Generalized min-max programming problems subject to addition-min fuzzy relational inequalities

In this paper, we explore a new generalized min-max programming problem with constraints of addition-min fuzzy relational inequalities. This new generalized min-max programming model provides unified settings that enable the system manager to understand the system congestion level or the worst individual cost in the BitTorrent-like peer-to-peer file-sharing system. Theoretical results are presented to illustrate how the optimal value of generalized min-max programming problem can be obtained by solving a single-variable optimization model. Two approaches (an analytic method and an iterative approach) are provided to solve this single-variable optimization model. The complexity analyses of these two approaches are provided. Numerical examples demonstrate our proposed approaches.