This paper addresses the use of residuated implication operators to create a fuzzy resemblance relation between cases so as to model the CBR basic principle “the more similar two problem descriptions are, the more similar are their solutions”. We describe how this fuzzy relation can be exploited to identify case clusters, based of a finite number of level cuts from that relation, that are in turn used to solve a new problem. The paper proposes some formal results that characterize the sets of clusters obtained from the various level-cuts of the resemblance relation.


case-based reasoning residuated implication similarity relations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aamodt, A., Plaza, E.: Case-based reasoning: foundational issues, methodological variations and system approaches. AI Commun. 7(1), 39–59 (1994)Google Scholar
  2. 2.
    Armengol, E., Esteva, F., Godo, L., Torra, V.: On learning similarity relations in fuzzy case-based reasoning. Trans. on Rough Sets, 14–32 (2004)Google Scholar
  3. 3.
    Bouchon-Meunier, B., Laurent, A., Lesot, M.-J., Rifqi, M.: Strengthening fuzzy gradual rules through “all the more” clauses. In: Proc. FuzzIEEE 2010 (WCCI 2010), pp. 2940–2946 (2010)Google Scholar
  4. 4.
    Dubois, D., Prade, H.: Possibility theory: an approach to computerized processing of uncertainty. Plenum Press (1988)Google Scholar
  5. 5.
    Dubois, D., Prade, H.: Gradual inference rules in approximate reasoning. Information Sciences 61(1-2), 103–122 (1982)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Esteva, F., Garcia-Calves, P., Godo, L.: Fuzzy similarity-based models in case-based reasoning. In: Proc. FuzzIEEE 2002, vol. 2, pp. 1348–1353 (2002)Google Scholar
  7. 7.
    Hüllermeier, E., Dubois, D., Prade, H.: Fuzzy rules in case-based reasoning. In: Proc. AFIA 1999, pp. 45–54 (1999)Google Scholar
  8. 8.
    Fanoiki, T., Drummond, I., Sandri, S.: Case-based reasoning retrieval and reuse using case resemblance hypergraphs. In: Proc. FuzzIEEE 2010 (WCCI 2010), pp. 1–7 (2010)Google Scholar
  9. 9.
    Hüllermeier, E.: Implication-Based Fuzzy Association Rules. In: Siebes, A., De Raedt, L. (eds.) PKDD 2001. LNCS (LNAI), vol. 2168, pp. 241–252. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Kolodner, J.: Cased-based reasoning. Morgan Kaufmann (1993)Google Scholar
  11. 11.
    Martins-Bedé, F.T., Godo, L., Sandri, S., Dutra, L.V., Freitas, C.C., Carvalho, O.S., Guimarães, R.J.P.S., Amaral, R.S.: Classification of Schistosomiasis Prevalence Using Fuzzy Case-Based Reasoning. In: Cabestany, J., Sandoval, F., Prieto, A., Corchado, J.M. (eds.) IWANN 2009, Part I. LNCS, vol. 5517, pp. 1053–1060. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Sandri, S., Mendonça, J., M.-Bedê, F., Guimarães, R., Carvalho, O.: Weighted fuzzy similarity relations in case-based reasoning: a case study in classification. In: WCCI 2012 (to appear, 2012)Google Scholar
  13. 13.
    Sandri, S., Toledo Martins-Bedé, F.: Order Compatible Fuzzy Relations and Their Elicitation from General Fuzzy Partitions. In: Liu, W. (ed.) ECSQARU 2011. LNCS, vol. 6717, pp. 640–650. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Torra, V.: On the learning of weights in some aggregation operators: the weighted mean and OWA operators. Math. and Soft Comp. 6 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sandra Sandri
    • 1
  1. 1.Instituto Nacional de Pesquisas Espaciais - INPESão José dos CamposBrazil

Personalised recommendations