The paper presents a comprehensive study on predictive models for Alzheimer's disease (AD) and Mild cognitive impairment (MCI) diagnosis, implementing a combination of cognitive scores and artificial intelligence algorithms. The research includes detailed analyses of clinical and demographic variables such as age, education, and various cognitive and functional scores, investigating their distributions and correlations with AD and MCI. The study utilizes several machine-learning classifiers, comparing their performance through metrics like accuracy, precision, and area under the ROC curve (AUC). Key findings include the influence of gender on AD prevalence, the potential protective effect of education, and the significance of functional decline and cognitive performance scores in the models. The results demonstrate the effectiveness of ensemble methods and the robustness of the models across different data subsets, highlighting the potential of artificial intelligence in enhancing diagnostic accuracy for Alzheimer's disease and Mild cognitive impairment.