Reducing Concept Lattices from Rough Set Theory

  • M. José Benítez-Caballero
  • Jesús Medina
  • Eloísa Ramírez-PoussaEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)


Due to real databases usually contain redundant information, reducing them preserving the main information is one of the most important branches of study within the theory of Formal Concept Analysis (FCA). Taking advantage of the close relationship between Rough Set Theory (RST) and FCA, in this work, we address the problem of attribute reduction in FCA using the reduction mechanism given in RST. We analyze the properties obtained from this kind of reduction and show an illustrative example.


Attribute reduction Formal concept analysis Rough set theory 


  1. 1.
    Chen, J., Li, J., Lin, Y., Lin, G., Ma, Z.: Relations of reduction between covering generalized rough sets and concept lattices. Inf. Sci. 304, 16–27 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: Irreducible elements in multi-adjoint concept lattices. Int. Conf. Fuzzy Log. Technol. EUSFLAT 2013, 125–131 (2013)zbMATHGoogle Scholar
  3. 3.
    Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: Attribute reduction in multi-adjoint concept lattices. Inf. Sci. 294, 41–56 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Davey, B., Priestley, H.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)CrossRefzbMATHGoogle Scholar
  5. 5.
    Denecke, K., Erné, M., Wismath, S.L. (eds.): Galois Connections and Applications. Kluwer Academic Publishers, Dordrecht (2004)zbMATHGoogle Scholar
  6. 6.
    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
  7. 7.
    Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundation. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  8. 8.
    Medina, J.: Relating attribute reduction in formal, object-oriented and property-oriented concept lattices. Comput. Math. Appl. 64(6), 1992–2002 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: On multi-adjoint concept lattices: definition and representation theorem. Technical report, University of Málaga (2006).
  10. 10.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)CrossRefzbMATHGoogle Scholar
  11. 11.
    Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems, pp. 331–362. Springer, Netherlands (1992)Google Scholar
  12. 12.
    Wei, L., Qi, J.-J.: Relation between concept lattice reduction and rough set reduction. Knowl.-Based Syst. 23(8), 934–938 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • M. José Benítez-Caballero
    • 1
  • Jesús Medina
    • 1
  • Eloísa Ramírez-Poussa
    • 1
    Email author
  1. 1.Department of MathematicsUniversity of CádizCádizSpain

Personalised recommendations