A New Perspective on L-Fuzzy Ideals in MV-Algebras

In this paper, we investigate some properties of L-fuzzy ideals in MV-algebras from a new perspective by taking the completely distributive lattice L as the lattice-valued context. Firstly, we introduce the notion of the L-fuzzy ideal degree in an MV-algebra, which can illustrate the extent to which an L-fuzzy subset qualifies as an L-fuzzy ideal. Secondly, we further use four kinds of cut sets to characterize the L-fuzzy ideal degree. Furthermore, we show that the L-fuzzy ideal degree is precisely an L-fuzzy convex structure in an MV-algebra and discuss its related properties. Finally, we demonstrate that the collection of all L-fuzzy ideals in an MV-algebra forms an L-convex structure and present its L-convex hull formula.