Multi Criteria Decision Making (MCDM) methods are mathematical tools that help take decisions in scenarios where many possible alternatives are to be evaluated over multiple conflicting criteria. The final aim is to identify the best alternative in highly complex situations.

In the related literature several MCDM techniques are available, and their application fields are numerous, ranging from the supplier selection problem, to the technical evaluation of tenderers, to the resolution of scheduling problems, and many more.

Originally, researchers have developed deterministic MCDM techniques. However, a critical issue when applying MCDC approaches is that nowadays uncertainty is inherent in data of real applications. In fact, uncertainty is present, to a greater or lesser intensity, in almost any project, due, for instance to changes in modern markets, in technology, in competitors, or in governmental regulations. Therefore, modern MCDM techniques have to be able to deal with such uncertain or vague data. To this aim, when reliable historical data are lacking, fuzzy set theory can be used to model uncertainty by expert evaluations. Consequently fuzzy MCDM techniques arise.

The aim of this lecture is to provide the basic notions on two well-known MCDM techniques, both in their deterministic and fuzzy settings, and to perform a comparative analysis among them in order to better understand their similarities and differences, so that the attendees have the basic guidelines to select which MCDM method is able to properly support the specific decision making process.

In particular, among the existing MCDM techniques, this lecture focuses on the most commonly adopted methods, namely the Analytic Hierarchy Process (AHP) and the Data Envelopment Analysis (DEA), as well as their fuzzy counterparts, i.e., the Fuzzy Analytic Hierarchy Process (FAHP) and the Fuzzy Data Envelopment Analysis (FDEA).

These MCDM methods are illustrated through a real case study, consisting in the evaluation of public procurement tenders at a European Institution, where the lecturer has cooperated to the application of these tools and these techniques are currently being tested.