Imprecise data in databases were originally denoted as null values, 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. We define a set of extended aggregate operations, namely sum, average, count, maximum, and minimum, which can be applied to an attribute containing partial values. Two types of aggregate operators are considered: scalar aggregates and aggregate functions. We study the properties of the aggregate operations and develop efficient algorithms for count, maximum and minimum. However, for sum and average, we point out that in general it takes exponential time complexity to do the computations.

For original paper, see A. Ola and G. Ozsoyoglu, ibid., vol. 5, no. 2, pp. 293-308 (1993). In that paper, a family of relational database models (M-1 to M-5) were proposed to represent unknown values by intervals. Relational operators were extended for evaluating queries on these models. In this paper, we stultify the theorems, claiming that query evaluation in models M-2, M-3 and M-5 is sound.

We elaborate on how to interpret the query answer on exclusive disjunctive databases and how to reduce the query answer into a more concise form. Exclusive disjunctive data are represented as a pair of value set and variable set in Pv-table which is an extension of the relational model. A value set corresponds to a finite set of possible values in which exactly one value is the true value. By variable sets, tuples may be related with certain relationships, namely disjunctive relationship and join relationship. Three kinds of tuple sets are classified according to these relationships, each possesses an important property, namely co-exist, co-nonempty, or co-instance. Based on these properties, the interpretation of Pv-tables can be formalized in a semantically meaningful way, Also, the redundant and mergeable tuples can be identified. After removing and merging tuples accordingly, a more concise Pv-table can thus provide a better understanding of the query result.