An Interval-valued Hellwig’s Approach to Composite Indices Based on a Single-valued Matrix
摘要
This study introduces an interval-valued extension of Hellwig’s numerical taxonomy (HNT) that addresses key limitations of single-value composite indices, which fail to account for indicator imbalance across observations. By incorporating three levels of compensation—fully compensatory, partially compensatory, and fully non-compensatory—this method creates a unified, aspiration-based index. The process determines interval bounds by breaking down Manhattan distances to a common ideal (“champion”) vector. The midpoint of this interval combines the regional distance to a predefined goal with the internal indicator imbalance. Although not its primary purpose, each aspiration gap can also be compared across different regions. The method is illustrated using seven public health indicators across the eight Slovakian NUTS-3 regions. This example employs an interval average as a reference to develop policy-relevant typologies by combining the midpoint with the interval range. The approach preserves Hellwig’s original simplicity, is computationally efficient, scalable for large datasets, and easy to implement with standard software.