Formalization of OLAP-cubes and relational databases with the algebra of sets

摘要

Mathematical formalization of OLAP-cubes is developed. Dimensions of cube and Cartesian products are supplied with an algebra of sets and measure. These sets are involved in queries. Operations projection and cross section are consistent with the algebra of dimension. Relational connections between dimensions realized with the help of index maps on the works of these dimensions. We introduce three types of index maps to the dimension corresponding to the three types of relational ties. It is shown that the relational database is an OLAP-cube with the corresponding index maps, and can be written by one formula. As an example the analytical processing of the questionnaires