Characterizations and properties of bounded $L$-fuzzy sets

In 1997, Fang proposed the concept of boundedness of $L$-fuzzy sets in $L$-topological vector spaces. Since then, this concept has been widely accepted and adopted in the literature. In this paper, several characterizations of bounded $L$-fuzzy sets in $L$-topological vector spaces are obtained and some properties of bounded $L$-fuzzy sets are investigated.