Resolution of the sec-max-product fuzzy relation inequalities system 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, namely the lexicographic minimum solution, is further proposed and studied in the sec-max-product system, for minimizing all the variables under some fixed priority grade. An efficient resolution algorithm is developed for computing the lexicographic minimum solution of the sec-max-product system, with several illustrative examples.