In the psychological assessment, product design, product testing and evaluation, personnel training, human-computer interaction, artificial intelligence and other fields, user’s thinking, user expectations and other brain activities of user are desired to know, these brain activities are summarized as user cognition in this paper. As a complex subject, user cognition is difficult to encode and measure because of its subjectivity, ambiguity and evolvability, system or expert will not be able to make decision if user cognition could not be understood, therefore, there are obstacles to human-computer interaction, product design and evaluation, user psychological assessment, etc. Scholars from philosophy, linguistics, psychology, education, library science, management science and computational science and other fields tried to perceive and visualize user cognition. There are flaws: over-reliance on experts which lead to a strong subjectivity; unable to express user cognition mathematically but descript it; no analysis of the membership. In order to solve the problems mentioned above, fuzzy expression and concept extension were applied to express user cognition. The concept of cognition derived from cognitive psychology, it is the mental action or process of acquiring knowledge and understanding through thought, experience, and the senses. Previous studies on user cognition mostly based on statistical mathematics which prefer focusing on results to expression of research object. With the development of computer technology, the emergence of machine learning, deep neural networks and artificial intelligence technology are used to user cognition study, Machine understanding research is becoming more and more important, Research on the mathematical expression of user cognition solves the problem essentially. Therefore, fuzzy expression was applied to express user cognition which convert the research of complex subject into the research on behalf of its factor set. A solution was proposed that using internet big data to get factor set which was processed in quantity by weighting algorithm and fuzzy statistics. Take intelligent refrigerator for the research object in this paper. Crawl fifty thousand pages on the internet to acquire factor set related to intelligent refrigerator. Each membership of factor was computed to verify the authenticity of the factor set which turn out all the membership of factors are in a high value. To further demonstration that factor set reflect the user cognition acquired by fuzzy expression and text mining (FE-TM), our research group has conducted a traditional user research (TUR) lasted for two months, including online survey, competitive analysis, user in-depth interviews, questionnaire survey, its experimental data was compared to FE-TM. As it shows in table 2 that the experimental data of FE-TM has good coherence with experimental data of TUR which means FE-TM has a high practical and scientific. Since all the factors and its membership are both acquired and computed, mathematical expression of user cognition is finally settled and proved. User cognition is a very basic concept in cognitive psychology disciplines. Although the concept of cognition proposed for a long time, but the research on mathematics expression of user cognition is rare which make it impossible to deeper studies. For example, In the field of cognitive psychology, it is a consensus that user cognition and user behavior has a certain relevance, but what is the relationship? Whether the relationship enables the mutual conversion between each other? How to use their relationship to achieve more natural and more dimensions of human-computer interaction is rarely studied. In this paper, fuzzy expression and text mining technology together were applied to express user cognition which was demonstrated through the intelligent refrigerator project. More importantly, this solution is suitable for any other complex objects. Compared with the traditional methods of user research, this solution has the following advantages: more sensitive perception of new technologies; predict trends of user cognition; provide a basis theory for further research; saving consumption with high precision.