Multi-criteria preference disaggregation analysis for classification: an application to model colour preferences

Classification or discrimination problems consider the assignment of a set of alternatives into predefined groups. In some situations, groups are defined in an ordinal way from the most to the least preferred. In the multi-criteria decision-aid (MCDA) literature, this is known as a `sorting' or `learning preferences' problem. Capturing the decision makers (DMs) tacit knowledge, by providing them a training sample to be sorted in an ordinal way, is considered of interest in the knowledge management field. Extracting and mathematically framing the preference system of the decision maker (expert) enables us to predict preferences for cases that are outside of the training sample. Much effort has been made in this direction in the area of artificial intelligence, specifically in fuzzy set theory and machine learning systems. Preference disaggregation, as one of the most popular approaches for capturing the preference system of DMs, in MCDA is used to infer global preference models from given preferential patterns. Among others, we can highlight: UTA (UTilites Additives); UTASTAR; UTADIS (UTilites Additives Discriminates); ELECTRE TRI ; and MHDIS methods. The aim of these approaches is to provide a model that is as consistent as possible with the decisions made by the DM. This research includes a literature review of the existing methodologies for learning preferences and a comparison between some of them. An application related to colour preferences is used to compare these methodologies. Finally, managerial applications involving learning colour preferences are studied.