Affiliations:
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, PR China
Correspondence:
[*]
Corresponding author. Bin Zhao, College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, PR China. Tel.: +86 29 85310085; Fax: +86 29 85310097; E-mail: zhaobin@snnu.edu.cn.
Note: [1] The research is supported by the National Natural Science Foundation of China (Grant Nos. 11531009, 11301316) and the Fundamental Research Funds for the Central Universities (GK 201501001)
Abstract: In this paper, based on a complete residuated lattice, we introduce the concept of fuzzy cut-stable maps and discuss the relationship between fuzzy cut-stable maps and some special maps. We also obtain the extension property of fuzzy cut-stable maps. Furthermore, it is proved that the category of fuzzy complete (continuous) lattices with fuzzy complete homomorphisms is a full reflective subcategory of the category of fuzzy (precontinuous) posets with fuzzy cut-stable maps.
