An Iterative Algorithm for Min-max Programming Problem with Addition-min Fuzzy Relational Inequalities in P2P File Sharing Systems

In this paper, we formulate the P2P file sharing system into addition-min fuzzy relation inequalities. The objective of the problem is to minimize the network congestion of the P2P file sharing system. To reduce this factor, we have considered the min-max optimization problem subject to addition-min fuzzy relation inequalities. To solve this problem, we first discuss some properties of addition-min fuzzy relation inequalities. Using these properties, notion of binding variables is introduced and an iterative algorithm is proposed based on greedy approach. The algorithm is designed in such a way that the maximum value corresponding to the component of the solution vector remains as small as possible. The proposed greedy algorithm provides the approximate optimal solution for the problem. The sufficiency condition for the optimality of the solution is also derived. The proposed algorithm is illustrated using some examples.