Kybernetika 46 no. 3, 548-557, 2010

On hyperplanes and semispaces in max-min convex geometry

Viorel Nitica and Sergeĭ Sergeev


The concept of separation by hyperplanes and halfspaces is fundamental for convex geometry and its tropical (max-plus) analogue. However, analogous separation results in max-min convex geometry are based on semispaces. This paper answers the question which semispaces are hyperplanes and when it is possible to "classically'' separate by hyperplanes in max-min convex geometry.


tropical convexity, fuzzy algebra, separation


52A01, 52A30, 08A72