An Explainable and Interpretable Composite Indicator Based on Decision Rules
Salvatore Corrente, Salvatore Greco, Roman Słowiński, Silvano Zappalà
Abstract
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.