NEUTRO-FUP: Neutrosophic Fuzzy Pooling

Convolutional Neural Networks (CNNs) are widely used for tasks such as image segmentation, object recognition, and classification, with pooling operations playing a key role in reducing computational complexity and model parameters. While traditional and fuzzy-based pooling methods have been extensively studied, recent approaches have introduced intuitionistic fuzzy pooling to address local imprecision in feature maps. However, this method relies on the assumption that the indeterminacy is simply the complement of membership and non-membership degrees—an assumption that can be inaccurate in complex environments. To overcome this limitation, we propose a novel pooling operation based on Neutrosophic Fuzzy Sets (NFSs), which explicitly incorporates a degree of indeterminacy. Our method, called Neutrosophic Pooling, operates in four stages: bi-fuzzification using membership, non-membership, and indeterminacy maps; a first aggregation converting Neutrosophic Fuzzy Set NFS into a classical fuzzy set; a second aggregation using a sum operator; and finally, defuzzification through a max operation. This new pooling layer can be seamlessly integrated into CNN architectures, replacing standard, fuzzy, or intuitionistic pooling layers. Experimental evaluations across several benchmark datasets demonstrate that the proposed NFS-based pooling significantly enhances classification performance, especially in uncertain or noisy environments, outperforming state-of-the-art pooling methods.