The rapid progression of diseases in the elderly, such as Alzheimer's Dementia (AD), necessitates effective early detection mechanisms to ensure appropriate healthcare provision. Given the consistently increasing prevalence of AD, the potential for emerging socio-economic challenges is significant. This underlines the importance of developing early detection strategies to mitigate the progression of this disease. Electroencephalograms (EEG) present a promising avenue for the early diagnosis of AD. EEG signals harbor crucial information pertaining to neuronal death triggered by amyloid plaque accumulation, a characteristic feature of AD. Spectral analysis reveals a deceleration in signal activity in AD patients when compared to healthy elderly individuals. However, this method is frequently compromised by low-frequency noise, necessitating the exploration of alternative approaches for analyzing EEG signal features for early AD detection. Considering the complex nature of EEG signals, it is hypothesized that pathological conditions, such as AD, may induce alterations in signal complexity. In this study, an early detection model for AD was simulated utilizing an approach that focused on EEG signal complexity. Complexity analysis, incorporating Spectral Entropy (SpecEn) and fractal dimensions, was calculated across 19 EEG channels from a total of 34 subjects (16 normal and 18 with Mild Cognitive Impairment (MCI)). Performance validation of the proposed method was achieved through Linear Discriminant Analysis (LDA), yielding an accuracy of 82.4%, specificity of 77.8%, and sensitivity of 87.5%. The findings from this study suggest that EEG analysis can serve as a reliable tool for the early detection of AD.