Skip to main content
SpringerLink
Log in

Preclusivity and Simple Graphs: The n–cycle and n–path Cases

  • Conference paper
  • First Online:
Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9437))

Abstract

Two classes of graphs, the n–cycles and n–paths, are interpreted as preclusivity spaces. In this way, it is possible to define two pairs of approximations on them: one based on a preclusive relation and another one based on a similarity relation. Further, two relations can be defined among the set of vertices and they define two different graphs, which are here studied.

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Cattaneo, G.: Generalized rough sets (Preclusivity fuzzy-intuitionistic (BZ) lattices). Studia Logica 01, 47–77 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cattaneo, G.: Abstract approximation spaces for rough theories. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1: Methodology and Applications. Studies in Fuzziness and Soft Computing, pp. 59–98. Physica Verlag, Heidelberg (1998)

    Google Scholar 

  3. Chiaselotti, G., Ciucci, D., Gentile, T.: Simple undirected graphs as formal contexts. In: Baixeries, J., Sacarea, C., Ojeda-Aciego, M. (eds.) ICFCA 2015. LNCS, vol. 9113, pp. 287–302. Springer, Heidelberg (2015)

    Chapter  MATH  Google Scholar 

  4. Chiaselotti, G., Ciucci, D., Gentile, T., Infusino, F.: Preclusivity and simple graphs. In: Yao, Y., Hu, Q., Yu, H. Grzymala-Busse, J. (eds.) RSFDGrC 2015. LNCS, vol. 9437, pp. 127–137. Springer, Heidelberg (2015)

    Google Scholar 

  5. Ciucci, D., Dubois, D., Prade, H.: The structure of oppositions in rough set theory and formal concept analysis - toward a new bridge between the two settings. In: Beierle, C., Meghini, C. (eds.) FoIKS 2014. LNCS, vol. 8367, pp. 154–173. Springer, Heidelberg (2014)

    Chapter  MATH  Google Scholar 

  6. Diestel, R.: Graph Theory. Graduate Text in Mathematics, 4th edn. Springer, Heidelberg (2010)

    Book  MATH  Google Scholar 

  7. Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Heidelberg (1999)

    Book  MATH  Google Scholar 

  8. Yao, J.T., Ciucci, D., Zhang, Y.: Generalized rough sets. In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, Chapter 25, pp. 413–424. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DISCo, Università di Milano – Bicocca, Viale Sarca 336 – U14, 20126, Milan, Italy

    Davide Ciucci

  2. Department of Mathematics and Informatics, University of Milano–Bicocca, Via Pietro Bucci, Cubo 30B, 87036, Arcavacata di Rende, CS, Italy

    Giampiero Chiaselotti, Tommaso Gentile & Federico Infusino

Authors
  1. Giampiero Chiaselotti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Davide Ciucci
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tommaso Gentile
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Federico Infusino
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Davide Ciucci .

Editor information

Editors and Affiliations

  1. University of Regina, Regina, SK, Canada

    Yiyu Yao

  2. Tianjin University, Tianjin, China

    Qinghua Hu

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Hong Yu

  4. University of Kansas, Lawrence, KS, USA

    Jerzy W. Grzymala-Busse

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Chiaselotti, G., Ciucci, D., Gentile, T., Infusino, F. (2015). Preclusivity and Simple Graphs: The n–cycle and n–path Cases. In: Yao, Y., Hu, Q., Yu, H., Grzymala-Busse, J.W. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Lecture Notes in Computer Science(), vol 9437. Springer, Cham. https://doi.org/10.1007/978-3-319-25783-9_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25783-9_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25782-2

  • Online ISBN: 978-3-319-25783-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation