In heterogeneous wireless networks, an important task for mobile terminals is to select the best network for various communications at any time anywhere, usually called network selection. In recent years, this topic has been widely studied by using various mathematical theories. The employed theory decides the objective of optimization, complexity and
performance, so it is a must to understand the potential mathematical theories and choose the appropriate one for obtaining the best result. Therefore, this paper systematically studies the most important mathematical theories used for modeling the network selection problem in the literature. With a carefully designed unified scenario, we compare the schemes of various
mathematical theories and discuss the ways to benefit from combining multiple of them together. Furthermore, an integrated scheme using multiple attribute decision making as the core of the selection procedure is proposed.
