On Min–Max Optimization for Systems with Addition-Min-Product Fuzzy Relational Inequalities

In the literature, a min–max programming model with addition-min-product fuzzy relational inequalities constraints has been proposed to explore network congestion and data transmission problems in a BitTorrent-like peer-to-peer file-sharing system. In this paper, we slightly extend its objective function and provide a new method for finding an optimal solution. We show that solving our generalized min–max optimization problem can be reduced into a single-variable optimization problem. A polynomial-time interactive approach is then to obtain its optimal value. When a linear function is in the place of its objective subject to the same addition-min-product constraints, the optimization problem can be solved by a linear programming approach. Numerical examples are given to illustrate the procedures.