A note on variable threshold concept lattices: Threshold-based operators are reducible to classical concept-forming operators

  • Authors:

  • Radim Belohlavek

  • Affiliations:

  • Department of Systems Science and Industrial Engineering, Binghamton University - SUNY, Binghamton, NY 12902, USA and Department of Computer Science, Palacky University, Olomouc, Czech Republic

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

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Abstract

The present paper deals with formal concept analysis of data with fuzzy attributes. We clarify several points of a new approach of [S.Q. Fan, W.X. Zhang, Variable threshold concept lattice, Inf. Sci., accepted for publication] which is based on using thresholds in concept-forming operators. We show that the extent- and intent-forming operators from [S.Q. Fan, W.X. Zhang, Inf. Sci., accepted for publication] can be defined in terms of basic fuzzy set operations and the original operators as introduced and studied e.g. in [R. Belohlavek, Fuzzy Galois connections, Math. Logic Quarterly 45 (4) (1999) 497-504; R. Belohlavek, Concept lattices and order in fuzzy logic, Ann. Pure Appl. Logic 128 (2004) 277-298; S. Pollandt, Fuzzy Begriffe, Springer-Verlag, Berlin/Heidelberg, 1997]. As a consequence, main properties of the new operators from [S.Q. Fan, W.X. Zhang, Inf. Sci., accepted for publication], including the properties studied in [S.Q. Fan, W.X. Zhang, Inf. Sci., accepted for publication], can be obtained as consequences of the original operators from [R. Belohlavek, 1999; R. Belohlavek, 2004; S. Pollandt, 1997].