In a supply chain system, the price of the goods should satisfy some requirements of the consumer. These requirements have been exactly characterized by a group of min-product fuzzy relation inequalities (FRIs). Correspondingly, any feasible pricing scheme is characterized by a solution of the min-product FRIs system. For a given pricing scheme, or say a given solution in the min-product FRIs, the flexibility is reflected by the maximum amplitude, or equivalently the maximum amplitude interval solution (MAIS). Motivated by such an application background, this work attempts to study the MAIS in min-product FRIs. An efficient algorithm is discovered for computing the MAIS of a solution within the given min-product system. The MAIS will help the system manager be aware of the flexibility of a given pricing scheme and produce better decision-making.

Recently, max-min fuzzy relation inequalities (FRIs) have been used to model a (peer-to-peer) P2P network system. Any feasible scheme in the P2P network system is reflected by a solution of the max-min FRIs. One of the objectives of system managers is to decrease network congestion. To satisfy this objective, we attempt to minimize a weighted minimax function motivated by existing research. As a consequence, we establish a weighted minimax programming model in which the constraint is the max-min FRIs. Our goal in this work is to develop an effective algorithm to obtain the optimal solution of the optimization model. The so-called SCP-based algorithm is proposed to find the optimal solution. A numerical example shows the efficiency of our proposed SCP-based algorithm.