BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES

Authors

  • Bin Pang School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R.China
  • Zhen-Yu Xiu College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, P.R.China
Abstract:

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbases can be used to characterize CP mappings and CC mappings between $M$-fuzzifying convex spaces.

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Journal title

volume 15  issue 2

pages  75- 87

publication date 2018-04-29

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