Several large uncertain knowledge bases (KBs) are available on the Web where facts are associated with a certainty degree. When querying these uncertain KBs, users seek high-quality results, i.e., results that have a certainty degree greater than a given threshold α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}. However, as they usually have only a partial knowledge of the KB contents, their queries may be failing i.e., they return no result for the desired certainty level. To prevent this frustrating situation, instead of returning an empty set of answers, our approach explains the reasons of the failure with a set of α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}minimal failing subqueries (α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}MFSs) and computes alternative relaxed queries, called α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}maXimal succeeding subqueries (α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}XSSs), that are as close as possible to the initial failing query. Moreover, as the user may not always be able to provide an appropriate threshold α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}, we propose three algorithms to compute the α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}MFSs and α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}XSSs for other thresholds, which also constitutes a relevant feedback for the user. Multiple experiments with the WatDiv benchmark show the relevance of our algorithms compared to a baseline method.
