Classes of discrete convexity properties
In the general first-level classification of the convexity properties for sets [\textit{G. Cristescu} and \textit{L. Lupsa}, Bul. Stünt. Univ. Baia Mare, Ser. B 18, 23--30 (2002; Zbl 1036.52001)], discrete convexities appear in more classes. A second-level classification identifies more subclasses containing discrete convexity properties, which appear as approximations either of classical convexity or of fuzzy convexity. In this paper the authors prove that all these convexity concepts are defined by segmential methods. The subclasses containing the convexity properties that have discrete particular cases are also presented. Axiomatic convexities that allow the construction of various discrete models are not considered in this paper. The authors prefer to make a unifying systematic discussion of the discrete convexities that appear in various applications in integer programming or in pattern recognition for instance.
scientific article; zbMATH DE number 2123199