Abstract
In this paper, supereigenvalue and constrained supereigenvalue problems of an addition-min fuzzy matrix are investigated. In a peer-to-peer file sharing system, the download requirement of the terminals could be described by a constant constraint system with addition-min fuzzy relation inequalities. Without considering the constant constraint system, we first study the supereigenvalue problem. While considering the constant constraint system, the so-called constrained supereigenvalue is further proposed and investigated. A constrained supereigenvalue represents the ratio of the data-download quality to the data-sending quality under a constant constraint. In order to arouse the enthusiasm of the terminals to share their local file data, we aim to maximize the constrained supereigenvalue. A nonlinear programming approach is developed to find the unique maximum constrained supereigenvalue, with some illustrative examples.
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