[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Rough approximations based on soft binary relations and knowledge bases

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Aktas H, Cağman N (2007) Soft sets and soft groups. Inf Sci 177:2726–2735

    Article  MathSciNet  MATH  Google Scholar 

  • Ali MI (2011) A note on soft sets, rough soft sets and fuzzy soft sets. Appl Soft Comput 13:3329–3332

    Google Scholar 

  • Davey BA, Priestley HA (1990) Introduction to lattices and order. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Feng F, Li C, Davvaz B, Irfan Ali M (2010) Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput 14:899–911

    Article  MATH  Google Scholar 

  • Feng F, Liu X, Leoreanu-Fotea V, Jun Y (2011) Soft sets and soft rough sets. Inf Sci 181:1125–1137

    Article  MathSciNet  MATH  Google Scholar 

  • Ge X, Li Z, Ge Y (2011) Topological spaces and soft sets. J Comput Anal Appl 13:881–885

    MathSciNet  MATH  Google Scholar 

  • Jiang Y, Tang Y, Chen Q, Wang J, Tang S (2010) Extending soft sets with description logics. Comput Math Appl 59:2087–2096

    Article  MathSciNet  MATH  Google Scholar 

  • Li Z, Xie T (2014) The relationship among soft sets, soft rough sets and topologies. Soft Comput 18:717–728

    Article  MATH  Google Scholar 

  • Li Z, Xie N, Wen G (2015) Soft coverings and their parameter reductions. Appl Soft Comput 31:48–60

    Article  Google Scholar 

  • Liu G, Zhu W (2008) The algebraic structures of generalized rough set theory. Inf Sci 178:4105–4113

    Article  MathSciNet  MATH  Google Scholar 

  • Maji PK, Roy AR (2002) An application of soft sets in a decision making problem. Comput Math Appl 44:1077–1083

    Article  MathSciNet  MATH  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9:589–602

    Google Scholar 

  • Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45:555–562

    Article  MathSciNet  MATH  Google Scholar 

  • Molodtsov D (1999) Soft set theory-first result. Comput Math Appl 37:19–31

    Article  MathSciNet  MATH  Google Scholar 

  • Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  • Pawlak Z, Skowron A (2007a) Rudiments of rough sets. Inf Sci 177:3–27

  • Pawlak Z, Skowron A (2007b) Rough sets: some extensions. Inf Sci 177:28–40

  • Pawlak Z, Skowron A (2007c) Rough sets and Boolean reasoning. Inf Sci 177:41–73

  • Qian Y, Liang J, Dang C (2009) Knowledge structure, knowledge granulation and knowledge distance in a knowledge base. Int J Approx Reason 50:174–188

    Article  MathSciNet  MATH  Google Scholar 

  • Qian Y, Zhang H, Li F, Hu Q, Liang J (2014) Set-based granular computing: a lattice model. Int J Approx Reason 55:834–852

    Article  MathSciNet  MATH  Google Scholar 

  • Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203:412–418

    Article  MATH  Google Scholar 

  • Shabir M, Naz M (2011) On soft topological spaces. Comput Math Appl 61:1786–1799

    Article  MathSciNet  MATH  Google Scholar 

  • Skowron A, Stepaniuk J (1996) Tolerance approximation spaces. Fundam Inform 27:245–253

    MathSciNet  MATH  Google Scholar 

  • Slowinski R, Vanderpooten D (1995) Similarity relation as a basis for rough approximations. ICS Res Rep 53:249–250

    Google Scholar 

  • Yao YY (1998) Constructive and algebraic methods of the theory of rough sets. Inf Sci 109:21–47

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang W, Wu W, Liang J, Li D (2001) Rough set theory and methods. Chinese Scientific Publishers, Beijing

    Google Scholar 

Download references

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.

Author information

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

Authors
  1. Zhaowen Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ningxin Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ninghua Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhaowen Li.

Ethics declarations

Conflict of interest

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

Additional information

Communicated by A. Di Nola.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-016-2077-2

Keywords

Search

Navigation