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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 249183, 12 pages
http://dx.doi.org/10.1155/2014/249183
Research Article

A New Approach to the Fuzzification of Convex Structures

School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Received 26 April 2014; Revised 19 June 2014; Accepted 27 June 2014; Published 31 August 2014

Academic Editor: Jin Liang

Copyright © 2014 Fu-Gui Shi and Zhen-Yu Xiu. 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. M. Berger, “Convexity,” The American Mathematical Monthly, vol. 97, no. 8, pp. 650–678, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. L. J. van de Vel, Theory of Convex Structures, North-Holland, New York, NY, USA, 1993. View at MathSciNet
  3. M. V. Rosa, “On fuzzy topology fuzzy convexity spaces and fuzzy local convexity,” Fuzzy Sets and Systems, vol. 62, no. 1, pp. 97–100, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. M. V. Rosa, A study of fuzzy convexity with special reference to separation properties [Ph.D. thesis], Cochin University of Science and Technology, 1994.
  5. Y. Maruyama, “Lattice-valued fuzzy convex geometry,” RIMS Kokyuroku, vol. 164, pp. 22–37, 2009. View at Google Scholar
  6. P. Dwinger, “Characterization of the complete homomorphic images of a completely distributive complete lattice I,” Indagationes Mathematicae, vol. 85, pp. 403–414, 1982. View at Google Scholar · View at MathSciNet · View at Scopus
  7. G. J. Wang, “Theory of topological molecular lattices,” Fuzzy Sets and Systems, vol. 47, no. 3, pp. 351–376, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. H. Huang and F. Shi, “L-fuzzy numbers and their properties,” Information Sciences, vol. 178, no. 4, pp. 1141–1151, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. C. V. Negoita and D. A. Ralescu, Applications of Fuzzy Sets to Systems Analysis, Birkhäuser, Basel, Switzerland; Stuttgart and Halsted Press, New York, NY, USA, 1975. View at MathSciNet
  10. F.-G. Shi, “Theory of Lβ-nested sets and Lα-nested sets and its applications,” Fuzzy Systems and Mathematics, vol. 4, pp. 65–72, 1995 (Chinese). View at Google Scholar
  11. F. G. Shi, “L-fuzzy sets and prime element nested sets,” Journal of Mathematical Research and Exposition, vol. 16, no. 3, pp. 398–402, 1996 (Chinese). View at Google Scholar · View at MathSciNet
  12. F.-G. Shi, “Theory of molecular nested sets and its applications,” Journal of Yantai Teachers University (Natural Science), vol. 1, pp. 33–36, 1996 (Chinese). View at Google Scholar
  13. F. Shi, “$L$-fuzzy relations and $L$-fuzzy subgroups,” Journal of Fuzzy Mathematics, vol. 8, no. 2, pp. 491–499, 2000. View at Google Scholar · View at MathSciNet
  14. W. Kubis, Abstract convex structures in topology and set theory [Ph.D. thesis], University of Silesia, Katowice, Poland, 1999.
  15. F.-G. Shi and B. Pang, “Categories isomorphic to the category of L-fuzzy closure system spaces,” Iranian Journal of Fuzzy Systems, vol. 10, no. 5, pp. 127–146, 2013. View at Google Scholar · View at MathSciNet
  16. M.-S. Ying, “A new approach for fuzzy topology (I),” Fuzzy Sets and Systems, vol. 39, no. 3, pp. 303–321, 1991. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. A. K. Katsaras and D. B. Liu, “Fuzzy vector spaces and fuzzy topological vector spaces,” Journal of Mathematical Analysis and Applications, vol. 58, no. 1, pp. 135–146, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. J. Fang and P. Chen, “One-to-one correspondence between fuzzifying topologies and fuzzy preorders,” Fuzzy Sets and Systems, vol. 158, no. 16, pp. 1814–1822, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus