Dichotomy algorithm for solving weighted min-max programming problem with addition-min fuzzy relation inequalities constraint

Abstract

Addition-min fuzzy relation inequalities were introduced for describing the quantitative relationship in the peer-to-peer (P2P) file sharing system. In order to reduce the network congress, the system manager has to minimize the variables in the addition-min fuzzy relation inequalities. The corresponding min-max programming has been established in the existing works. However in such model, all the variables are viewed equally. In this paper, considering the different important degrees of the variables, we propose and investigate the weighted min–max programming subject to the addition-min fuzzy relation inequalities. Due to the different objective function, the existing methods are no longer effective for our proposed problem. Dichotomy algorithm has been developed in this paper for searching the approximate optimal solution of the weighted min-max programming. The feasibility and effectiveness of the dichotomy algorithm is illustrated by numerical example.