Degrees of fuzzy compactness in L-fuzzy topological spaces

In this paper, we introduce the notion of the degree of fuzzy compactness in L-fuzzy topological spaces by means of an inequality proposed by Shi in 2007. The notion is a generalization of the definition of fuzzy compactness in L-topological spaces. Some properties of this new notion are researched. The Tychonoff theorem is generalized. It is pointed out that our notion is not equivalent to other definition of degree of compactness.