Affiliations: [a] College of Science, North China University of Technology, Beijing 100144, P.R. China
| [b] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China
| [c]
The Second Middle School of Fengcheng, Jiangxi Province, P.R. China
Correspondence:
[*]
Corresponding author. Yu Zhong, E-mail: zhongyu@ncut.edu.cn. This work is supported by the National Natural Science Foundation of China (11871097, 11371002) and Specialized Research Fund for the Doctoral Program of Higher Education (20131101110048).
Abstract: In this paper, we introduce the degree to which a mapping
C:LX⟶M
is an (L, M)-fuzzy convexity. When
(X,CX)
and
(Y,CY)
are (L, M)-fuzzy convex spaces to some extent, the degrees to which a mapping f : X ⟶ Y is convexity-preserving or convex-to-convex are defined. Finally, the degree to which a surjective mapping f : X ⟶ Y is a quotient mapping is also defined. We not only give their characterizations but also discuss the relationships among them.
