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Rough Fuzzy Set Approximations in Fuzzy Formal Contexts

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Rough Sets and Current Trends in Computing (RSCTC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4259))

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Abstract

In the paper, we introduce a new kind of fuzzy formal concept derived from an adjoint pair of operations. Based on the discussed fuzzy formal concepts, a pair of rough fuzzy set approximations in fuzzy formal contexts is introduced. The properties of the proposed approximation operators are examined in details.

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References

  1. Belohlavek, R.: Lattices of fixed points of fuzzy Galois connections. Math. Logic Quaterly 47, 111–116 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Belohlavek, R.: Fuzzy closure operators. I. J. Math. Anal. Appl. 262, 473–489 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Belohlavek, R.: Concept lattice and order in fuzzy logic. Annals of pure and Apll. Logic 128(1-3), 277–298 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Burusco, A., Fuentes-Gonzalez, R.: Construction of the L-Fuzzy concept lattice. Fuzzy Sets and systems 97, 109–114 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  5. Burusco, A., Fuentes-Gonzalez, R.: Concept lattices defined from implication operators. Fuzzy Sets and systems 114(3), 431–436 (1998)

    Article  MathSciNet  Google Scholar 

  6. Dubois, D., Prade, H.: Twofold fuzzy sets and rough sets-some issuess in knowledge representation. Fuzzy sets and Systems 23, 3–18 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gediga, G., Wille, R.: Formal Concept Analysis. Mathematic Foundations. Springer, Berlin (1999)

    Google Scholar 

  8. Gediga, G., Duntsch, I.: Modal-style operators in qualitative data analysis. In: Proceedings of the 2002 IEEE International Conference on Data Mining, pp. 155–162 (2002)

    Google Scholar 

  9. Georgescu, G., Popescu, A.: Non-dual fuzzy connections. Archive for Mathematic Logic 43(8), 1009–1039 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Hu, K., Sui, Y., Lu, Y.-c., Wang, J., Shi, C.-Y.: Concept approximation in concept lattice. In: Cheung, D., Williams, G.J., Li, Q. (eds.) PAKDD 2001. LNCS, vol. 2035, pp. 167–173. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. Kent, R.E.: Rough concept analysis: a synthesis of rough sets and formal concept analysis. Fundamenta Informaticae 27, 169–181 (1996)

    MATH  MathSciNet  Google Scholar 

  12. Morsi, N.N., Yakout, M.M.: Axiomatics for fuzzy rough sets. Fuzzy sets and Systems 100, 327–342 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  13. Pawlak, Z.: Rough sets. International Journal of Computer and Information Science 11, 341–356 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  14. Popescu, A.: A general approach to fuzzy concept. Math. Logic Quaterly 50(3), 1–17 (2001)

    Google Scholar 

  15. Radzikowska, A.M., Kerre, E.E.: A comparative study of fuzzy rough sets. Fuzzy sets and Systems 126, 137–155 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  16. Saquer, J., Deogun, J.S.: Formal rough concept analysis. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS, vol. 1711, pp. 91–99. Springer, Berlin (1999)

    Chapter  Google Scholar 

  17. Shao, M.W., Zhang, W.X.: The Set Approximation in Formal Contexts. In: Ślęzak, D., et al. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 43–53. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. Shao, M.W., Zhang, W.X.: Rough set approximations in fuzzy concept lattices (2005) (manuscript)

    Google Scholar 

  19. Wang, G.J.: Non-Classical Mathematical Logic and Approximate. Science Press, Beijing (2000)

    Google Scholar 

  20. Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel, Dordrecht (1982)

    Google Scholar 

  21. Wolff, K.E.: A conceptual view of knowledge bases in rough set theory. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS, vol. 2005, pp. 220–228. Springer, Berlin (2001)

    Chapter  Google Scholar 

  22. Wu, W.Z., Mi, J.S., Zhang, W.X.: Generalized fuzzy rough sets. Information Sciences 151, 263–282 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  23. Yao, Y.Y.: Concept lattices in rough set theory. In: Proceedings of 2004 Annual Meeting of the North American Fuzzy Information Processing Society, pp. 796–801 (2004)

    Google Scholar 

  24. Yao, Y.Y.: A Comparative Study of Formal Concept Analysis and Rough Set Theory in Data Analysis. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS, vol. 3066, pp. 59–68. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  26. Yao, Y.Y., Chen, Y.: Rough set approximations in formal concept analysis. In: Proceedings of 2004 Annual Meeting of the North American Fuzzy Information Processing Society, pp. 73–78 (2004)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Automation, Tsinghua University, Beijing, 100084, China

    Ming-Wen Shao & Min Liu

  2. School of Information Technology, Jiangxi University of Finance & Economics, Nanchang, Jiangxi, 330013, P.R. China

    Ming-Wen Shao

  3. Faculty of Science, Xi’an Jiaotong University, Xi’an, Shaan’xi, 710049, China

    Wen-Xiu Zhang

Authors
  1. Ming-Wen Shao
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  2. Min Liu
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  3. Wen-Xiu Zhang
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco

  2. Graduate School of Engineering, Department of Electrical Engineering and Computer Sciences, University of Hyogo, 2167 Shosha, 671-2280,, Himeji, Hyogo, Japan

    Yutaka Hata

  3. Department of Medical Informatics, Faculty of Medicine, Shimane University, 89-1 Enya-cho, Izumo, 693-8501, Shimane, Japan

    Shoji Hirano

  4. Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Masahiro Inuiguchi

  5. Department of Risk Engineering, School of Systems and Information Engineering, University of Tsukuba, 305-8573, Ibaraki, Japan

    Sadaaki Miyamoto

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

    Hung Son Nguyen

  7. Systems Research Institute, Polish Academy of Sciences, 01-447, Warsaw, Poland

    Roman Słowiński

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© 2006 Springer-Verlag Berlin Heidelberg

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Shao, MW., Liu, M., Zhang, WX. (2006). Rough Fuzzy Set Approximations in Fuzzy Formal Contexts. In: Greco, S., et al. Rough Sets and Current Trends in Computing. RSCTC 2006. Lecture Notes in Computer Science(), vol 4259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11908029_16

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  • DOI: https://doi.org/10.1007/11908029_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-47693-1

  • Online ISBN: 978-3-540-49842-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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