Formal concept analysis of higher order

Abstract

The second-order formal context is a formal context such that its object and attribute sets are disjoint unions of object and attribute sets of external formal contexts. Every subset of object or attribute set will be evaluated from concept lattice of the corresponding external formal context. The paper provides a method how to compute such second-order formal concepts by using of bonds between external formal contexts or by using heterogeneous formal context methods. The last part of the paper shows how this structure generalizes homogeneous fuzzy formal context and its derivation operators.

Keywords:

• External formal context
• second-order formal concept
• fuzzy operators

Notes

No potential conflict of interest was reported by the authors.

1 Although the CLLOS acronym was introduced in the previous paper, here we prefer to use the acronym $L$-CLOS to better reflect that we are working on an $L$-fuzzy extension in an effort to use the notation from recent work of Krídlo and Ojeda-Aciego (2012).

Additional information

Funding

This work was partly supported by grant number VEGA 1/0832/12 and by the Slovak Research and Development Agency under contract APVV-0035-10 “Algorithms, Automata, and Discrete Data Structures”.