Stability of the Solution in P2P Network System Based on Two-Sided Fuzzy Relation Inequality

Considering the download traffic requirements of the terminals within a certain range, the two-sided fuzzy relation inequalities with addition-min have been recently introduced for modeling the P2P network system. In such a model, the solutions of the FRIs correspond the feasible flow schemes in the P2P network system. To characterize the stability of a given flow scheme, we define the amplitude of the corresponding solution, in this work. If a solution has a bigger amplitude, then it is able to bear a larger perturbation among its components. Accordingly, the corresponding flow scheme is considered to be more stable. For obtaining the amplitude of a given solution, we propose some effective algorithms to compute the upper and lower amplitudes. Following our proposed algorithms, the stability of any pair of solutions could be compared, based on the obtained amplitudes. Our provided results are demonstrated by some numerical examples