Alzheimer's disease (AD) is a devastating neurological condition affecting a significant portion of the world's aging population. Magnetic resonance imaging (MRI) has been widely adopted to visualize and analyze the structural atrophies and other brain deformities caused by AD. Due to the differences in brain anatomy, brain sub-regions such as grey matter (GM), white matter (WM), and cerebrospinal fluid (CSF) deteriorate. Research shows that changes in GM, WM, and CSF are among the earliest detectable AD markers, supporting their use in early diagnosis and monitoring disease progression. In this paper, GM, WM, and CSF have been extracted from the T1-weighted MRI scan acquired from the ADNI database. A fine-tuned DL model has been implemented for automated and all levels of feature extraction. For classification, the data points from the input space are explicitly translated into a randomized feature space using a neural network with randomly generated weights for the hidden layer. After feature projection, the extended features train classification models, where two non-parallel hyperplanes are optimized, with all associated parameters undergoing fuzzification to enhance model robustness. The proposed classifier, a randomized vectored fuzzy least square twin support vector machine, adeptly manages the challenges of uncertain, imbalanced, and nonlinear data commonly found in medical imaging. It integrates fuzzy membership functions to systematically address data uncertainty and employs a least squares formulation to optimize the model efficiently, ensuring high accuracy and scalability. The performance of the proposed model is tested and compared with popular state-of-the-art models, showing significant improvements in effectiveness.