In multi-scale information systems, the information is often characterized at multi scales and multi levels. To facilitate the computational process of multi-scale information systems, we employ the matrix method to represent the multi-scale information systems and to select the optimal scale combination of multi-scale decision information systems in this study. To this end, we first describe some important concepts and properties of information systems using some relational matrices. The relational matrix is then introduced into multi-scale information systems, and used to describe some main concepts in systems, including the lower and upper approximate sets and the consistence of systems. Furthermore, from the view of the relation matrix, the scale significance is defined to describe the global optimal scale and the local optimal scale of multi-scale information systems. Finally, the relational matrix is used to compute the scale significance and to construct the optimal scale selection algorithms. The efficiency of these algorithms is examined by several practical examples and experiments.

Supplier selection is a MADM problem. In this paper, a new method to deal with the supplier selection problem is proposed. The work procedure is as follows: firstly, perfects the method of comparing grey numbers with their probability distribution. Secondly, applies the method of multiple attribute decision making based on dominance-base rough sets to the supplier selection problem. Finally, an example of supplier selection problem is used to illustrate the proposed approach.