Probabilistic Range Queries (PRQ) retrieve objects which, according to imprecise object properties, are (with a given probability) inside a precise range. When the query range is based on some imprecise object properties, which makes the query range imprecise as well, then Uncertain Probabilistic Range Queries (UPRQ) arise. Unfortunately, in the literature UPRQs ranges are constrained to be balls, i.e., the range is defined by providing a certain radius around an imprecise object property. Moreover, another important issue is the efficiency of answering UPRQs due to the necessary numerical operations to calculate probabilities.

In this work we give a novel definition for UPRQs with query ranges of any shape; in addition we prove that any UPRQ can be reduced to a PRQ. Concerning the efficiency of UPRQs, we adopt and improve the usual way to address this family of queries (i.e., constructing indexes to prune/validate which objects belong to the answer, avoiding unnecessary numerical calculations) presenting: (1) a method to improve the filtering capabilities of the indexes when dealing with uniform distributions over rectangles or balls; and (2) a new index (eUD-Index), which enhances the state of the art, for any type of probability distribution. Our experiments show the feasibility of the proposals.

根据不精确的对象属性，概率范围查询（PRQ）检索对象（具有给定的概率）在精确范围内。当查询范围基于某些不精确的对象属性时，这也会使查询范围也不精确，因此会出现不确定概率范围查询（UPRQ）。不幸的是，在文献中，UPRQs的范围被约束为球形，即，该范围是通过围绕不精确的对象属性提供一定的半径来定义的。此外，另一个重要问题是由于计算概率所必需的数值运算，因此回答UPRQ的效率高。

在这项工作中，我们为具有任何形状的查询范围的UPRQ提供了新颖的定义。此外，我们证明任何UPRQ都可以简化为PRQ。关于UPRQ的效率，我们采用并改进了解决此系列查询的常用方法（即，构造索引以修剪/验证哪些对象属于答案，避免了不必要的数值计算），该方法提出：（1）一种改进处理矩形或球形的均匀分布时索引的过滤能力；（2）新索引（eUD-Index），用于增强任何类型概率分布的最新技术水平。我们的实验证明了这些建议的可行性。