Learning monotone preferences using a majority rule sorting model

• Published in: International transactions in operational research 2019-09, Vol.26 (5), p.1786-1809
• Main Authors: Sobrie, Olivier, Mousseau, Vincent, Pirlot, Marc
• Format: Article
• Language: English
• Subjects: Algorithms; classification; Computer Science; Decision analysis; Experimentation; heuristic; Machine learning; Majority rule; majority rule sorting; multiple criteria decision analysis; Multiple criterion; Operations Research; preference learning; Regression analysis
• ISSN: 0969-6016; 1475-3995
• DOI: 10.1111/itor.12512

We consider the problem of learning a function assigning objects into ordered categories. The objects are described by a vector of attribute values and the assignment function is monotone w.r.t. the attribute values (monotone sorting problem). Our approach is based on a model used in multicriteria decision analysis (MCDA), called MR‐Sort. This model determines the assigned class on the basis of a majority rule and an artificial object that is a typical lower profile of the category. MR‐Sort is a simplified variant of the ELECTRE TRI method. We describe an algorithm designed for learning such a model on the basis of assignment examples. We compare its performance with choquistic regression, a method recently proposed in the preference learning community, and with UTADIS, another MCDA method leaning on an additive value function (utility) model. Our experimentation shows that MR‐Sort competes with the other two methods, and leads to a model that is interpretable.