Skip to main content
SpringerLink
Log in

Viewing Morphisms Between Pattern Structures via Their Concept Lattices and via Their Representations

  • Conference paper
  • First Online:
Book cover Foundations of Intelligent Systems (ISMIS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10352))

Included in the following conference series:

  • 1626 Accesses

Abstract

In continuation of [13], we investigate pattern structures and their morphisms aiming to provide a theoretical background for complexity reduction. Our results follow a top-down strategy starting with a general setup of poset adjunctions; then we specify the situation for pattern structures and their representations. In particular, we discuss the situation where morphisms between pattern structures induce morphisms between their representations.

Morphisms between adjunctions turn out to be of crucial interest for a better understanding of morphisms between concept lattices of pattern structures.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References

  1. Blyth, T.S., Janowitz, M.F.: Residuation Theory, pp. 1–382. Pergamon Press, Oxford (1972)

    Book  MATH  Google Scholar 

  2. Buzmakov, A., Kuznetsov, S.O., Napoli, A.: Revisiting pattern structure projections. In: Baixeries, J., Sacarea, C., Ojeda-Aciego, M. (eds.) ICFCA 2015. LNCS, vol. 9113, pp. 200–215. Springer, Cham (2015). doi:10.1007/978-3-319-19545-2_13

    Chapter  Google Scholar 

  3. Dubois, D., Prade, H., Rico, A.: The cube of opposition: a structure underlying many knowledge representation formalisms. In: IJCAI 2015, pp. 2933–2939 (2015)

    Google Scholar 

  4. Ganter, B., Kuznetsov, S.O.: Pattern structures and their projections. In: Delugach, H.S., Stumme, G. (eds.) ICCS-ConceptStruct 2001. LNCS, vol. 2120, pp. 129–142. Springer, Heidelberg (2001). doi:10.1007/3-540-44583-8_10

    Chapter  Google Scholar 

  5. Erné, M., Koslowski, J., Melton, A., Strecker, G.E.: A primer on Galois connections. Ann. N. Y. Acad. Sci. 704(1), 103–125 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  6. Erné, M.: Adjunctions and Galois connections. In: Galois Connections and Applications, pp. 1–138 (2004)

    Google Scholar 

  7. Kaiser, T.B., Schmidt, S.E.: Some remarks on the relation between annotated ordered sets and pattern structures. In: Kuznetsov, S.O., Mandal, D.P., Kundu, M.K., Pal, S.K. (eds.) PReMI 2011. LNCS, vol. 6744, pp. 43–48. Springer, Heidelberg (2011). doi:10.1007/978-3-642-21786-9_9

    Chapter  Google Scholar 

  8. Kaytoue, M., Kuznetsov, S.O., Napoli, A., Duplessis, S.: Mining gene expression data with pattern structures in formal concept analysis. Inf. Sci. (Elsevier) 181, 1989–2001 (2011)

    Article  MathSciNet  Google Scholar 

  9. Kuznetsov, S.O.: Pattern structures for analyzing complex data. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS (LNAI), vol. 5908, pp. 33–44. Springer, Heidelberg (2009). doi:10.1007/978-3-642-10646-0_4

    Chapter  Google Scholar 

  10. Kuznetsov, S.O.: Scalable knowledge discovery in complex data with pattern structures. In: Maji, P., Ghosh, A., Murty, M.N., Ghosh, K., Pal, S.K. (eds.) PReMI 2013. LNCS, vol. 8251, pp. 30–39. Springer, Heidelberg (2013). doi:10.1007/978-3-642-45062-4_3

    Chapter  Google Scholar 

  11. Lumpe, L., Schmidt, S.E.: A note on pattern structures and their projections. In: Baixeries, J., Sacarea, C., Ojeda-Aciego, M. (eds.) ICFCA 2015. LNCS, vol. 9113, pp. 145–150. Springer, Cham (2015). doi:10.1007/978-3-319-19545-2_9

    Chapter  Google Scholar 

  12. Lumpe, L., Schmidt, S.E.: Pattern structures and their morphisms. In: CLA 2015, pp. 171–179 (2015)

    Google Scholar 

  13. Lumpe, L., Schmidt, S.E.: Morphisms between pattern structures and their impact on concept lattices. In: FCA4AI, pp. 25–33 (2016)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität Dresden, 01062, Dresden, Germany

    Lars Lumpe & Stefan E. Schmidt

Authors
  1. Lars Lumpe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefan E. Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lars Lumpe .

Editor information

Editors and Affiliations

  1. Warsaw University of Technology, Warsaw, Poland

    Marzena Kryszkiewicz

  2. University of Bari Aldo Moro, Bari, Italy

    Annalisa Appice

  3. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  4. Faculty of Electronics & Information, Warsaw University of Technology, Warsaw, Poland

    Henryk Rybinski

  5. Institute of Mathematics, Warsaw University, Warsaw, Poland

    Andrzej Skowron

  6. Department of Computer Science, University of North Carolina at Charlotte, North Carolina, USA

    Zbigniew W. Raś

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Lumpe, L., Schmidt, S.E. (2017). Viewing Morphisms Between Pattern Structures via Their Concept Lattices and via Their Representations. In: Kryszkiewicz, M., Appice, A., Ślęzak, D., Rybinski, H., Skowron, A., Raś, Z. (eds) Foundations of Intelligent Systems. ISMIS 2017. Lecture Notes in Computer Science(), vol 10352. Springer, Cham. https://doi.org/10.1007/978-3-319-60438-1_59

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-60438-1_59

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60437-4

  • Online ISBN: 978-3-319-60438-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation