Fuzzy closure operators and their applications

Fuzzy closure operators play a significant role in fuzzy order theory. This paper aims to further enrich and improve the study of fuzzy closure operators. Based on the work of Belohlávek and Yao, we shall continue to study the relative properties of fuzzy closure operators. First, we shall consider the extensions of $L$-subsets via fuzzy closure operators. Then we give an application of fuzzy closure operators, that is, by fuzzy closure operators we shall prove that the category CFPos of complete fuzzy posets and their fuzzy-join preserving maps is a reflective full subcategory of FPos, where FPos denotes the category of fuzzy posets and their fuzzy-existing-join preserving maps.