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Evidence theory based optimal scale selection for multi-scale ordered decision systems

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Abstract

In real data sets, objects are usually measured by multiple scales under the same attribute. Many information systems are given dominance relations on account of various factors which make classical equivalence relations change accordingly. This paper investigates the optimal scale selection for multi-scale ordered decision systems based on evidence theory. Five concepts of optimal scales related to rough set theory and the Dempster–Shafer theory of evidence in multi-scale ordered information/decision systems are first defined. Relationships are then clarified among \(\ge\)-optimal scale, \(\ge\)-lower approximation and \(\ge\)-upper approximation optimal scales as well as \(\ge\)-belief and \(\ge\)-plausibility optimal scales in multi-scale ordered information systems and consistent multi-scale ordered decision systems respectively. Finally, in inconsistent multi-scale ordered decision systems, by introducing a notion of \(\ge\)-generalized decision optimal scale, relationships among different types of optimal scales are also examined.

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Acknowledgements

This work was supported by grants from the National Natural Science Foundation of China (grant numbers 61976194, 41631179 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

    Jia-Wen Zheng, Wei-Zhi Wu, Han Bao & An-Hui Tan

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

    Jia-Wen Zheng, Wei-Zhi Wu, Han Bao & An-Hui Tan

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  1. Jia-Wen Zheng
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  2. Wei-Zhi Wu
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  3. Han Bao
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  4. An-Hui Tan
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Correspondence to Wei-Zhi Wu.

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Zheng, JW., Wu, WZ., Bao, H. et al. Evidence theory based optimal scale selection for multi-scale ordered decision systems. Int. J. Mach. Learn. & Cyber. 13, 1115–1129 (2022). https://doi.org/10.1007/s13042-021-01438-x

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  • DOI: https://doi.org/10.1007/s13042-021-01438-x

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