This paper presents the FuzzyDistillViT-MobileNet model, a novel approach for lung cancer (LC) classification, leveraging dynamic fuzzy logic-driven knowledge distillation (KD) to address uncertainty and complexity in disease diagnosis. Unlike traditional models that rely on static KD with fixed weights, our method dynamically adjusts the distillation weight using fuzzy logic, enabling the student model to focus on high-confidence regions while reducing attention to ambiguous areas. This dynamic adjustment improves the model ability to handle varying uncertainty levels across different regions of LC images. We employ the Vision Transformer (ViT-B32) as the instructor model, which effectively transfers knowledge to the student model, MobileNet, enhancing the student generalization capabilities. The training process is further optimized using a dynamic wait adjustment mechanism that adapts the training procedure for improved convergence and performance. To enhance image quality, we introduce pixel-level image fusion improvement techniques such as Gamma correction and Histogram Equalization. The processed images (Pix1 and Pix2) are fused using a wavelet-based fusion method to improve image resolution and feature preservation. This fusion method uses the wavedec2 function to standardize images to a 224x224 resolution, decompose them into multi-scale frequency components, and recursively average coefficients at each level for better feature representation. To address computational efficiency, Genetic Algorithm (GA) is used to select the most suitable pre-trained student model from a pool of 12 candidates, balancing model performance with computational cost. The model is evaluated on two datasets, including LC25000 histopathological images (99.16% accuracy) and IQOTH/NCCD CT-scan images (99.54% accuracy), demonstrating robustness across different imaging domains.