Electre Tree A Machine Learning Approach to Infer Electre Tri B Parameters
This work addresses the parameter elicitation challenge in multicriteria decision-making for decision-makers, but it is incremental as it adapts existing machine learning methods to a specific domain.
The paper tackles the problem of inferring all or any combination of ELECTRE Tri-B parameters, such as criteria weights and reference profiles, by proposing the ELECTRE Tree algorithm, which uses a Random Forest-inspired ensemble technique and genetic optimization, resulting in the generation of both linear and non-linear decision boundaries suitable for different problem types.
Purpose: This paper presents an algorithm that can elicitate (infer) all or any combination of ELECTRE Tri-B parameters. For example, a decision-maker can maintain the values for indifference, preference, and veto thresholds, and our algorithm can find the criteria weights, reference profiles, and the lambda cutting level. Our approach is inspired by a Machine Learning ensemble technique, the Random Forest, and for that, we named our approach as ELECTRE Tree algorithm. Methodology: First, we generate a set of ELECTRE Tri-B models, where each model solves a random sample of criteria and alternatives. Each sample is made with replacement, having at least two criteria and between 10% to 25% of alternatives. Each model has its parameters optimized by a genetic algorithm that can use an ordered cluster or an assignment example as a reference to the optimization. Finally, after the optimization phase, two procedures can be performed, the first one will merge all models, finding in this way the elicitated parameters, and in the second procedure each alternative is classified (voted) by each separated model, and the majority vote decides the final class. Findings: We have noted that concerning the voting procedure, non-linear decision boundaries are generated, and they can be suitable in analyzing problems with the same nature. In contrast, the merged model generates linear decision boundaries. Originality: The elicitation of ELECTRE Tri-B parameters is made by an ensemble technique that is composed of a set of multicriteria models that are engaged in generating robust solutions.