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Rough approximations based on soft binary relations and knowledge bases

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Abstract

This paper studies rough approximations based on soft binary relations. Firstly, two pairs of rough approximations based on soft binary relations are investigated, and their properties are determined. Secondly, rough sets with respect to some parameter and the set of parameters are introduced, and the fact that every rough set is a special case of E-rough sets where E is the set of parameters is demonstrated. Thirdly, rough soft sets induced by soft binary relations are proposed, and their lattice structures are given. Fourthly, two kinds of topologies induced by soft reflexive relations are investigated. Finally, the fact that there exists a one-to-one correspondence between the family of all knowledge bases and the family of all soft equivalence relations is proved, and soft characterizations of knowledge structures in knowledge bases are provided, which shows that we can study knowledge bases using soft set theory.

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Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for their valuable suggestions which have helped immensely in improving the quality of the paper. This work is supported by the National Natural Science Foundation of China (11461005), the Natural Science Foundation of Guangxi (2014GXNSFAA118001), Guangxi University Science and Technology Research Project (KY2015YB075, KY2015YB081, KY2015YB266), Special Funds of Guangxi Distinguished Experts Construction Engineering and Key Laboratory of Optimization Control and Engineering Calculation in Department of Guangxi Education.

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Authors and Affiliations

  1. School of Science, Guangxi University for Nationalities, Nanning, 530006, Guangxi, China

    Zhaowen Li & Ninghua Gao

  2. College of Information Science and Engineering, Guangxi University for Nationalities, Nanning, 530006, Guangxi, China

    Ningxin Xie

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  1. Zhaowen Li
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  2. Ningxin Xie
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  3. Ninghua Gao
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Correspondence to Zhaowen Li.

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All authors declare that they have no conflicts of interest regarding the publication of this manuscript.

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Communicated by A. Di Nola.

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Li, Z., Xie, N. & Gao, N. Rough approximations based on soft binary relations and knowledge bases. Soft Comput 21, 839–852 (2017). https://doi.org/10.1007/s00500-016-2077-2

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