, Nanyang Avenue, 639798, Singapore

    Lipo Wang

  2. Life Science Research Center, School of Electronic Engineering, Xidian University,, 710071, Xi’an, Shaanxi, China

    Licheng Jiao

  3. School of Electrical and Electronic Engineering, Xidian University, 710071, Xi’an, China

    Guanming Shi

  4. School of Information Technology and Electrical Engineering, The University of Queensland, 4072, Brisbane, Queensland, Australia

    Xue Li

  5. College of Mathematics and Information Science, Hebei Normal University, 050016, Shijiazhuang, Hebei, P.R. China

    Jing Liu

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Zhu, W., Wang, FY. (2006). Binary Relation Based Rough Sets. In: Wang, L., Jiao, L., Shi, G., Li, X., Liu, J. (eds) Fuzzy Systems and Knowledge Discovery. FSKD 2006. Lecture Notes in Computer Science(), vol 4223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11881599_31

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  • DOI: https://doi.org/10.1007/11881599_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45916-3

  • Online ISBN: 978-3-540-45917-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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