Classes of Discrete Convexity Properties

In the general first-level classification of theconvexity properties for sets, discrete convexities appearin moreclasses. A second-level classification identifies more subclasses containingdiscrete convexity properties, which appear as approximations either of classical convexity or of fuzzy convexity.First, we prove that all these convexity concepts are defined by segmental methods. The typeof segmental method involved in the construction of discrete convexitydetermines the subclass to which it belongs. The subclasses containing theconvexity properties that have discrete particular cases are also presented.