Summary: At present, the three-way formal concept analysis is only applicable to the traditional formal context, and can’t deal with the formal context in the fuzzy environment. In order to solve this problem, this paper combines the three-way formal concept analysis with the theory of fuzzy set, proposes the fuzzy three-way operator and its inverse operator, and studies its related important properties. On this basis, two kinds of fuzzy three-way concepts are defined, namely attribute-induced fuzzy three-way concepts and object-induced fuzzy three-way concepts. Then, taking the object-induced fuzzy three-way concept as an example, the concept-cognitive learning approach to the fuzzy three-way concept is discussed, and the cognitive learning of the incomplete fuzzy three-way concept is realized in the environment. Finally, in order to explain and illustrate precisely the proposed theory, the paper gives a case study and designs an algorithm. At the same time, it uses some data sets for experimental evaluation. These results further enrich the theory of three-way formal concept analysis and concept-cognitive learning.