Biomedical Master Thesis

Promotor, co-promotor, advisor : johan.gyselinck@ulb.be, - , Kris Verdonck, A Two Dogs Company (ATDC), kris@atdc.be

Research Unit : BEAMS/ELECTRICAL ENERGY

Description

See the document attached.

attached pdf document

Promotor, co-promotor, advisor : yves.de.smet@ulb.be, - , Alexandre Flachs

Research Unit : CODE-SMG

Description

Project title

Application of game theory to PROMETHEE II

Context

Operational research relies on the concept of optimisation. Multiple criteria decision making (MCDM), in particular, deals with problems where a set of alternatives are evaluated according to multiple conflicting criteria. The problem of optimising simultaneously multiple criteria generally does not admit global optimal solutions. Since the 1960's, many MCDM methods have been developed to help decision makers in this process, in general by refining the problem definition to include their personal preferences. Some popular MCDM methods are ELECTRE, AHP, TOPSIS, or PROMETHEE.

PROMETHEE was first proposed by J.P. Brans (VUB - ULB) in 1982. It is based on pairwise comparisons and the concept of outranking, evaluating a function from the set of alternatives to perform MCDM tasks. Theoretical studies on MCDM methods often consider the evaluations of the alternatives as fixed, and focus on the properties of the methods. However, recent research on PROMETHEE methods studied the following problem: how much should one alternative be improved (regarding some criteria) to be ranked higher than another one? This can for example be of interest in the context of a negotiation between multiple parts (the alternatives). In this case, each part wants to know how much to improve its evaluations (and eventually, on which criteria) to be ranked the best.

Some solutions to this problem have been proposed in the literature. This naturally raises questions on the dynamics of the evaluations, which reminds game theory. For example, the alternatives could be the players and the value they give to their evaluations are the strategies the players can choose. What is the best strategy for a player with a given range of action?

Objective

In this master thesis, the student will apply tools from game theory in the context of MCDM, and in particular the PROMETHEE II method.

After a literature review on the relationship between game theory and MCDM, the student should propose a game theory model based on the PROMETHEE II method, study its properties, implement the model and test it on reprenstative examples. The model could be compared to existing methods in the literature, and eventually extended to other MCDM methods.

Prerequisite

The student should be interested in operational research. No prior knowledge in game theory is required but a good mathematical background is encouraged. Students should be aware of the rather theoretical nature of the project.

Contact person

For more information please contact : yves.de.smet@ulb.be or alexandre.flachs@ulb.be