A degree approach to fuzzy convexity in vector subspaces

Abstract

Based on a completely distributive lattice L, the degree to which an
L-subset in a vector space is an L-fuzzy subspace is introduced via the implication operation on L. By using four kinds of cut sets, several characterizations of L-fuzzy subspace degree are given. Further, it is shown that the L-fuzzy subspace degree of a vector space can induce an L-fuzzy convexity in a natural way and the linear mappings between vector spaces are L-fuzzy convexity-preserving and L-fuzzy convex-to-convex mappings between the induced L-fuzzy convex spaces.