Abstract
One of the main targets in formal concept analysis (FCA) and in rough set theory (RST) is the reduction of redundant information. Feature selection mechanisms have been studied separately in many works. In this paper, we analyse the result of applying the reduction mechanisms given in FCA to RST, and give interpretations of such reductions.
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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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 Mathematices (ESCIM 2015), pp. 257–263 (2015)
Benítez-Caballero, M.J., Medina, J., Ramírez-Poussa, E.: Attribute reduction in rough set theory and formal concept analysis. In: Polkowski, L., Yao, Y., Artiemjew, P., Ciucci, D., Liu, D., Ślęzak, D., Zielosko, B. (eds.) IJCRS 2017. LNCS (LNAI), vol. 10314, pp. 513–525. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60840-2_37
Benítez-Caballero, M.J., Medina, J., Ramírez-Poussa, E., Ślȩzak, D.: Bireducts with tolerance relations. Inf. Sci. 435, 26–39 (2018)
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)
Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: A comparative study of adjoint triples. Fuzzy Sets Syst. 211, 1–14 (2013)
Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: Attribute reduction in multi-adjoint concept lattices. Inf. Sci. 294, 41–56 (2015)
Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: Multi-adjoint algebras versus non-commutative residuated structures. Int. J. Approximate Reasoning 66, 119–138 (2015)
Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: On the use of irreducible elements for reducing multi-adjoint concept lattices. Knowl.-Based Syst. 89, 192–202 (2015)
Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: Characterizing reducts in multi-adjoint concept lattices. Inf. Sci. 422, 364–376 (2018)
Cornelis, C., Jensen, R., Hurtado, G., Ślȩzak, D.: Attribute selection with fuzzy decision reducts. Inf. Sci. 180, 209–224 (2010)
Cornelis, C., Medina, J., Verbiest, N.: Multi-adjoint fuzzy rough sets: definition, properties and attribute selection. Int. J. Approximate Reasoning 55, 412–426 (2014)
Fariñas del Cerro, L., Prade, H.: Rough sets, twofold fuzzy sets and modal logic–fuzziness in indiscernibility and partial information. In: Nola, A.D., Ventre, A. (ed.) The Mathematics of Fuzzy Systems, pp. 103–120. Verlag TUV Rheinland (1986)
Guan, L., Huang, D., Han, F.: Tolerance dominance relation in incomplete ordered decision systems. Int. J. Intell. Syst. 33(1), 33–48 (2018)
Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: Formal concept analysis via multi-adjoint concept lattices. Fuzzy Sets Syst. 160(2), 130–144 (2009)
Pawlak, Z.: Information systems theoretical foundations. Inf. Syst. 6(3), 205–218 (1981)
Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)
Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Słowiński, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, pp. 331–362. Kluwer Academic Publishers (1992)
Stawicki, S., Ślȩzak, D., Janusz, A., Widz, S.: Decision bireducts and decision reducts - a comparison. In. J. Approximate Reasoning 84, 75–109 (2017)
Wei, L., Qi, J.-J.: Relation between concept lattice reduction and rough set reduction. Knowl.-Based Syst. 23(8), 934–938 (2010)
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel (1982)
Yang, B., Hu, B.Q.: On some types of fuzzy covering-based rough sets. Fuzzy Sets and Syst. 312, 36–65 (2017). Theme: Fuzzy Rough Sets
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Benítez-Caballero, M.J., Medina, J., Ramírez-Poussa, E. (2018). FCA Attribute Reduction in Information Systems. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_47
Download citation
DOI: https://doi.org/10.1007/978-3-319-91473-2_47
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91472-5
Online ISBN: 978-3-319-91473-2
eBook Packages: Computer ScienceComputer Science (R0)