Kybernetika 46 no. 3, 501-512, 2010

Maximal solutions of two-sided linear systems in max-min algebra

Pavel Krbálek and Alena Pozdílková


Max-min algebra and its various aspects have been intensively studied by many authors \cite{Baccelli,Green79} because of its applicability to various areas, such as fuzzy system, knowledge management and others. Binary operations of addition and multiplication of real numbers used in classical linear algebra are replaced in max-min algebra by operations of maximum and minimum. We consider two-sided systems of max-min linear equations \begin{math}\emph{A}\otimes\emph{x}= B\otimes\emph{x}\end{math}, with given coefficient matrices \emph{A} and \emph{B}. We present a polynomial method for finding maximal solutions to such systems, and also when only solutions with prescribed lower and upper bounds are sought.


two-sided linear systems, lower bound, upper bound, max-min algebra


15A06, 15A24