%0 Journal Article
%T Duality and interval analysis over idempotent semirings
%A T. Brunsch
%A L. Hardouin
%A J. Raisch
%A C. A. Maia
%J Mathematics
%D 2013
%I arXiv
%R 10.1016/j.laa.2012.06.025
%X In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose of this paper is to consider a dual product, denoted $\odot$, and the dual residuation of matrices, in order to solve the following inequality $ A \otimes X \preceq X \preceq B \odot X$. Sufficient conditions ensuring the existence of a non-linear projector in the solution set are proposed. The results are extended to semirings of intervals.
%U http://arxiv.org/abs/1306.1129v1