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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.
Arbee L.P. Chen, Jui-Shang Chiu, Frank S.C. Tseng, "Evaluating Aggregate Operations Over Imprecise Data", IEEE Transactions on Knowledge & Data Engineering, vol. 8, no. , pp. 273-284, April 1996, doi:10.1109/69.494166
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