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Journal of Applied Mathematics
Volume 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.

Citations to this Article [18 citations]

The following is the list of published articles that have cited the current article.

  • Qiu Jin, and Lingqiang Li, “On the embedding of convex spaces in stratified L-convex spaces,” SpringerPlus, vol. 5, no. 1, 2016. View at Publisher · View at Google Scholar
  • Bin Pang, and Fu-Gui Shi, “Subcategories of the category of L-convex spaces,” Fuzzy Sets and Systems, 2016. View at Publisher · View at Google Scholar
  • Fugui Shi, and Erqiang Li, “The restricted hull operator of M-fuzzifying convex structures,” Journal Of Intelligent & Fuzzy Systems, vol. 30, no. 1, pp. 409–421, 2016. View at Publisher · View at Google Scholar
  • Xiu-Yun Wu, and Shi-Zhong Bai, “On M-fuzzifying JHC convex structures and M-fuzzifying Peano interval spaces,” Journal Of Intelligent & Fuzzy Systems, vol. 30, no. 4, pp. 2447–2458, 2016. View at Publisher · View at Google Scholar
  • Bin Pang, Yi Zhao, and Zhen-Yu Xiu, “A new definition of order relation for the introduction of algebraic fuzzy closure operators,” International Journal of Approximate Reasoning, 2017. View at Publisher · View at Google Scholar
  • Bin Pang, and Zhen-Yu Xiu, “Lattice-valued interval operators and its induced lattice-valued convex structures,” IEEE Transactions on Fuzzy Systems, 2017. View at Publisher · View at Google Scholar
  • Zhen-Yu Xiu, and Bin Pang, “M-fuzzifying cotopological spaces and M-fuzzifying convex spaces as M-fuzzifying closure spaces,” Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 613–620, 2017. View at Publisher · View at Google Scholar
  • Xiu-Yun Wu, B. Davvaz, and S.Z. Bai, “On M-fuzzifying convex matroids and M-fuzzifying independent structures,” Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 269–280, 2017. View at Publisher · View at Google Scholar
  • Xiu-Yun Wu, Er-Qiang Li, and Shi-Zhong Bai, “Geometric properties of M-fuzzifying convex structures,” Journal of Intelligent & Fuzzy Systems, vol. 32, no. 6, pp. 4273–4284, 2017. View at Publisher · View at Google Scholar
  • Xiu-Yun Wu, and Shi-Zhong Bai, “M-fuzzifying gated amalgamations of M-fuzzifying geometric interval spaces,” Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 4017–4029, 2017. View at Publisher · View at Google Scholar
  • Lingqiang Li, “On the category of enriched (L, M)-convex spaces,” Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3209–3216, 2017. View at Publisher · View at Google Scholar
  • Yu Zhong, and Fu-Gui Shi, “Formulations of L-convex hulls on some algebraic structures,” Journal of Intelligent and Fuzzy Systems, vol. 33, no. 3, pp. 1385–1395, 2017. View at Publisher · View at Google Scholar
  • Yu Zhong, Shao-Jun Yang, and Fu-Gui Shi, “The relationship between L-subuniverses and L-convexities,” Journal of Intelligent and Fuzzy Systems, vol. 33, no. 6, pp. 3363–3372, 2017. View at Publisher · View at Google Scholar
  • Chengyu Liang, and Fanghui Li, “A degree approach to separation axioms in M-fuzzifying convex spaces,” Journal of Intelligent & Fuzzy Systems, pp. 1–9, 2018. View at Publisher · View at Google Scholar
  • Zhen-Yu Xiu, and Bin Pang, “A degree approach to special mappings between M-fuzzifying convex spaces,” Journal of Intelligent & Fuzzy Systems, pp. 1–12, 2018. View at Publisher · View at Google Scholar
  • Erqiang Li, and Fu-Gui Shi, “Some properties of M -fuzzifying convexities induced by M -orders,” Fuzzy Sets and Systems, 2018. View at Publisher · View at Google Scholar
  • Bin Pang, and Fu-Gui Shi, “Fuzzy counterparts of hull operators and interval operators in the framework of L -convex spaces,” Fuzzy Sets and Systems, 2018. View at Publisher · View at Google Scholar
  • Fan-Hong Chen, Chong Shen, and Fu-Gui Shi, “A new approach to the fuzzification of arity, JHC and CUP of L-convexities,” Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 221–231, 2018. View at Publisher · View at Google Scholar