Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Study on the Necessity Operator to Factorize Formal Contexts in a Multi-adjoint Framework

  • Conference paper
  • First Online:
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1601))

Abstract

Dubois and Prade have already shown that the necessity operator is helpful in the decomposition of Boolean data tables into independent sub-tables. In this paper, we carry out a preliminary study on the properties satisfied by the necessity operator to factorize formal contexts. We will see what properties this operator satisfies in the classical framework and how these properties are translated into more general frameworks, such as the fuzzy framework provided by the multi-adjoint paradigm.

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

Access this chapter

Log in via an institution

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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Antoni, L., Cornejo, M.E., Medina, J., Ramirez, E.: Attribute classification and reduct computation in multi-adjoint concept lattices. IEEE Trans. Fuzzy Syst. 29, 1 (2020)

    Google Scholar 

  2. Bělohlávek, R.: Fuzzy concepts and conceptual structures: induced similarities. In: Joint Conference on Information Sciences, pp. 179–182 (1998)

    Google Scholar 

  3. Bělohlávek, R.: Optimal decompositions of matrices with entries from residuated lattices. J. Logic Comput. 22, 1–21 (2011)

    MathSciNet  Google Scholar 

  4. Belohlavek, R., Krmelova, M.: Beyond boolean matrix decompositions: toward factor analysis and dimensionality reduction of ordinal data. In: 2013 IEEE 13th International Conference on Data Mining, pp. 961–966 (2013)

    Google Scholar 

  5. Belohlavek, R., Outrata, J., Trnecka, M.: Factorizing boolean matrices using formal concepts and iterative usage of essential entries. Inf. Sci. 489, 37–49 (2019)

    Article  MathSciNet  Google Scholar 

  6. Belohlavek, R., Trnecka, M.: A new algorithm for boolean matrix factorization which admits overcovering. Discrete Appli. Math. 249, 6–52 (2018). Concept Lattices and Applications: Recent Advances and New Opportunities

    Google Scholar 

  7. Bělohlávek, R., Trneckova, M.: Factorization of matrices with grades via essential entries. Fuzzy Sets Syst. 360, 97–116 (2019)

    Article  MathSciNet  Google Scholar 

  8. Belohlavek, R., Vychodil, V.: Discovery of optimal factors in binary data via a novel method of matrix decomposition. J. Comput. Syst. Sci. 76(1), 3–20 (2010). Special Issue on Intelligent Data Analysis

    Google Scholar 

  9. Burusco, A., Fuentes-González, R.: The study of \({L}\)-fuzzy concept lattice. Math. Soft Comput. 3, 209–218 (1994)

    MathSciNet  MATH  Google Scholar 

  10. Chen, Y., Yao, Y.: A multiview approach for intelligent data analysis based on data operators. Inf. Sci. 178(1), 1–20 (2008)

    Article  MathSciNet  Google Scholar 

  11. Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: A comparative study of adjoint triples. Fuzzy Sets Syst. 211, 1–14 (2013)

    Article  MathSciNet  Google Scholar 

  12. 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 

  13. Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: Characterizing reducts in multi-adjoint concept lattices. Inf. Sci. 422, 364–376 (2018)

    Article  MathSciNet  Google Scholar 

  14. Dubois, D., de Saint-Cyr, F.D., Prade, H.: A possibility-theoretic view of formal concept analysis. Fund. Inform. 75(1–4), 195–213 (2007)

    MathSciNet  MATH  Google Scholar 

  15. Dubois, D., Prade, H.: Possibility theory and formal concept analysis: characterizing independent sub-contexts. Fuzzy Sets Syst. 196, 4–16 (2012)

    Article  MathSciNet  Google Scholar 

  16. Ganter, B., Wille, R.: Formal Concept Analysis. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-642-59830-2

    Book  MATH  Google Scholar 

  17. Gediga, G., Düntsch, I.: Modal-style operators in qualitative data analysis. In: Proceedings IEEE International Conference on Data Mining, pp. 155–162 (2002)

    Google Scholar 

  18. Georgescu, G., Popescu, A.: Non-dual fuzzy connections. Arch. Math. Log. 43(8), 1009–1039 (2004)

    Article  MathSciNet  Google Scholar 

  19. Medina, J.: Multi-adjoint property-oriented and object-oriented concept lattices. Inf. Sci. 190, 95–106 (2012)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  21. Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: Formal concept analysis via multi-adjoint concept lattices. Fuzzy Sets Syst. 160(2), 130–144 (2009)

    Article  MathSciNet  Google Scholar 

  22. Yao, Y., Chen, Y.: Rough set approximations in formal concept analysis. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 285–305. Springer, Heidelberg (2006). https://doi.org/10.1007/11847465_14

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Cádiz, Cádiz, Spain

    Roberto G. Aragón, Jesús Medina & Eloísa Ramírez-Poussa

Authors
  1. Roberto G. Aragón
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jesús Medina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eloísa Ramírez-Poussa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roberto G. Aragón .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Oviedo, Oviedo, Spain

    Inés Couso

  3. University of Cádiz, Cádiz, Spain

    Jesús Medina

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. University of Perugia, Perugia, Italy

    Davide Petturiti

  6. Sorbonne Université, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Aragón, R.G., Medina, J., Ramírez-Poussa, E. (2022). Study on the Necessity Operator to Factorize Formal Contexts in a Multi-adjoint Framework. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-08971-8_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08970-1

  • Online ISBN: 978-3-031-08971-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics