Maximum-Amplitude Solution of Addition-Min Fuzzy Relation Inequalities Considering the Stability in the P2P Network System - Xue, Huanbin; Yang, Xiao-Peng (IEEE transactions on fuzzy systems, 2022)
Maximum amplitude and its corresponding maximum-amplitude solution are defined in an addition-min fuzzy relation inequalities system. The maximum-amplitude solution could be viewed as a stable solution, since it is able to survive the biggest fluctuation or perturbation appearing in its components. For solving the maximum amplitude and maximum-amplitude solution, we construct a relevant optimization problem and then convert it into several subproblems. Some auxiliary functions and index sets are introduced to deal with these subproblems. Algorithm I is developed to find their optimal solutions. Based on the optimal solutions of the subproblems, we further propose Algorithm II for obtaining the maximum amplitude and maximum-amplitude solution of an addition-min fuzzy relation inequalities system. Numerical examples illustrate the validness and efficiency of our proposed algorithms.