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A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making

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Abstract

This paper introduces the notion of Z-soft rough fuzzy sets of hemirings, which is an extended notion of soft rough sets and rough fuzzy sets. It is pointed out that this novel concept removes the limiting condition that full soft sets require in Feng-soft rough fuzzy sets and Meng-soft rough fuzzy sets. We study roughness in hemirings with respect to a ZS-approximation space. Some new soft rough fuzzy operations over hemirings are explored. In particular, Z-lower and Z-upper soft rough fuzzy ideals (k-ideals, h-ideals, strong h-ideals) are investigated. Finally, we put forth an approach for decision making problem based on Z-soft rough fuzzy sets and give an example. Corresponding decision making methods based on Z-soft rough fuzzy sets are analysed.

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Acknowledgments

This research is partially supported by a grant of National Natural Science Foundation of China (11561023).

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Authors and Affiliations

  1. Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei Province, 445000, China

    Jianming Zhan & Kuanyun Zhu

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  1. Jianming Zhan
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  2. Kuanyun Zhu
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Correspondence to Jianming Zhan.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by A. Di Nola.

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Zhan, J., Zhu, K. A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making. Soft Comput 21, 1923–1936 (2017). https://doi.org/10.1007/s00500-016-2119-9

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