A mathematical model of a decision support system aimed at stimulating the subject's intellectual activity for making intuitive-experimental decisions is considered. The model is based on semiotic mental space model built by an expert. Methods for solving the inverse problem for finding formal solutions to achieve some goal are proposed. To interpret of formal solutions, it is proposed to apply vector static (Word2Vec) and dynamic (ruBERT, ruGPT) language models obtained by training neural networks with a text corpus. Examples of formal solutions interpretation of the inverse problem with the help of the language vector models are considered, and their possibilities of stimulating the intellectual activity of the subject for making intuitive-experimental decisions are analyzed.