Comparação de índices de validação de agrupamento Fuzzy com componente de sobreposição e aplicação no domínio de segmentação de consumidores

Abstract

Fuzzy clustering has emerged as a relevant approach for data segmentation in scenarios with diffuse boundaries and overlapping groups. However, assessing the quality of fuzzy partitions remains a challenge, particularly due to the lack of objective and universal criteria for fuzzy cluster validation. This study investigates whether incorporating overlap measures into validation indices can provide additional and more robust information for cluster analysis when compared to indices that assess only cohesion, separation, or membership distribution. To this end, several fuzzy validity indices are analyzed—among them Xie–Beni, Fukuyama–Sugeno, VMPE, VMPF, VHSS, and VHY—applied to synthetic datasets with varying levels of compactness and overlap, as well as to a real dataset related to consumer segmentation. The Fuzzy C-Means (FCM) algorithm is used to generate the partitions, combined with the elbow method to investigate the optimal number of clusters. The results show that indices explicitly incorporating overlap, such as VHY and VHSS, offer greater ability to distinguish complex fuzzy structures, providing richer interpretations and stronger support for segmentation. The study concludes that these indices add analytical value, especially in real-world scenarios marked by strong heterogeneity, complementing traditional metrics based solely on cohesion, separation, or membership values.