Xiu, Z., Pang, B. (2018). BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES. Iranian Journal of Fuzzy Systems, 15(2), 75-87. doi: 10.22111/ijfs.2018.3760

Zhen-Yu Xiu; Bin Pang. "BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES". Iranian Journal of Fuzzy Systems, 15, 2, 2018, 75-87. doi: 10.22111/ijfs.2018.3760

Xiu, Z., Pang, B. (2018). 'BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES', Iranian Journal of Fuzzy Systems, 15(2), pp. 75-87. doi: 10.22111/ijfs.2018.3760

Xiu, Z., Pang, B. BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES. Iranian Journal of Fuzzy Systems, 2018; 15(2): 75-87. doi: 10.22111/ijfs.2018.3760

BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES

^{1}College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, P.R.China

^{2}School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, 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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