Resolution of the sec-max-product fuzzy relation inequalities and its lexicographic minimum solution ∗

In this paper we consider the wireless Server-to-Client (S2C) network system with server peers and user (client) peers. The server peers provide the data resources to the user peers. In order to describe the wireless S2C network system in which there exists at least one candidate server for each user, we define and investigate the so-called sec-max-product fuzzy relation inequalities. Basic properties and the structure of the solution set have been studied for the sec-max-product fuzzy relation inequalities system. Moreover, the optimal solution under a lexicographic order is further proposed and studied for such sec-max-product system, which is able to minimize all the variables under some fixed priority grade. In addition, an efficient resolution algorithm is developed with illustrative examples.