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Saddle point equilibrium model for uncertain discrete systems

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Abstract

Uncertainty theory is a newly founded mathematical tool for modeling subjective indeterminacy. This type of indeterminate events is described as uncertain events and measured by belief degrees. In this paper, a saddle point equilibrium game model is studied for an uncertain discrete system, where the system is disturbed by an uncertain event at each stage. Applying Bellman’s dynamic programming approach, recurrence equations for this model are presented. The explicit solution of a bang–bang game model for the uncertain discrete system is obtained. Furthermore, for general cases, a hybrid intelligent algorithm is provided to approximate the solution numerically. Finally, a discrete game of duopoly is discussed to show the effectiveness of our results.

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Acknowledgements

This work is sponsored by NUPTSF (Grant No. NY219137), Natural Science Foundation of Jiangsu Province (CN) (Grant No. BK20190723), National Natural Science Foundation of China (Grant No. 61673011) and Natural Science Foundation of Jiangsu Province (CN) (Grant No. BK20170916).

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Authors and Affiliations

  1. School of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Yun Sun

  2. School of Science, Nanjing Forestry University, Nanjing, 210037, China

    Hongyan Yan

  3. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Yuanguo Zhu

Authors
  1. Yun Sun
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  2. Hongyan Yan
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  3. Yuanguo Zhu
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Correspondence to Yuanguo Zhu.

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Communicated by V. Loia.

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Sun, Y., Yan, H. & Zhu, Y. Saddle point equilibrium model for uncertain discrete systems. Soft Comput 25, 1099–1112 (2021). https://doi.org/10.1007/s00500-020-05206-x

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