Advertisement

Abstract

Concept lattices fulfil one of the aims of classification by providing a description by attributes of each class of objects. We introduce here two new similarity/dissimilarity measures: a similarity measure between concepts (elements) of a lattice and a dissimilarity measure between concept lattices defined on the same set of objects and attributes. Both measures are based on the overhanging relation previously introduced by the author, which are a cryptomorphism of lattices.

References

  1. Barbut, M., & Monjardet, B. (1970). Ordres et classification: Algèbre et combinatoire (tome II). Paris: Hachette.Google Scholar
  2. Birkhoff, G. (1967). Lattice theory, (3rd ed.). Providence: American Mathematical Society.zbMATHGoogle Scholar
  3. Caspard, N., Leclerc, B., & Monjardet, B. (2012). Finite ordered sets: Concepts, results and uses. Cambridge: Cambridge University Press.Google Scholar
  4. Caspard, N., & Monjardet, B. (2003). The lattices of Moore families and closure operators on a finite set: A survey. Discrete Applied Mathematics, 127, 241–269.CrossRefzbMATHMathSciNetGoogle Scholar
  5. Davey, B. A., & Priestley, H. A. (2002). Introduction to lattices and order (2nd ed.). Cambridge: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  6. Domenach, F., & Leclerc, B. (2004). Closure systems, implicational systems, overhanging relations and the case of hierarchical classification. Mathematical Social Sciences, 47(3), 349–366.Google Scholar
  7. Ganter, B., & Wille, R. (1996). Formal concept analysis: Mathematical foundations. New York: Springer.zbMATHGoogle Scholar
  8. Leacock, C., & Chodorow, M. (1998). Combining local context and wordnet similarity for word sense identification. In C. Fellbaum (Ed.), WordNet: An electronic lexical database (pp. 265–283). Cambridge: MIT.Google Scholar
  9. Rada, R., Mili, H., Bicknell, E., & Blettner, M. (1989). Development and application of a metric on semantic nets. IEEE Transactions SMC, 19, 17–30.Google Scholar
  10. Tversky, A. (1977). Features of similarity. Psychological Review, 84(4), 327–352.CrossRefGoogle Scholar
  11. Wille, R. (1982). Restructuring lattice theory: An approach based on hierarchies of concepts. In I. Rival (Ed.), Ordered sets (pp. 314–339).Google Scholar
  12. Wu, Z., & Palmer, M. (1994). Verb semantics and lexical selection. In Proceedings of the 32nd Annual Meeting of the Associations for Computational Linguistics (pp. 33–138).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Computer Science DepartmentUniversity of NicosiaNicosiaCyprus

Personalised recommendations