On the dimension of max–min convex sets

Viorel Nitica, Sergey Sergeev

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Abstract

We introduce a notion of dimension of max–min convex sets, following the approach of tropical convexity. We introduce a max–min analogue of the tropical rank of a matrix and show that it is equal to the dimension of the associated polytope. We describe the relation between this rank and the notion of strong regularity in max–min algebra, which is traditionally defined in terms of unique solvability of linear systems and the trapezoidal property.
Original languageEnglish
Pages (from-to)88-101
JournalFuzzy Sets and Systems
Volume271
Early online date18 Oct 2014
DOIs
Publication statusPublished - 15 Jul 2015

Keywords

  • Max–min algebra
  • Dimension
  • Tropical convexity
  • Tropical rank
  • Strongly regular matrix

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