Comparing principal component analysis and multidimensional scaling for the representation of PROMETHEE results

Abstract

In this paper, we present a new method of visualising the results of PROMETHEE and a comparison of the new method with the common GAIA method (Mareschal and Brans, 1988) and reveal its application in the context of choice for alternative vehicles. Visualisation methods make the impact of each single criterion and its weight on every single alternative visible. The most common method for visualising the results of PROMETHEE models is the GAIA method. To evaluate if GAIA itself or visualisation methods themselves are difficult to handle for the decision maker a new visualisation method for PROMETHEE results is developed and compared with the GAIA method. The method we introduce in this paper is based on the classical multidimensional scaling (MDS) (Chatfield and Collins, 1980). MDS is extended by property fitting to integrate each single criterion into the visualisation (Homburg and Krohmer, 2009). We compare the results by applying the procrustes analysis (Gower and Dijksterhuis, 2004). Finally, we give an outlook of future research aspects on the comparison and the new visualisation method in particular.