The L-fuzzy vector subspace degrees and its induced convex structure

This study aimed to investigate the degree to which an L-fuzzy subset of a vector space could be considered an L-fuzzy vector subspace. Characterizations of this relationship were provided, and a novel approach to the fuzzification of a vector space was introduced. In the case where L was a complete distributive lattice, an L-fuzzy convex structure was obtained using L-fuzzy vector subspace degrees, thereby forming an L-fuzzy convex space. Additionally, it was proved that a linear mapping between vector spaces precisely corresponded to an L-fuzzy convexity-preserving mappings and L-fuzzy convex-to-convex mappings.