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Leximax minimum solution of addition-min fuzzy relation inequalities. (English) Zbl 1458.90664
Summary: Addition-min fuzzy relation inequalities are introduced to characterize the Peer-to-Peer (P2P) network system. In order to decrease the network congestion, considering both efficiency and fairness, we define the leximax minimum solution for system of addition-min fuzzy relation inequalities. The leximax-optimality refines both Pareto-optimality and max-optimality. For solving the leximax minimum solution, concepts of minimum zero point and minimax value are defined, with corresponding resolution algorithms, i.e. Algorithms I and II. Based on these two algorithms, Algorithm III is further developed to find the unique leximax minimum solution. Numerical examples illustrate the validity of our proposed algorithms.
##### MSC:
 90C70 Fuzzy and other nonstochastic uncertainty mathematical programming 90C35 Programming involving graphs or networks
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