A categorical view at generalized concept lattices

Stanislav Krajči

Kybernetika (2007)

  • Volume: 43, Issue: 2, page 255-264
  • ISSN: 0023-5954

Abstract

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We continue in the direction of the ideas from the Zhang’s paper [Z] about a relationship between Chu spaces and Formal Concept Analysis. We modify this categorical point of view at a classical concept lattice to a generalized concept lattice (in the sense of Krajči [K1]): We define generalized Chu spaces and show that they together with (a special type of) their morphisms form a category. Moreover we define corresponding modifications of the image / inverse image operator and show their commutativity properties with mapping defining generalized concept lattice as fuzzifications of Zhang’s ones.

How to cite

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Krajči, Stanislav. "A categorical view at generalized concept lattices." Kybernetika 43.2 (2007): 255-264. <http://eudml.org/doc/33856>.

@article{Krajči2007,
abstract = {We continue in the direction of the ideas from the Zhang’s paper [Z] about a relationship between Chu spaces and Formal Concept Analysis. We modify this categorical point of view at a classical concept lattice to a generalized concept lattice (in the sense of Krajči [K1]): We define generalized Chu spaces and show that they together with (a special type of) their morphisms form a category. Moreover we define corresponding modifications of the image / inverse image operator and show their commutativity properties with mapping defining generalized concept lattice as fuzzifications of Zhang’s ones.},
author = {Krajči, Stanislav},
journal = {Kybernetika},
keywords = {fuzzy concept lattice; Chu space; category theory; fuzzy concept lattice; Chu space; category theory},
language = {eng},
number = {2},
pages = {255-264},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A categorical view at generalized concept lattices},
url = {http://eudml.org/doc/33856},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Krajči, Stanislav
TI - A categorical view at generalized concept lattices
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 2
SP - 255
EP - 264
AB - We continue in the direction of the ideas from the Zhang’s paper [Z] about a relationship between Chu spaces and Formal Concept Analysis. We modify this categorical point of view at a classical concept lattice to a generalized concept lattice (in the sense of Krajči [K1]): We define generalized Chu spaces and show that they together with (a special type of) their morphisms form a category. Moreover we define corresponding modifications of the image / inverse image operator and show their commutativity properties with mapping defining generalized concept lattice as fuzzifications of Zhang’s ones.
LA - eng
KW - fuzzy concept lattice; Chu space; category theory; fuzzy concept lattice; Chu space; category theory
UR - http://eudml.org/doc/33856
ER -

References

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  8. Krajči S., The basic theorem on generalized concept lattice, In: Proc. 2nd Internat. Workshop CLA 2004 (V. Snášel and R. Bělohlávek, eds.), Ostrava 2004, pp. 25–33 
  9. Krajči S., Every concept lattice with hedges is isomorphic to some generalized concept lattice, In: Proc. 3nd Internat. Workshop CLA 2004 (R. Bělohlávek and V. Snášel, eds.), Olomouc 2005, pp. 1–9 
  10. Krajči S., Cluster based efficient generation of fuzzy concepts, Neural Network World 13 (2003), 5, 521–530 
  11. Pollandt S., Fuzzy Begriffe, Springer–Verlag, Berlin 1997 Zbl0870.06008MR1710383
  12. Pollandt S., Datenanalyse mit Fuzzy–Begriffen, In: Begriffliche Wissensverarbeitung, Methoden und Anwendungen (G. Stumme and R. Wille, eds.), Springer–Verlag, Heidelberg 2000, pp. 72–98 Zbl0958.68162
  13. Shostak A., Fuzzy categories versus categories of fuzzily structured sets: Elements of the theory of fuzzy categories, In: Mathematik–Arbeitspapiere N 48: Categorical Methods in Algebra and Topology (A collection of papers in honor of Horst Herrlich, Hans-E. Porst, ed.), Bremen 1977, pp. 407–438 (1977) 
  14. Zhang G. Q., Chu spaces, concept lattices, and domains, In: Proc. Nineteenth Conference on the Mathematical Foundations of Programming Semantics, Montreal 2003, Electronic Notes in Theoretical Computer Science 83, 2004 

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