In this paper we apply message-passing algorithms to solve Sudoku puzzles. We provide explicit expression for the sum-product algorithm and the max-product algorithm and analyze the difference between the algorithms in terms of performance and efficiency. The failure of the max-product algorithm when been applied to Sudoku problem is due to the existence of stopping-sets. We show empirically th...

Let (A n) n∈N be a sequence of stationary topical (i.e. isotone and ad-ditively homogeneous) operators. Let x(n, x 0) be defined by x(0, x 0) = x 0 and x(n + 1, x 0) = A n x(n, x 0). This can modelize a wide range of systems including, train or queuing networks, job-shop, timed digital circuits or parallel processing systems. When (A n) n∈N has the memory loss property, (x(n, x 0)) n∈N satisfy ...

In this paper a definition of the exploration performed by stochastic algorithms is proposed. It is based on the observation through cluster analysis of the solutions generated during a run. The probabilities associated by an algorithm to solution components are considered. Moreover, a consequent method for quantifying the exploration is provided. Such a measurement is applied toMAX–MIN Ant Sys...

in this paper, we study the finitely many constraints of fuzzy relation inequalities problem and optimize the linear objective function on this region which is defined with fuzzy max-lukasiewicz operator. in fact lukasiewicz t-norm is one of the four basic t-norms. a new simplification technique is given to accelerate the resolution of the problem by removing the components having no effect on ...

A central limit theorem for stochastic recursive sequences of topical operators. Abstract Let (A n) n∈N be a stationary sequence of topical (i.e. isotone and ad-ditively homogeneous) operators. Let x(n, x 0) be defined by x(0, x 0) = x 0 and x(n + 1, x 0) = A n x(n, x 0). It can modelize a wide range of systems including train or queuing networks, job-shop, timed digital circuits or parallel pr...

We study Max-Product and Max-Plus Systems with Markovian Jumps and focus on stochastic stability problems. At first, a Lyapunov function is derived for the asymptotically stable deterministic Max-Product Systems. This Lyapunov function is then adjusted to derive sufficient conditions for the stochastic stability of Max-Product systems with Markovian Jumps. Many step Lyapunov functions are then ...

Recently we generalized the max algebra system to the class of nonnegative  tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and i...

In this study, we introduce a new kind of nonlinear Bernstein-Chlodowsky operators based on q-integers. Firstly, define the q?Bernstein-Chlodowsky max-product kind. Then, give an error estimation for q?Bernstein Chlodowsky by using suitable generalizition Shisha-Mond Theorem. There follows upper estimates approximation some subclasses functions.

In this paper we show that the problem of minimizing a nonlinear objective function subject to a system of fuzzy relational equations with max-min composition can be reduced to a 0-1 mixed integer programming problem. The reduction method can be extended to the case of fuzzy relational equations with max-T composition as well as those with more general composition.