In designing online analytical processing (OLAP) databases or preparing data warehouses providing the bases of OLAP data marts, it is an essential aspect to define index and measure attributes that are suitable for aggregating basic values along some other attributes: dimensions. The authors of this paper give a thorough discussion on the former investigation of the theme, referring mostly to the work of H.-J. Lenz and A. Shoshani [1], and of R. Kimball and M. Ross [2]. They give a measure categorization, which is a synthesis (generalization and a refinement) of the two aforementioned ones. Moreover, they give formal definitions for the categories, describe criteria, and characterize an implemented tool to determine whether a limited multidimensional expressions (MDX)-like query calculates valid aggregations or not. Beyond summarization, the treatment covers the varied behavior of the common statistical scales and aggregation functions. They generalize those properties of temporal dimensions that make it possible to reckon correct aggregations of index attributes along the temporal-like ones (some geography dimensions, for example).

The notions introduced in the paper are clarified by many relevant and effective examples, most of them based on a simple database.

In the concluding part of the paper, the authors enumerate the novelties of their work. Then, they discuss possible future work.

The authors propose that this descriptive formal theory and algorithmic model (categorization information and rules) should be incorporated in practical applications in the meta-database (possibly with the help of suitably improved OLAP designer tools), instead of their proof-of-concept implementation examining MDX-like queries on the ground level. They would construct unified modeling language (UML) classes based on their model.

I recommend this paper for those who are interested in the theory or the implementation of OLAP database design tools or databases themselves.