Skip to main content

Unifying Reducts in Formal Concept Analysis and Rough Set Theory

  • Chapter
  • First Online:
Trends in Mathematics and Computational Intelligence

Abstract

Attribute reduction is a fundamental part in different mathematical tools devoted to data analysis, such as, Rough Set Theory and Formal Concept Analysis. These last mathematical theories are closely related and, in this paper, we establish connections between attribute reduction in both frameworks. Mainly, we have introduced a sufficient and necessary condition in order to ensure that the reducts in both theories coincide.

Partially supported by the State Research Agency (AEI) and the European Regional Development Fund (ERDF) project TIN2016-76653-P.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    We assume that the reader is familiar with the notions related to classical theory of propositional logic [6, 8].

References

  1. Benítez, M., Medina, J., Ślȩzak, D.: Delta-information reducts and bireducts. In: Alonso, J.M., Bustince, H., Reformat, M. (eds.) 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (IFSA- EUSFLAT-15), Gijón, Spain, pp. 1154–1160. Atlantis Press (2015)

    Google Scholar 

  2. Benítez, M., Medina, J., Ślȩzak, D.: Reducing information systems considering similarity relations. In: Kacprzyk, J., Koczy, L., Medina, J. (eds.) 7th European Symposium on Computational Intelligence and Mathematics (ESCIM 2015), pp. 257–263 (2015)

    Google Scholar 

  3. Benítez-Caballero, M.J., Medina, J., Ramírez-Poussa, E.: Attribute Reduction in Rough Set Theory and Formal Concept Analysis, pp. 513–525. Springer International Publishing, Cham (2017)

    Chapter  Google Scholar 

  4. Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: Irreducible elements in multi-adjoint concept lattices. In: International Conference on Fuzzy Logic and Technology, EUSFLAT, vol. 2013, pp. 125–131 (2013)

    Google Scholar 

  5. Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: Attribute reduction in multi-adjoint concept lattices. Inf. Sci. 294, 41–56 (2015)

    Article  MathSciNet  Google Scholar 

  6. Davey, B., Priestley, H.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press (2002)

    Google Scholar 

  7. Dias, S., Vieira, N.: Reducing the size of concept lattices: the JBOS approach. In: 7th International Conference on Concept Lattices and Their Applications (CLA 2010), vol. 672, pp. 80–91 (2010)

    Google Scholar 

  8. Gabbay, D.M., Guenthner, F. (eds.): Handbook of Philosophical Logic. Volume I: Elements of Classical Logic, vol. I. Springer Netherlands (1983)

    Google Scholar 

  9. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundation. Springer (1999)

    Google Scholar 

  10. Janusz, A., Ślȩzak, D., Nguyen, H.S.: Unsupervised similarity learning from textual data. Fundam. Inf. 119(319–336), 01 (2012)

    MathSciNet  MATH  Google Scholar 

  11. Medina, J.: Relating attribute reduction in formal, object-oriented and property-oriented concept lattices. Comput. Math. Appl. 64(6), 1992–2002 (2012)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  13. Ślȩzak, D., Janusz, A.: Ensembles of bireducts: towards robust classification and simple representation. In: Kim, T.-H., Adeli, H., Ślȩzak, D., Sandnes, F., Song, X., Chung, K.-I., Arnett, K. (eds.) Future Generation Information Technology. Lecture Notes in Computer Science, vol. 7105, pp. 64–77. Springer, Berlin (2011)

    Chapter  Google Scholar 

  14. Stawicki, S., Ślȩzak, D.: Recent advances in decision bireducts: complexity, heuristics and streams. In: Lecture Notes in Computer Science, vol. 8171, pp. 200–212 (2013)

    Chapter  Google Scholar 

  15. Wei, L., Qi, J.-J.: Relation between concept lattice reduction and rough set reduction. Knowl. Based Syst. 23(8), 934–938 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Eloísa Ramírez-Poussa .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Benítez-Caballero, M.J., Medina, J., Ramírez-Poussa, E. (2019). Unifying Reducts in Formal Concept Analysis and Rough Set Theory. In: Cornejo, M., Kóczy, L., Medina, J., De Barros Ruano, A. (eds) Trends in Mathematics and Computational Intelligence. Studies in Computational Intelligence, vol 796. Springer, Cham. https://doi.org/10.1007/978-3-030-00485-9_10

Download citation

Publish with us

Policies and ethics