Mathematical Applications in the Measurement of Multidimensional Poverty in Colombia: An Approach Based on Aggregation Operators

Source abstract

The main objective of this study is to propose a new method to estimate multidimensional poverty in Colombia using aggregation operators that incorporate expert assessment into the calculation process. To this end, it proposes three operators: the poverty ordered weighted averaging (OWA) operator, the poverty-induced OWA operator, and the poverty penalty OWA operator. Each one integrates different types of subjective information, such as preferences, priorities, and levels of agreement regarding the need to improve access. Based on the structure of the official Multidimensional Poverty Index and responses from five experts, a mathematical model is developed to compare the results of the traditional method with measurements generated by the proposed operators. The findings show that expert judgment significantly influences the magnitude of the index and the severity attributed to deprivation, especially in dimensions such as Housing and Children and Youth. Likewise, it is shown that ordered operators allow for capturing variations in the relative importance of the indicators, reinforcing the usefulness of these methodologies for generating complementary and more flexible analyses in the evaluation of multidimensional poverty. Received: 10 April 2026 | Revised: 9 July 2026 | Accepted: 16 August 2026 Conflicts of Interest The authors declare that they have no conflicts of interest to this work. Data Availability Statement Data are available from the corresponding author upon reasonable request. Author Contribution Statement Danna Suárez-Gomez: Conceptualization, Methodology, Validation, Investigation, Data curation, Writing – original draft. Fabio Blanco-Mesa: Conceptualization, Methodology, Writing – original draft, Writing – review & editing, Supervision, Project administration, Funding acquisition. Ernesto León-Castro: Software, Formal analysis, Resources, Writing – original draft, Visualization, Supervision. Luis Asuncion Pérez-Domínguez: Software, Formal analysis, Resources, Writing – review & editing. Víctor G. Alfaro-García: Validation, Investigation, Data curation, Visualization.