The integration of rough sets into formal concept analysis is an important method for data analysis and information processing, which is of great significance for data knowledge discovery. Two rough approximation operators are defined in an interval-valued fuzzy formal context, and a new type of one-side concept lattice, namely, crisp-interval-valued fuzzy concept lattice, is derived, and its attribute reduction is meanly studied. According to the definition of attribute reduction of interval-valued fuzzy formal context, the judgement of consistent attribute sets is considered, and by using the techniques of discernibility matrix of rough sets, the calculation method of reducts is explored. The new concept model can provide new approaches for the knowledge discovery of interval-valued fuzzy formal contexts, and the obtained reduction method is beneficial to develop efficient attribute reduction algorithms.