Year: 2026
Type: preprint
Abstract: In this paper we prove that Dubois--Prade's eight possibilistic operators in Formal Concept Analysis arise canonically from Kan extensions of the underlying boolean profunctor. This provides a conceptual explanation for the result that $NΠ$-pairs are the formal concepts of the complement context. We further prove that the FCA closure operator and the $NΠ$-pairs are the only symmetric or asymmetric operator compositions that give formal concepts. Finally we use these eight possibilistic operators to construct new closure operators on a formal context via standard categorical arguments.
Source: arXiv (Cornell University)
Author: Aambø, Torgeir
Topic: Rough Sets and Fuzzy Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171817293
Cites:
Cited by:
Related to: