A PROMETHEE software timeline

Important elements for the success of the PROMETHEE methods have been the development of numerous extensions and interactive software. The purpose of the paper is to show the evolution of the PROMETHEE methods and of their software implementation over time. Starting with PROMCALC and the first visual sensitivity analysis tools (Walking Weights), we stress less known extensions of the methodology including a.o.: • The introduction of variable (percentage) thresholds in the preference functions in PROMCALC. • The hierarchical criteria structure first available in the Decision Lab software. • The group decision extension of PROMETHEE and GAIA introduced in Decision Lab. We then focus on the current Visual PROMETHEE software that includes: • New visualizations of the PROMETHEE rankings. • Visual weight sensitivity analysis. • Enhancements of the GAIA analysis. • Improved group decision features. • GIS-integration of PROMETHEE and GAIA with Google Maps. • Unified PROMETHEE Sort procedure for sorting problems. • Efficiency (input/output) analysis. We conclude by outlining the future of PROMETHEE software, especially the features that will be available in Visual PROMETHEE 2. Axiomatic approaches to Promethee Marc Pirlot Université de Mons, Belgium Characterizing multiple criteria aggregation methods by means of axioms has several benefits. Two of the most important are the following: • getting a clearer understanding of the conditions under which a given aggregation procedure can be advisedly used; • providing a precise interpretation of the parameters of the aggregation method, which can help driving their elicitation procedure and avoiding ambiguities. The universal recognition of the Additive Value Function model is partly due to the existence of meaningful axiomatic characterizations for this model, which led for instance to a precise understanding of the tradeoffs idea. Is there some sort of characterization of the Promethee method? Actually, several approaches can be followed to give axiomatic characterizations of Promethee or of methods close to it. It should first be noted that different sorts of axiomatizations can be given for a specific method. One consists of characterizing a particular procedure as a mechanism taking as input an alternatives performance matrix and some other information (e.g. information about the importance of the criteria, information about the nature of the criteria evaluation scales) and transforming this into an output that can be e.g. an overall score assigned to each alternative or an overall preference relation. Along this line, Marchant (1996) published a characterization of the “generalized Borda method” which has close connections with Promethee. The aggregation method is characterized by some of its properties which, basically, describe how the method deals with the input data to produce the output. Another line of thought, in an axiomatization perspective, consists of characterizing the overall preference relations that can be represented by means of a given aggregation model. This approach provides ways of testing, by asking appropriate questions to the decision maker, whether his/her preference could be possibly represented using the model. Usually such characterizations belong to the theory of conjoint measurement (Krantz et al., 1971). This theory essentially deals with the question of measuring multidimensional objects, such as alternatives assessed on several criteria. To date, no such characterization has been established for the whole Promethee method. However, we may look at Promethee in a different way, i.e. as a two-phase method. In a first step, Promethee produces a valued (outranking) relation, which