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Alzheimer's disease (AD) is a gradually progressing neurodegenerative irreversible disorder. Mild cognitive impairment convertible (MCIc) is the clinical forerunner of AD. Precise diagnosis of MCIc is essential for effective treatments to reduce the progressing rate of the disease. The other cognitive states included in this study are mild cognitive impairment non-convertible (MCInc) and cognitively normal (CN). MCInc is a stage in which aged people suffer from memory problems, but the stage will not lead to AD. The classification between MCIc and MCInc is crucial for the early detection of AD. In this work, an algorithm is proposed which concatenates the output layers of Xception, InceptionV3, and MobileNet pre-trained models. The algorithm is tested on the baseline T1-weighted structural magnetic resonance imaging (MRI) images obtained from Alzheimer's disease neuroimaging initiative database. The proposed algorithm provided multi-class classification accuracy of 85%. Also, the proposed algorithm gave an accuracy of 85% for classifying MCIc vs MCInc, an accuracy of 94% for classifying AD vs CN, and an accuracy of 92% for classifying MCIc vs CN. The results exhibit that the proposed algorithm outruns other state-of-the-art methods for the multi-class classification and classification between MCIc and MCInc.