The Solution Closest to a Given Vector in the System of Fuzzy Relation Inequalities

In recent years, the fuzzy relation inequalities, with addition-min or max-min composition, were introduced for describing the P2P network system. A solution of the fuzzy relation inequalities corresponds to a feasible scheme in the P2P network system. In this work, we aim to find a solution of the max-min fuzzy relation inequalities, which is closest to a given vector. Here, the given vector is not a solution. We propose an novel method for obtaining the closest solution. A numerical example is given to illustrate our proposed method.