Purpose

This paper presents an algorithm that can elicitate (infer) all or any combination of elimination and choice expressing reality (ELECTRE) Tri-B parameters. For example, a decision maker can maintain the values for indifference, preference and veto thresholds, and the study’s algorithm can find the criteria weights, reference profiles and the lambda cutting level. The study’s approach is inspired by a machine learning ensemble technique, the random forest, and for that, the authors named the study’s approach as ELECTRE tree algorithm.

Design/methodology/approach

First, the authors generate a set of ELECTRE Tri-B models, where each model solves a random sample of criteria and alternates. Each sample is made with replacement, having at least two criteria and between 10% and 25% of alternates. Each model has its parameters optimized by a genetic algorithm (GA) 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 alternate is classified (voted) by each separated model, and the majority vote decides the final class.

Findings

The authors have noted that concerning the voting procedure, nonlinear decision boundaries are generated and they can be suitable in analyzing problems of the same nature. In contrast, the merged model generates linear decision boundaries.

Originality/value

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.

中文翻译：

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电树：一种推断电三B参数的机器学习方法

目的

本文提出了一种算法，该算法可以引出（推断）消除和选择表达现实 (ELECTRE) Tri-B 参数的全部或任意组合。例如，决策者可以保留冷漠、偏好和否决阈值的值，而研究的算法可以找到标准权重、参考资料和 lambda 削减水平。该研究的方法受到机器学习集成技术随机森林的启发，为此，作者将该研究的方法命名为 ELECTRE 树算法。

设计/方法/方法

首先，作者生成了一组 ELECTRE Tri-B 模型，其中每个模型解决标准和替代方案的随机样本。每个样本都是有替换的，至少有两个标准和 10% 到 25% 的替代项。每个模型都有通过遗传算法 (GA) 优化的参数，遗传算法可以使用有序集群或分配示例作为优化的参考。最后，在优化阶段之后，可以执行两个程序；第一个将合并所有模型，以这种方式找到引出的参数，在第二个过程中，每个备用模型由每个分离的模型分类（投票），多数投票决定最终类别。

发现

作者已经注意到，关于投票程序，会产生非线性决策边界，它们可以适用于分析相同性质的问题。相比之下，合并模型生成线性决策边界。

原创性/价值

ELECTRE Tri-B 参数的导出是通过集成技术进行的，该技术由一组参与生成稳健解决方案的多标准模型组成。