Maximum-Amplitude Solution of Addition-Min Fuzzy Relation Inequalities Considering the Stability in the P2P Network System

• Published in: IEEE transactions on fuzzy systems Vol. 30; no. 1; pp. 1 - 13
• Main Authors: Xue, Huanbin, Yang, Xiao-Peng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Addition-min composition; Algorithms; Amplitudes; fuzzy relation equation (FRE); fuzzy relation inequality (FRI); Indexes; Inequalities; Linear programming; maximum amplitude; maximum-amplitude solution; Numerical stability; Optimization; Peer to peer computing; Perturbation; Perturbation methods; Stability criteria
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2020.3029633

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.