Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 836137, 9 pages
http://dx.doi.org/10.1155/2014/836137
Research Article

Attribute Extended Algorithm of Lattice-Valued Concept Lattice Based on Congener Formal Context

1School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
2Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, China

Received 9 April 2014; Revised 9 June 2014; Accepted 11 June 2014; Published 30 June 2014

Academic Editor: Ker-Wei Yu

Copyright © 2014 Li Yang and Yang Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Birkhoff, Lattice Theory: American Mathematical Society Colloquium Publications Volume XXV, American Mathematical Society, Providence, RI, USA, 1967.
  2. R. Wille, “Restructuring lattice theory: an approach based on hierarchies of concepts. I,” in Ordered Sets (Banff, Alta., 1981), I. Rival, Ed., vol. 83 of NATO Advanced Study Institute Series C: Mathematical and Physical Sciences, pp. 445–470, Reidel, Dordrecht, The Netherlands, 1982. View at Google Scholar · View at MathSciNet
  3. B. Ganter and R. Wille, Formal Concept Analysis: Mathematical Foundations, Springer, Berlin, Germany, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. Bělohlávek, V. Sklenář, and J. Zacpal, “Crisply generated fuzzy concepts,” in Proceedings of the 3rd International Conference on Formal Concept Analysis (ICFCA '05), Lecture Notes in Artificial Intelligence, pp. 269–284, February 2005. View at Scopus
  5. W. X. Zhang, Y. Y. Yao, and Y. Liang, Rough Set and Concept Lattice, Xi’an Jiaotong University Press, Xi’an, China, 2006.
  6. M. Shao, M. Liu, and W. Zhang, “Set approximations in fuzzy formal concept analysis,” Fuzzy Sets and Systems, vol. 158, no. 23, pp. 2627–2640, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. M. H. Hu, L. Zhang, and F. L. Ren, “Fuzzy formal concept analysis and fuzzy concept lattices,” Journal of Northeastern University (Natural Science), vol. 28, no. 9, pp. 1274–1277, 2007. View at Google Scholar · View at MathSciNet · View at Scopus
  8. J. Z. Pang, X. Y. Zhang, and W. H. Xu, “Attribute reduction in intuitionistic fuzzy concept lattices,” Abstract and Applied Analysis, vol. 2013, Article ID 271398, 12 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  9. P. Butka, J. Pocs, and J. Pocsova, “Representation of fuzzy concept lattices in the framework of classical FCA,” Journal of Applied Mathematics, vol. 2013, Article ID 236725, 7 pages, 2013. View at Publisher · View at Google Scholar
  10. L. Yang and Y. Xu, “Decision making with uncertainty information based on lattice-valued fuzzy concept lattice,” Journal of Universal Computer Science, vol. 16, no. 1, pp. 159–177, 2010. View at Google Scholar · View at MathSciNet · View at Scopus
  11. L. Yang and Y. Xu, “A decision method based on uncertainty reasoning of linguistic truth-valued concept lattice,” International Journal of General Systems, vol. 39, no. 3, pp. 235–253, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. L. Yang, Y. H. Wang, and Y. Xu, “A combination algorithm of multiple lattice-valued concept lattices,” International Journal of Computational Intelligence Systems, vol. 6, no. 5, pp. 881–892, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Xu, “Lattice implication algebras,” Journal of Southwest Jiaotong University, vol. 289, pp. 20–27, 1993 (Chinese). View at Google Scholar
  14. Y. Xu, D. Ruan, K. Qin, and J. Liu, Lattice-Valued Logic-An Alternative Approach to Treat Fuzziness and Incomparability, vol. 132, Springer, Berlin, Germany, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  15. Y. Xu, S. Chen, and J. Ma, “Linguistic truth-valued lattice implication algebra and its properties,” in Proceedings of the IMACS Multiconference on Computational Engineering in Systems Applications (CESA '06), pp. 1413–1418, Beijing, China, October 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. Y. Li and Z. T. Liu, “Theoretical research on the distributed construction of concept lattices,” in Proceedings of the 2nd International Conference on Machine Learning and Cybernetics, pp. 474–479, Xian, China, 2003.
  17. R. Xie, Z. Pei, and C. L. He, “Reconstructing algorithm of concept lattice in adding attribute process,” Journal of Systems Engineering, vol. 22, no. 4, pp. 426–431, 2007. View at Google Scholar
  18. Y. Li, Z. T. Liu, L. C. Chen, X. H. Xu, and W. C. Cheng, “Horizontal union algorithm of multiple concept lattices,” Acta Electronica Sinica, vol. 32, no. 11, pp. 1849–1854, 2004. View at Google Scholar · View at Scopus
  19. L. Zhang, X. J. Shen, D. J. Han et al., “Vertical union algorithm of concept lattices based on synonymous concept,” Computer Engineering and Applications, vol. 43, no. 2, pp. 95–98, 2007. View at Google Scholar
  20. M. Liu, M. Shao, W. Zhang, and C. Wu, “Reduction method for concept lattices based on rough set theory and its application,” Computers & Mathematics with Applications, vol. 53, no. 9, pp. 1390–1410, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. X. Wang and W. X. Zhang, “Relations of attribute reduction between object and property oriented concept lattices,” Knowledge-Based Systems, vol. 21, no. 5, pp. 398–403, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. S. Y. Zhao and E. C. C. Tsang, “On fuzzy approximation operators in attribute reduction with fuzzy rough sets,” Information Sciences, vol. 178, no. 16, pp. 3163–3176, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus