Direct Factorization by Similarity of Fuzzy Concept Lattices by Factorization of Input Data

  • Radim Belohlavek
  • Jan Outrata
  • Vilem Vychodil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4923)

Abstract

The paper presents additional results on factorization by similarity of fuzzy concept lattices. A fuzzy concept lattice is a hierarchically ordered collection of clusters extracted from tabular data. The basic idea of factorization by similarity is to have, instead of a possibly large original fuzzy concept lattice, its factor lattice. The factor lattice contains less clusters than the original concept lattice but, at the same time, represents a reasonable approximation of the original concept lattice and provides us with a granular view on the original concept lattice. The factor lattice results by factorization of the original fuzzy concept lattice by a similarity relation. The similarity relation is specified by a user by means of a single parameter, called a similarity threshold. Smaller similarity thresholds lead to smaller factor lattices, i.e. to more comprehensible but less accurate approximations of the original concept lattice. Therefore, factorization by similarity provides a trade-off between comprehensibility and precision. We first recall the notion of factorization. Second, we present a way to compute the factor lattice of a fuzzy concept lattice directly from input data, i.e. without the need to compute the possibly large original concept lattice.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Radim Belohlavek
    • 1
    • 2
  • Jan Outrata
    • 2
  • Vilem Vychodil
    • 1
    • 2
  1. 1.Dept. Systems Science and Industrial Engineering T. J. Watson School of Engineering and Applied ScienceBinghamton University–SUNYBinghamtonUSA
  2. 2.Dept. Computer SciencePalacky UniversityOlomoucCzech Republic

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