Iteration algorithm for solving Ax = b in max–min algebra Masoud Allame * , Behnaz Vatankhahan Department of Mathematics, Azad University, P.O. Box 81595-158, Khorasgan, Isfahan, Iran Abstract For solving the linear system A  x = b we introduce some iteration algorithms, where A =(a ij ) and b = b i a given matrix and a column vector with elements from a Brouwerian lattice, and  is a max–min composite operation. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Fuzzy membership matrix; Max–min algebra; Brouwerian lattice; Jacobs algorithm; Gauss–Seidel algorithm 1. Introduction In many applications, e.g. in fuzzy control systems, in discrete dynamic sys- tems, or in knowledge engineering, fuzzy relation equations play an important role. Application of systems of linear equations over structures different from the classical field were studied in the 1960s and in recent years have again received increasing attention as a tool for modeling discrete event systems or 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.07.028 * Corresponding author. E-mail addresses: masoudallame@yahoo.com (M. Allame), bvatankhahan@yahoo.com (B. Vatankhahan). Applied Mathematics and Computation 175 (2006) 269–276 www.elsevier.com/locate/amc