Loreto Bravo

Abstract—Dimensions in Data Warehouses (DWs) are modeled using a hierarchical schema of categories. A dimension should satisfy a set of constraints to ensure that queries can be answered efficiently using pre-computed answers. For many reasons a dimension might become inconsistent and there might be several ways to fix it. In order to represent this uncertainty, we introduce the concept of extended dimensions, that is, dimensions where categories contain sets of elements which allow to represent ambiguity. In this article we formalize extended dimensions and a suitable way to answer queries from them. I. PROBLEM STATEMENT Data Warehouses (DWs) are data repositories that integrate data from different sources, and keep historical data for analysis and decision support. DWs organize data according to the multidimensional model, in which, dimensions reflect the perspectives upon which facts are viewed, and the facts correspond to events which are usually associated to numeric values known as measures, and are referenced using the dimension elements. Dimensions are modeled as hierarchies of elements, where each element belongs to a category. The categories are also organized into a hierarchy called hierarchy schema. Figure 1(a) shows a Football Teams dimension with