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The notion of near compactness degrees is introduced in L-topological spaces by means of the implication operator of L. An L-set G is near compact if and only if its near compactness degree NCD(G) = T. Some properties of near compactness degrees are investigated.
The notion of almost compactness degrees is introduced in L-topological spaces by means of the implication operator "→" of L. An L-set G is almost compact if and only if its almost compactness degree ACD(G) = T. Some properties of almost compactness degrees are investigated.
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...
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