The Classification of Alternatives Based a Multi-criteria Analysis Technique and the Combination of AHP and the Weighted Sum

The difficulty of the methods of decision aid is what seeking optimal solutions to complex problems in general and for nature multicriteria, or the concept of optimality is no sense in a multicriteria context.

In this paper, we propose a mathematical modelling, in the context of multicriteria multi- decision-makers aid methods, with a decision-making process allowing the decision-makers to choose the most appropriate solutions according to their orientations, an independent manner, taking into account the objective of the problem.

After identifying the objective and determining the set of actions, we decompose the objective to different dimensions, which gives a system of criteria to different levels.

We use the principle of the AHP method to calculate different weight, related to our decomposition. Also the weighted sums method helps us transform the multi-criteria problem to a mono criterion problem, and obtain a mathematical expression of actions evaluation on which each decision maker bases to choose the optimal action. Therefore, we get a partial order of potential actions on each dimension, and a global order examining all the criteria of the studied system. Which allows to mathematically judge the selection of an action rather than another.

Finally, we start with the data of the company Rabat-Sale tramway and apply the proposed process to judge the choice of the tram as a means of transport instead of the bus.

This is a concrete example of large financial size showing the effectiveness of our proposal.