Skip to main content
SpringerLink
Log in

Generalized rough set models determined by multiple neighborhoods generated from a similarity relation

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

Abstract

Rough set theory is widely used to deal with uncertainty. Original rough set model is mainly based on equivalence relations. To extend the application scope, classical rough set model based on equivalence relations is generalized to rough set model based on similarity relations. In the present paper, we propose and investigate three new generalized rough set models by introducing new definitions of lower and upper approximations based on multiple neighborhoods generated from a similarity relation. The characteristics of the proposed approximations are investigated. Theoretically, analysis indicates the monotonicity of the corresponding uncertainty measures including accuracy, roughness and approximation accuracy. Experiments indicate that the constructed monotonic measures can be used in attribute reduction.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Abo-Tabl EA (2011) A comparison of two kinds of definitions of rough approximations based on a similarity relation. Inf Sci 181(12):2587–2596

    Article  MathSciNet  MATH  Google Scholar 

  • Abu-Donia HM (2008) Comparison between different kinds of approximations by using a family of binary relations. Knowl Based Syst 21(8):911–919

    Article  Google Scholar 

  • Abu-Donia HM (2012) Multi knowledge based rough approximations and applications. Knowl Based Syst 26:20–29

    Article  Google Scholar 

  • Blake C, Merz C (2016) UCI repository of machine learning databases. In: http://www.ics.uci.edu/mlearn/mlrepository.html

  • Dai J (2013) Rough set approach to incomplete numerical data. Inf Sci 241:43–57

    Article  MathSciNet  MATH  Google Scholar 

  • Dai J, Tian H (2013) Fuzzy rough set model for set-valued data. Fuzzy Sets Syst 229:54–68

    Article  MathSciNet  MATH  Google Scholar 

  • Dai J, Xu Q (2012) Approximations and uncertainty measures in incomplete information systems. Inf Sci 198:62–80

    Article  MathSciNet  MATH  Google Scholar 

  • Dai J, Xu Q (2013) Attribute selection based on information gain ratio in fuzzy rough set theory with application to tumor classification. Appl Soft Comput 13(1):211–221

    Article  Google Scholar 

  • Dai J, Wang W, Xu Q, Tian H (2012a) Uncertainty measurement for interval-valued decision systems based on extended conditional entropy. Knowl Based Syst 27:443–450

  • Dai J, Xu Q, Wang W, Tian H (2012b) Conditional entropy for incomplete decision systems and its application in data mining. Int J Gen Syst 41(7):713–728

    Article  MathSciNet  MATH  Google Scholar 

  • Dai J, Wang W, Mi JS (2013a) Uncertainty measurement for interval-valued information systems. Inf Sci 251:63–78

    Article  MathSciNet  MATH  Google Scholar 

  • Dai J, Wang W, Tian H, Liu L (2013b) Attribute selection based on a new conditional entropy for incomplete decision systems. Knowl Based Syst 39:207–213

    Article  Google Scholar 

  • Dai J, Wang W, Xu Q (2013c) An uncertainty measure for incomplete decision tables and its applications. IEEE Trans Cybern 43(4):1277–1289

    Article  Google Scholar 

  • Dai J, Han H, Hu Q, Liu M (2016a) Discrete particle swarm optimization approach for cost sensitive attribute reduction. Knowl Based Syst 102:116–126

    Article  Google Scholar 

  • Dai J, Han H, Zhang X, Liu M, Wan S, Liu J, Lu Z (2016) Catoptrical rough set model on two universes using granule-based definition and its variable precision extensions. Inf Sci 390:70–81

  • Grzymala-Busse J, Rzasa W (2006) Local and global approximations for incomplete data. Lect Notes Comput Sci 4259:244–253

    Article  MathSciNet  MATH  Google Scholar 

  • Kryszkiewicz M (1998) Rough set approach to incomplete information systems. Inf sci 112(1–4):39–49

    Article  MathSciNet  MATH  Google Scholar 

  • Kryszkiewicz M (1999) Rules in incomplete information systems. Inf sci 113(3):271–292

    Article  MathSciNet  MATH  Google Scholar 

  • Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356

    Article  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Slowinski R, Vanderpooten D (2000) A genaralized definition of rough approximations based on similarity. IEEE Trans Knowl Data Eng 12:331–336

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Yao YY (1998b) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 111(1–4):239–259

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang X, Dai J, Yu Y (2015) On the union and intersection operations of rough sets based on various approximation spaces. Inf Sci 292:214–229

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu W (2007) Generalized rough sets based on relations. Inf Sci 177(22):4997–5011

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Nos. 61473259, 61070074, 60703038), the Zhejiang Provincial Natural Science Foundation (No. LY14F020029), the National Science and Technology Support Program of China (2015BAK26B00, 2015BAK26B01, 2015BAK26B02) and the PEIYANG Young Scholars Program of Tianjin University (2016XRX-0001).

Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Tianjin University, Tianjin, 300350, China

    Jianhua Dai & Shuaichao Gao

  2. Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), Hunan Normal University, Changsha, 410081, China

    Jianhua Dai

  3. College of Computer Science and Technology, Zhejiang University, Hangzhou, 310027, China

    Guojie Zheng

Authors
  1. Jianhua Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shuaichao Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guojie Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianhua Dai.

Ethics declarations

Conflict of interest

All authors declare that they have no conflict of interest.

Ethical approval

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

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

Dai, J., Gao, S. & Zheng, G. Generalized rough set models determined by multiple neighborhoods generated from a similarity relation. Soft Comput 22, 2081–2094 (2018). https://doi.org/10.1007/s00500-017-2672-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-017-2672-x

Keywords

Search

Navigation