Early detection and accurate diagnosis are essential to improving patient outcomes. The use of convolutional neural networks (CNNs) for tumor detection has shown promise, but existing models often suffer from overparameterization, which limits their performance gains. In this study, fuzzy sigmoid convolution (FSC) is introduced along with two additional modules: top-of-the-funnel and middle-of-the-funnel. The proposed methodology significantly reduces the number of trainable parameters without compromising classification accuracy. A novel convolutional operator is central to this approach, effectively dilating the receptive field while preserving input data integrity. This enables efficient feature map reduction and enhances the model's tumor detection capability. In the FSC-based model, fuzzy sigmoid activation functions are incorporated within convolutional layers to improve feature extraction and classification. The inclusion of fuzzy logic into the architecture improves its adaptability and robustness. Extensive experiments on three benchmark datasets demonstrate the superior performance and efficiency of the proposed model. The FSC-based architecture achieved classification accuracies of 99.17%, 99.75%, and 99.89% on three different datasets. The model employs 100 times fewer parameters than large-scale transfer learning architectures, highlighting its computational efficiency and suitability for detecting brain tumors early. This research offers lightweight, high-performance deep-learning models for medical imaging applications.