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Covering-based soft fuzzy rough theory and its application to multiple criteria decision making

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Abstract

Covering-based rough set model is a vital topic as a generalization of rough sets which is a tool for AI and data mining. For the purpose, we establish two classes of hybrid uncertain systems: soft rough fuzzy-covering models and soft fuzzy rough covering models by means of (fuzzy) soft neighborhoods. By means of fuzzy soft measure degrees, we deduce \(\alpha \)-soft rough fuzzy coverings, D-soft rough fuzzy coverings, \(\alpha \)-soft fuzzy rough coverings, and D-soft fuzzy rough coverings by these two hybrid uncertain systems, respectively. The relationships among the proposed covering-based rough set models are given. Based on the theoretical discussion for the combination of covering fuzzy rough sets and soft sets, we set forth a new method to multiple criteria decision-making problem. By comparative analysis, we obtain that the optimal results are the same between the aggregation operator method and our proposed method, which means that our method is reasonable and effective.

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Acknowledgements

The authors are thankful to associate editor and anonymous referees for their valuable comments on our manuscript. This research was supported by NNSFC (61866011; 11561023; 71571090; 61772019), the Fundamental Research Funds for the Central Universities (JB190602), the Youth Innovation Team of Shaanxi Universities, the Interdisciplinary Foundation of Humanities and Information (RW180167), and the National Science Foundation of Hubei Province (2017CFB353).

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  1. Department of Mathematics, Hubei Minzu University, Enshi, 445000, China

    Jianming Zhan

  2. School of Economics and Management, Xidian University, Xi’an, 710071, China

    Bingzhen Sun

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  1. Jianming Zhan
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Correspondence to Jianming Zhan.

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Zhan, J., Sun, B. Covering-based soft fuzzy rough theory and its application to multiple criteria decision making. Comp. Appl. Math. 38, 149 (2019). https://doi.org/10.1007/s40314-019-0931-4

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