The ability to identify neuronal damage resulting from HIV-1-associated dementia (HAD) is crucial for designing specific therapies for the treatment of HAD. This paper proposes a two-class model of multiple criteria linear programming (MCLP) to classify the HAD neural dendritic and synaptic damages. The damages are measured by a number of quantitative variables such as the change of neuritis, arbors, branch nodes, and cell bodies. Given certain classes, including brain derived neurotrophic factor (BDNF) treatment, non-treatment, glutamate treatment, and gpl20 (HIV-1 envelop protein) from laboratory cell observations, we use the two-class MCLP model to learn the data patterns between two classes so that we can discover the knowledge about the HAD neural dendritic and synaptic damages under different treatments. This knowledge can be applied to design and study specific therapies for the prevention or reversal of the neuronal demise associated with HAD. In the paper, we first describe the technical background of the two-class models that includes concepts, modeling and computer algorithms. Then, we conduct a series of learning experimental tests on the data of laboratory cell observations. We also illustrate some significance and implications of learning results in the HAD research.