Telling the user that there is no result for his/her query is very poorly informative and corresponds to the kind of situation cooperative systems try to avoid. Cooperative systems should rather explain the reason(s) of the failure, materialized by Minimal Failing Subqueries (MFS), and build alternative succeeding queries, called maXimal Succeeding Subqueries (XSS), that are as close as possible to the original query. In the particular context of fuzzy querying, we propose an efficient unified approach to the computation of gradual MFSs and XSSs that relies on a fuzzy-cardinality-based summary of the relevant part of the database.