1st ICAI 2020

International Conference on Automotive Industry 2020

Mladá Boleslav, Czech Republic

standard deviation of performances of all alternatives in terms of the given criterion as a reasonable and quite universal choice.

Figure 1: Gaussian preference function ( stands for a difference in performances between two alternatives, is a parameter of the function)

Source: Own elaboration.

(1) If we define the preference function for each criterion, the preference degrees P j is calculated for all n ⋅ ( n-1 ) pairs (number of 2-element variations of n objects). In the next steps of the method, the preference degrees are aggregated together. This aggregation depends on the aim of decision-making. In this paper, primarily, we want to compare the profiles of the alternatives, explore the similarities and discover the opposites. In line with Ishizaka and Nemery (2011), this can be done using the GAIA plane, which combines the PROMETHEE original methodology together with the Principle Component Analysis (PCA). For this purpose, the following steps must be done: 1. The single criterion net flows are derived using thus each alternative is represented by a k -dimensional vector ( π 1 ( A i ), π 2 ( A i ), …, π k ( A i )), which describes the profile of the i -th alternative (the greater net flow, the better alternative is in comparison with other alternatives). 2. The k -dimensional vectors are projected on a plane (so calledGAIA–Geometrical Analysis for Interactive Aid) using the PCA method, see Jolliffe and Cadima (2016) for the detailed description of PCA), so that as much information as possible is seen from this plane. The GAIA plane consists of criteria (projection of the axes denoted as vectors originating at the centre of the coordinate system) and alternatives (points). 3. Interpretation of information provided by the GAIA plane: (a) If an alternative lies in the same direction as a criterion axis, then the alternative performs well in terms of this criterion and vice versa; (b) If two alternatives are located close

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