In the modeling of human activities, in contrast to natural phenomena, quite frequently only the operations max (or min) and + are needed. A typical example is the performance evaluation of synchronized processes such as those encountered in manufacturing (dynamic systems made up of storage and queuing networks). Another typical example is the computation of a path of maximum weight in a graph ...

In this paper we consider sequences of consecutive powers of boolean matrices in the max-plus algebra, which is one of the frameworks that can be used to model certain classes of discrete event systems. The ultimate behavior of a sequence of consecutive max-plus-algebraic powers of a boolean matrix is cyclic. First we derive upper bounds for the length of the cycles as a function of the size of...

Max-plus linear systems belong to a special class of discrete-event systems that consists of systems with synchronization but no choice. Our focus in this paper is on stochastic max-plus linear systems, i.e., perturbed systems that are linear in the max-plus algebra. One interesting topic is the identification of such systems. Previous works report on a method for identifying the parameters of ...

we present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. first, we introduce a hyper bck-algebra induced by a max-min general fuzzy automaton. then, we study the properties of this hyper bck-algebra. particularly, some theorems and results for hyper bck-algebra are proved. for example, it is shown that this structure consists of different ty...

Abstract: Discrete event systems involving synchronization and delay phenomena can be described by a linear state representation over (max,+) algebra. Some discrete event systems involving choice phenomena could be transformed, under some conditions, into switching max-plus linear systems modeled as automata. The switching between states of these automata is governed by a switching variable. Th...

Linear systems over the max-plus algebra provide a suitable formalism to model discrete event where synchronization, without competition, is involved. In this paper, we consider formulation of matching problem for such class, in which output given system, called plant, forced, by input, track exactly that model. A necessary and sufficient condition its solvability obtained making use geometric ...