arXiv:2506.13259cs.LGmath.OC2025-06

用规则解释复合指标,让评分过程透明可懂。

An Explainable and Interpretable Composite Indicator Based on Decision Rules

  • 基于决策规则构建可解释的复合指标,通过条件判断明确评分逻辑。
  • 支持分类与连续评分,能处理缺失值,适用于多种实际场景。
  • 适合需要透明决策依据的政策评估、公共管理等应用者使用。

复合指标广泛用于多准则评估中对单位进行打分或分类。其构建通常涉及多个指标的聚合,常见于多准则决策辅助(MCDA)。除生成最终得分或分类外,确保可解释性、可理解性和透明性至关重要。本文提出一种基于若-则决策规则的新型复合指标构建框架。我们探讨四种场景:(i) 解释由序数指标编码之和得出的分类;(ii) 解析用于将单位分入分位数的不透明数值复合指标;(iii) 根据参考单位的分类偏好信息构建复合指标;(iv) 解释现有MCDA方法生成的分类结果。为从评分或分类单位中推导规则,采用基于优势的粗糙集方法。所得规则以清晰可读的方式将类别分配或得分与指标值的阈值条件关联,阐明内在逻辑并支持新单位的评估。主要方法论贡献在于引入基于决策规则的复合指标构建框架。此外,该框架自然扩展至连续复合指标,通过将每个不同得分视为有序类别实现。这得益于一种新算法,可在一次运行中高效生成所有最小规则。尽管可能产生大量规则,但通过仅展示与目标单位相关的规则,仍保持可解释性。最后,该方法可处理含缺失值的数据集,提升实际适用性。

原文摘要 · Abstract (English)

Composite indicators are widely used to score or classify units evaluated on multiple criteria. Their construction typically involves aggregating criteria evaluations, a common practice in Multiple Criteria Decision Aiding (MCDA). Beyond producing a final score or classification, however, ensuring explainability, interpretability, and transparency is crucial. This paper proposes a novel framework for constructing explainable and interpretable composite indicators using if-then decision rules. We explore four scenarios: (i) decision rules explaining classifications derived from the sum of ordinal indicator codes; (ii) interpretation of an opaque numerical composite indicator used to classify units into quantiles; (iii) construction of a composite indicator from decision-maker preference information, given as classifications of reference units; and (iv) explanation of classifications generated by an existing MCDA method. To induce the rules from scored or classified units, we apply the Dominance-based Rough Set Approach. The resulting rules relate class assignments or scores to threshold conditions on indicator values in a clear and intelligible way, clarifying the underlying rationale and supporting the assessment of new units. Our main methodological contribution is the introduction of a decision-rule-based framework for constructing composite indicators. Moreover, the framework extends naturally to continuous composite indicators by treating each distinct score as an ordered class. This is enabled by a new algorithm that efficiently induces all minimal rules in a single run. Although this may yield many rules, explainability is preserved by showing only those satisfied by the unit of interest. Finally, the methodology can handle datasets with missing values, enhancing its practical applicability.

复合指标决策规则可解释性粗糙集

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