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Classes of Discrete Convexity Properties

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Abstract

In the general first-level classification of the convexity properties for sets, 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. First, we prove that all these convexity concepts are defined by segmental methods. The type of segmental method involved in the construction of discrete convexity determines the subclass to which it belongs. The subclasses containing the convexity properties that have discrete particular cases are also presented.

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Correspondence to Gabriela Cristescu or Liana Lupsa.

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Cristescu, G., Lupsa, L. Classes of Discrete Convexity Properties. Discrete Comput Geom 31, 461–490 (2004). https://doi.org/10.1007/s00454-003-2877-x

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Keywords

  • Convexity Property
  • Segmental Method
  • Classical Convexity
  • Discrete Convexity
  • Fuzzy Convexity