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On Bonds for Generalized One-Sided Concept Lattices

Author

Listed:
  • Jozef Pócs

    (Mathematical Institute, Slovak Academy of Sciences, 040 01 Košice, Slovakia
    Department of Algebra and Geometry, Palacký University Olomouc, 771 46 Olomouc, Czech Republic)

  • Jana Pócsová

    (Faculty of Mining, Ecology, Process Control and Geotechnologies, Technical University of Košice, 042 00 Košice, Slovakia)

Abstract

The generalized one-sided concept lattices represent a generalization of the classical FCA method convenient for a hierarchical analysis of object-attribute models with different types of attributes. The mentioned types of object-attribute models are formalized within the theory as formal contexts of a certain type. The aim of this paper is to investigate some intercontextual relationships represented by the notion of bond. A composition of bonds is defined in order to introduce the category of formal contexts with bonds as morphisms. It is shown that there is a one-to-one correspondence between bonds and supremum preserving mappings between the corresponding generalized one-sided concept lattices. As the main theoretical result it is shown that the introduced category of formal contexts with bonds is equivalent to the category of complete lattices with supremum preserving mappings as morphisms.

Suggested Citation

  • Jozef Pócs & Jana Pócsová, 2021. "On Bonds for Generalized One-Sided Concept Lattices," Mathematics, MDPI, vol. 9(3), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:211-:d:484174
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