Basic theorem as representation of heterogeneous concept lattices

Pócs, Jozef; Pócsová, Jana

doi:10.1007/s11704-015-3162-x

Cited by 9 publications

(1 citation statement)

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“…Concerning fuzzy concept lattices, these topics represents a very active research area, cf. [20] or [8,9] for the case of generalized one-sided concept lattices reduction, and [21], where a representation of generalized fuzzy concept lattices as the classical ones is described. A possible application of bonds to the mentioned problematic is briefly discussed in the next section.…”

Section: Bonds Between Generalized One-sided Formal Contextsmentioning

confidence: 99%

On Bonds for Generalized One-Sided Concept Lattices

Pócs

Pócsová

2021

Mathematics

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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.

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