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Maximal consistent block based optimal scale selection for incomplete multi-scale information systems

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Abstract

Numerical incomplete data are common in many real-life applications, and they are often hierarchically structured at different levels of granularity. A numerical incomplete multi-scale information system (NIMIS) is a special hierarchical data set in which each object can take on different values at different scales. In such a data set, an important issue is to choose the optimal scale in order to maintain certain conditions for final decision. In this paper, by employing maximal consistent block technique, we study the optimal scale selection with various requirements in NIMISs and numerical incomplete multi-scale decision systems (NIMDSs). We first introduce the concept of scale in NIMISs and NIMDSs. We then define the optimal scale and the maximal consistent block based optimal scale. Finally, we examine the relationship between the maximal consistent block based optimal scale and the optimal scale. We show that the maximal consistent block based optimal scale and the optimal scale are equivalent for both NIMISs and consistent NIMDSs. And in inconsistent NIMDSs, there is no static relationship between notions of the maximal consistent block based lower-approximation optimal scale and the upper-approximation optimal scale.

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Acknowledgements

This work was supported by grants from the National Natural Science Foundation of China (grant numbers 61976194 and 62076221).

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Authors and Affiliations

  1. School of Information Engineering, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, People’s Republic of China

    Yu Sun, Wei-Zhi Wu & Xia Wang

  2. Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, People’s Republic of China

    Yu Sun, Wei-Zhi Wu & Xia Wang

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  1. Yu Sun
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Correspondence to Wei-Zhi Wu.

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Sun, Y., Wu, WZ. & Wang, X. Maximal consistent block based optimal scale selection for incomplete multi-scale information systems. Int. J. Mach. Learn. & Cyber. 14, 1797–1809 (2023). https://doi.org/10.1007/s13042-022-01728-y

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