## 2 Related Works  
Vertical Handover is an important step to acomplish the best QoS in an heterogeneous environment that needs a dynamic selection of the best convenient network, and the decision phase is the most crucial in this case. It is about assembling the performances of each candidate network, and ranking them in purpose to select the best network. It is leading a revolution in the internet by carrying an improved Quality of Experience (QoE) for users of wireless services. In the literature, different approaches have been proposed to handle the vertical handover decision problem: good network performance, user satisfaction, flexibility, efficiency, and multi-criteria solution. In the same context of heterogeneous environment, authors of [4] compared classical handover decision strategies (RSSbased), and came to the conclusion that they are not sufficient to make a vertical handover decision. They do not consider the current context or user preferences. Indeed, vertical handover decision strategy involves complex considerations and compromises. It needs to be flexible and efficient considering the useful criteria and reasonable policies or rules applicable to both the user's professional and personal communications. In this context, [5] conclude that the mobility management of heterogeneous networks not only depends on network parameters, but also on terminal's velocity, battery power, location information, user's preferences, service's capabilities and QoS requirements. [4,6] presented a panorama of vertical Handover Decisions. Using cost or utility functions; utility/cost refers to the satisfaction that a good or service provides to the decision maker. In the same context, [6] specified that other studies on the network selection issue could also evaluate networks based on utility/cost functions which combine multiple attributes. Furthermore, authors of [7], as well, proposed an algorithm for network selection based on averaged received signal strength, outage probability and distance. In [8], an intelligent handover decision mechanism has been proposed based on the context-aware strategy and Media Independent Handover in order to reduce the latency, to enable seamless vertical handover and always guarantee the best connected concept. However, some studies focus also on other mathematical models such as fuzzy logic methods which can be used in VHD. The authors of [9] proposed an utility-based Radio Access Technology (RAT) selection optimization in heterogeneous wireless networks, they introduced three utility-based optimization functions based on the type of application that users request. They formulated the terminal assignment problem as an optimization problem, which is recognized as NP-hard. The goal in vertical handover process is that a terminal should join the best Access Point to address the needs of the users. Interface selection turns into a \"decision making\" problem with multiple options -_Alternative networks_ - and attributes -_QoS Parameters_- user preferences and application requirements. Among several approaches that have been proposed for decision making and network selection, MADM is one of the most promising methods. In [10], MADM refers to making preference decision over the available alternatives that are characterized by multiple attributes. MADM problems have several common characteristics such as _Alternatives_, _Multiple attributes_, _Decision matrix_, _Attribute weights_ and _Normalization_. Most MADM algorithms that have been studied in [11; 12; 13; 14; 15] for the network selection problem are compensatory algorithms which means they combine multiple attributes to find the best alternatives, _versus_ non compensatory algorithms used to find acceptable alternatives that satisfy the minimum cutoff. The most popular classical MADM methods according to [4] are SAW, MEW and TOPSIS which are compensatory algorithms. The mathematical modeling of these methods is given in the next section.