Recently, there have been several attempts to propose definitions and algorithms for ranking queries on probabilistic data. However, these lack many intuitive properties of a top-k over deterministic data. We define numerous fundamental properties, including exact-k, containment, unique-rank, value-invariance, and stability, which are satisfied by ranking queries on certain data. We argue these properties should also be carefully studied in defining ranking queries in probabilistic data, and fulfilled by definition for ranking uncertain data for most applications. We propose an intuitive new ranking definition based on the observation that the ranks of a tuple across all possible worlds represent a well-founded rank distribution. We studied the ranking definitions based on the expectation, the median and other statistics of this rank distribution for a tuple and derived the expected rank, median rank and quantile rank correspondingly. We are able to prove that the expected rank, median rank and quantile rank satisfy all these properties for a ranking query. We provide efficient solutions to compute such rankings across the major models of uncertain data, such as attribute-level and tuple-level uncertainty. Finally, a comprehensive experimental study confirms the effectiveness of our approach.
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