Extended Galois Derivation Operators for Information Retrieval Based on Fuzzy Formal Concept Lattice
The obvious analogy between an Objects×Properties binary relationship (called a formal context) and a binary Documents×Terms incidence matrix has led to a growing interest for the use of formal concept analysis (FCA) in information retrieval (IR). The main advantage of using FCA for IR is the possibility of creating a conceptual representation of a given document collection in the form of a lattice. Also, potentials of FCA for IR have been highlighted by a number of research studies since its inception. It turns out that almost all existing FCA-based IR approaches rely on: i) a Boolean Documents×Terms incidence matrix and, ii) the use of the classical Galois connection initially proposed by Wille. In such a case, there is no way for expressing weighted queries as well as there is no way for ranking query results that is usually done by query refinement or empirical navigation trough the concept lattice. In this paper we first enlarge the use of FCA for IR to the fuzzy setting which allows for a fuzzy incidence matrix and weighted queries. For instance, an incidence matrix may now allow for (normalized) numerical entries that may be achieved using the well known term frequency measure. Furthermore, it is worth noticing that in the existing approaches, user queries are restricted to the conjunctive form. Thus, another contribution consists in considering, in an original way, the use of other Galois derivation operators (namely the possibility, necessity and dual sufficiency) in order to express disjunction and negation in queries.
KeywordsInformation Retrieval Formal Concept Complete Lattice Incidence Matrix Concept Lattice
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- 2.Bělohlávek, R., Vychodil, V.: What is a fuzzy concept lattice. In: Proceedings CLA 2005 Concept Lattices and their Applications, Olomounc, Czech Republic, pp. 34–45 (2005)Google Scholar
- 4.Carpineto, C., Romano, G.: Effective reformulation of boolean queries with concept lattices. In: FQAS, pp. 83–94 (1998)Google Scholar
- 7.Djouadi, Y., Prade, H.: Possibility-theoretic extension of derivation operators in formal concept analysis. Fuzzy Optimization and Decision Making (submitted, 2011)Google Scholar
- 8.Dubois, D., Prade, H.: Possibility theory and formal concept analysis in information systems. In: Proc. IFSA 2009, International Fuzzy Systems Association World Congress, Lisbon, Portugal, pp. 1021–1026 (2009)Google Scholar
- 11.ElQadi, A., Aboutadjine, D., Ennouary, Y.: Formal concept analysis for information retrieval. International Journal of Computer Science and Information Security 7(2), 119–125 (2010)Google Scholar
- 13.Gediga, G., Düntsch, I.: Modal-style operators in qualitative data analysis. In: Proc. ICDM 2002 IEEE Int. Conf. on Data Mining, pp. 9–12 (2002)Google Scholar
- 14.Latiri, C.C., Elloumi, S., Chevallet, J.P., Jaouay, A.: Extension of fuzzy Galois connection for information retrieval using a fuzzy quantifier. In: Proc. AICCSA 2003 Int. Conf. on Computer Systems and Applications, Tunis, Tunisia, pp. 81–91 (2003)Google Scholar
- 15.Messai, N., Devignes, M.D., Napoli, A., Smaïl-Tabbone, M.: Many-valued concept lattices for conceptual clustering and information retrieval. In: ECAI 2008 - 18th European Conference on Artificial Intelligence, Patras, Greece, July 21-25, pp. 127–131 (2008)Google Scholar
- 16.Nauer, E., Toussaint, Y.: Classification dynamique par treillis de concepts pour la recherche d’information sur le web. In: Proc. Conférence en Recherche d’Infomations et Applications - CORIA 2008, Trégastel, France, March 12-14, pp. 71–86 (2008)Google Scholar
- 17.Priss, U.: Lattice-based information retrieval. Knowledge Organization 27(3), 132–142 (2000)Google Scholar
- 18.Salton, G.: Automatic information organization and retrieval. McGraw-Hill, New York (1968)Google Scholar
- 19.Wille, R.: Restructuring Lattice Theory: an Approach Based on Hierarchies of Concepts. In: Rival, I. (ed.) Ordered Sets. Reidel, Dordrecht (1982)Google Scholar