Data reduction in Multidimensional Data Warehouses (MDWs) allows increasing the efficiency of analysis and facilitating decision-makers' tasks. In this paper, we model a MDW containing reduced data through a set of states. Each state is valid for a certain period of time; it contains only useful information according to decision-makers' needs. In order to carry out analyses in a MDW composed of multiple states, an extension of traditional OLAP analysis operators is required. In this paper, we define a set of OLAP operators compatible with reduced MDWs. For each operator, we propose a user-oriented definition along with an algorithmic translation. To show the feasibility and the efficiency of the proposed concepts, we implement the analysis operators in an R-OLAP framework.