Reactive motifs are short conserved sub-sequences discovered from functional regions of enzyme sequences. They can be used as an effective representation of proteins. However, lack of site information leads to a low-coverage power of reactive motifs. With the use of background knowledge, a generalisation method to make each reactive motif cover most of the enzyme sequences having similar function is needed. In this paper, we show that, a fuzzy concept lattice (FCL) provides an efficient representation of both single-value and multi-value biological background knowledge and an efficient computational support for the reactive motif generalisation. The result is a set of generalised reactive motifs with higher coverage than the initial reactive motifs. Compared to statistical and expert-based motifs, generalised reactive motifs with SVM classifier produce satisfactory classification accuracy in classifying new enzymes. Further, reactive motifs improve the interpretability of the results and provide more biological evidences to biologists. All of them are relevant to functional sites, and how they are combined to perform protein function is useful for numerous applications in bioinformatics.