An Integrated Attribute-Weighting Method Based on PCA and Entropy: Case of Study Marginalized Areas in a City

Abstract

The precise allocation of weights to criteria plays a fundamental role in multicriteria decision-making, exerting a significant influence on the obtained results. Ensuring an appropriate weighting of criteria is crucial for conducting a fair and accurate evaluation of various alternatives. In this context, we present an innovative solution that addresses the allocation of weights to attributes in datasets, aiming to overcome limitations and challenges associated with expert consultation in multicriteria problems. The proposed method is grounded in an objective approach and adopts a hybrid perspective by integrating the mathematical principles of Principal Component Analysis with the application of the Entropy Method. This method was implemented along with the exponential weighted sum model in a case study related to the classification of neighborhoods in Mexico City based on the level of marginalization. Results were compared with the marginalization index reported in official sources, using evaluation metrics MAE and MAPE with values of 0.24 and 11.3%, respectively. This research demonstrates the efficiency of the proposed method, which integrates techniques used for attribute weighting, providing a robust and reliable tool for decision-making.

Keywords

• multiple-attribute decision-making
• weighting of criteria
• PCA
• entropy