On Min–Max Optimization for Systems with Addition-Min-Product Fuzzy Relational Inequalities

• Published in: International journal of fuzzy systems Vol. 24; no. 6; pp. 2631 - 2642
• Main Authors: Wu, Yan-Kuen, Guu, Sy-Ming, Yang, Fu-Hung, Chang, Kuang-Ming
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2022; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Computational Intelligence; Data transmission; Engineering; Fuzzy systems; Inequalities; Linear functions; Linear programming; Management Science; Mathematical analysis; Operations Research; Optimization; Peers; Polynomials; Min–max programming problem; Addition-min-product inequality; Iterative approach
• ISSN: 1562-2479; 2199-3211
• DOI: 10.1007/s40815-022-01316-w

In the literature, a min–max programming model with addition-min-product fuzzy relational inequalities constraints has been proposed to explore network congestion and data transmission problems in a BitTorrent-like peer-to-peer file-sharing system. In this paper, we slightly extend its objective function and provide a new method for finding an optimal solution. We show that solving our generalized min–max optimization problem can be reduced into a single-variable optimization problem. A polynomial-time interactive approach is then to obtain its optimal value. When a linear function is in the place of its objective subject to the same addition-min-product constraints, the optimization problem can be solved by a linear programming approach. Numerical examples are given to illustrate the procedures.