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Mathematics 2019, 7(3), 290; https://doi.org/10.3390/math7030290

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

1
Fujian Province University Key Laboratory of Computational Science, School of Mathematics Sciences, Huaqiao University, Quanzhou 362021, China
2
School of Mathematics Sciences and Statistics, Minnan Normal University, Zhangzhou 363000, China
*
Author to whom correspondence should be addressed.
Received: 22 January 2019 / Revised: 13 March 2019 / Accepted: 17 March 2019 / Published: 21 March 2019
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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. View Full-Text
Keywords: rough sets; information system; relation matrix; multi-scale decision system; scale selection rough sets; information system; relation matrix; multi-scale decision system; scale selection
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Chen, Y.S.; Li, J.J.; Huang, J.X. Matrix Method for the Optimal Scale Selection of Multi-Scale Information Decision Systems. Mathematics 2019, 7, 290.

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