Alzheimer's disease (AD) is a neurodegenerative disorder characterized by a progressive cognitive decline, necessitating early diagnosis for effective treatment. This study presents the Relational Bi-level Aggregation Graph Convolutional Network with Dynamic Graph Learning and Puzzle Optimization for Alzheimer's Classification (RBAGCN-DGL-PO-AC), using denoised T1-weighted Magnetic Resonance Images (MRIs) collected from Alzheimer's Disease Neuroimaging Initiative (ADNI) repository. Addressing the impact of noise in medical imaging, the method employs advanced denoising techniques includes: the Modified Spline-Kernelled Chirplet Transform (MSKCT), Jump Gain Integral Recurrent Neural Network (JGIRNN), and Newton Time Extracting Wavelet Transform (NTEWT), to enhance the image quality. Key brain regions, crucial for classification such as hippocampal, lateral ventricle and posterior cingulate cortex are segmented using Attention Guided Generalized Intuitionistic Fuzzy C-Means Clustering (AG-GIFCMC). Feature extraction and classification using segmented outputs are performed with RBAGCN-DGL and puzzle optimization, categorize input images into Healthy Controls (HC), Early Mild Cognitive Impairment (EMCI), Late Mild Cognitive Impairment (LMCI), and Alzheimer's Disease (AD). To assess the effectiveness of the proposed method, we systematically examined the structural modifications to the RBAGCN-DGL-PO-AC model through extensive ablation studies. Experimental findings highlight that RBAGCN-DGL-PO-AC state-of-the art performance, with 99.25 % accuracy, outperforming existing methods including MSFFGCN_ADC, CNN_CAD_DBMRI, and FCNN_ADC, while reducing training time by 28.5 % and increasing inference speed by 32.7 %. Hence, the RBAGCN-DGL-PO-AC method enhances AD classification by integrating denoising, segmentation, and dynamic graph-based feature extraction, achieving superior accuracy and making it a valuable tool for clinical applications, ultimately improving patient outcomes and disease management. © 2025 Elsevier B.V., All rights reserved.