Matrix Method for the Optimal Scale Selection of Multi-Scale Information Decision Systems

Abstract

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.

Optimal scale combination selection for inconsistent multi-scale decision tables

“…The relationship between rule extraction and feature matrix is further studied Chen et al 2019). Finally, the matrix is used to describe the scale combination, and the matrix method for optimal scale combination selection and the optimal scale combination keeping the positive region unchanged in the consistent and inconsistent generalized multi-scale decision information system are given, respectively.…”