This study focuses on the bilateral requirements of terminals within a Peer-To-Peer (P2P) network system, specifically examining two-sided fuzzy relation inequalities using addition-min composition. Each solution derived from this two-sided fuzzy relation system represents a viable flow control strategy for the associated P2P network. The main topics covered include 1) identifying a minimal solution that is less than or equal to a specified solution, 2) identifying a maximal solution that is greater than or equal to a specified solution, and 3) outlining the structure of the solution set for the fuzzy relation system. The goals of 1) and 2) are to pinpoint particular minimal or maximal solutions within the two-sided system. We introduce two algorithms, Algorithm I and II, to determine these specific minimal and maximal solutions with polynomial computational complexities. Their effectiveness is demonstrated through various numerical examples. It is observed that all minimal and maximal solutions can entirely characterize the complete solution set for the two-sided system, and it may also be non-convex.