Centralized solution in max-min fuzzy relation inequalities

In recent years, the peer-to-peer (P2P) educational information sharing system was modeled by a system of fuzzy relation inequalities (FRIs) with addition-min or max-min composition. The max-min FRIs system was applicable to the P2P network considering the highest download traffic among the terminals. Moreover, every solution to such a max-min FRIs system corresponds exactly to one feasible flow control scheme. To embody the stability of a given feasible scheme, we introduce the concept of the widest symmetrical interval solution (WSIS), regarding the corresponding solution in the max-min FRIs system. Some effective procedures are proposed to find the WSIS regarding a provided solution. In addition, aiming to find the most stable feasible scheme, we further define the concept of a centralized solution. Some effective procedures are also proposed to find the centralized solution regarding the max-min FRIs system. Some numerical examples are provided, respectively, to demonstrate our proposed resolution procedures. Our obtained centralized solution will provide decision support for system administrators considering the stability of the feasible scheme.