The last few years, we have studied different set pattern mining techniques from binary data. It includes the computation of formal concepts to support various knowledge discovery processes. For instance, when considering post-genomics, we can exploit Boolean data sets that encode a relation between some genes and the proteins that may regulate them. In such a context, it appears interesting to exploit the analogy between a putative transcriptional module (i.e., a typically important hypothesis for gene regulation understanding) and a formal concept that holds within such data. In this paper, we assume that knowledge nuggets can be captured by collections of formal concepts and we discuss the challenging issue of mining/selecting actionable patterns from these collections, i.e., looking for relevant patterns that really support knowledge discovery. Therefore, a major issue concerns the computation of complete collections of formal concepts that satisfy user-defined constraints. This is useful not only to avoid the computation of too small patterns that might be due to noise (e.g., using size constraints on both their intents and extents) but also to introduce some fault-tolerance. We discuss the pros and the cons of some recent proposals in that direction.