Document Type: Research Paper


School of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China


In this paper, the notion of $L$-convex fuzzy sublattices is introduced and their characterizations are given. Furthermore,  the notion of the degree to which an $L$-subset is an $L$-convex fuzzy sublattice is proposed and its some  characterizations are given. Besides, the $L$-convex fuzzy sublattice degrees of the homomorphic image and pre-image of an $L$-subset are studied. Finally, we obtain an $L$-fuzzy convexity, which is induced by the $L$-convex fuzzy sublattice degrees, in the sense of Shi and Xiu.


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