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<p><b>Abstract</b>—Imprecise data in databases were originally denoted as <it>null values</it>, which represent the meaning of "values unknown at present." More generally, a partial value corresponds to a finite set of possible values for an attribute in which exactly one of the values is the "true" value. In this paper, we define a set of extended aggregate operations, namely <it>sum</it>, <it>average</it>, <it>count</it>, <it>maximum</it>, and <it>minimum</it>, which can be applied to an attribute containing partial values. Two types of aggregate operators are considered: <it>scalar aggregates</it> and <it>aggregate functions</it>. We study the properties of the aggregate operations and develop efficient algorithms for <it>count</it>, <it>maximum</it> and <it>minimum</it>. However, for <it>sum</it> and <it>average</it>, we point out that in general it takes exponential time complexity to do the computations.</p>
Relational databases, null values, partial values, scalar aggregates, aggregate functions, graph theory.

A. L. Chen, F. S. Tseng and J. Chiu, "Evaluating Aggregate Operations Over Imprecise Data," in IEEE Transactions on Knowledge & Data Engineering, vol. 8, no. , pp. 273-284, 1996.
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