Knowledge space theory, which uses mathematical language for the knowledge evaluation and learning guide of learners, belongs to the research field of mathematical psychology. Skills and problems are the two basic elements of knowledge space, and an in-depth study of the relationship between them is the inherent requirement of knowledge state description and knowledge structure analysis. In the existing knowledge space theory, no explicit bi-directional mapping between skills and problems has been established, which makes it difficult to put forward a knowledge structure analysis model under intuitive conceptual meanings. Moreover, the partial order relationship between knowledge states has not been clearly obtained, which is not conducive to depicting the differences between knowledge states and planning the learning path of learners. In addition, the existing achievements mainly focus on the classical knowledge space, without considering the uncertainties of data in practical problems. To this end, this study introduces formal concept analysis and fuzzy sets into knowledge space theory and builds the fuzzy concept lattice models for knowledge structure analysis. Specifically, fuzzy concept lattice models of knowledge space and closure space are presented. Firstly, the fuzzy concept lattice of knowledge space is constructed, and it is proved that the extents of all concepts form a knowledge space by the upper bounds of any two concepts. The idea of granule description is introduced to define the skill-induced atomic granules of problems, whose combinations can help determine whether a combination of problems is a state in the knowledge space. On this basis, a method to obtain the fuzzy concepts in the knowledge space from the problem combinations is proposed. Secondly, the fuzzy concept lattice of closure space is established, and it is proved that the extents of all concepts form the closure space by the lower bounds of any two concepts. Similarly, the problem-induced atomic granules of skills are defined, and their combinations can help determine whether a skill combination is the skills required by a knowledge state in the closure space. In this way, a method to obtain the fuzzy concepts in the closure space from the skill combinations is presented. Finally, the effects of the number of problems, the number of skills, the filling factor, and the analysis scale on the sizes of knowledge space and closure space are analyzed by some experiments. The results show that the fuzzy concepts in the knowledge space are different from any existing concept and cannot be derived from other concepts. The fuzzy concepts in the closure space are attribute-oriented one-sided fuzzy concepts in essence. In the formal context of two-valued skills, there is one-to-one correspondence between the states in knowledge space and closure space, but this relationship does not hold in the formal context of fuzzy skills.