Min-Max Programming Problem Subject to Addition-Min Fuzzy Relation Inequalities

A BitTorrent-like peer-to-peer file-sharing system can be reduced into a system of addition-min fuzzy relation inequalities. Addition-min is a new composition, and the solution set of addition-min fuzzy relation inequalities differs much from that of general max-t-norm fuzzy relation inequalities or equations. In order to avoid network congestion and improve the stability of data transmission, a min-max programming problem is proposed subject to addition-min fuzzy relation inequalities in this paper. Based on some relevant theorems on resolution, a novel algorithm is developed step by step to find an optimal solution of the proposed problem. Moreover, an application example is given to illustrate the feasibility and efficiency of the algorithm. Finally, some further discussions are made concerning the optimal solution of the proposed problem.