Dismantling allows for the removal of elements from a poset, or in our case lattice, without disturbing the remaining structure. In this paper we have extended the notion of dismantling by single elements to the dismantling by intervals in a lattice. We utilize theory from Formal Concept Analysis (FCA) to show that lattices dismantled by intervals correspond to closed subrelations in the respective formal context, and that there exists a unique core with respect to dismantling by intervals. Furthermore, we show that dismantling intervals can be identified directly in the formal context utilizing a characterization via arrow relations and provide an algorithm to compute all dismantling intervals.
%0 Journal Article
%1 FELDE2023108931
%A Felde, Maximilian
%A Koyda, Maren
%D 2023
%J International Journal of Approximate Reasoning
%K Arrow_relations Closed_subrelations Concept_lattice Dismantling_intervals Formal_concept_analysis myown
%P 108931
%R 10.1016/j.ijar.2023.108931
%T Interval-dismantling for lattices
%U https://www.sciencedirect.com/science/article/pii/S0888613X23000622
%V 159
%X Dismantling allows for the removal of elements from a poset, or in our case lattice, without disturbing the remaining structure. In this paper we have extended the notion of dismantling by single elements to the dismantling by intervals in a lattice. We utilize theory from Formal Concept Analysis (FCA) to show that lattices dismantled by intervals correspond to closed subrelations in the respective formal context, and that there exists a unique core with respect to dismantling by intervals. Furthermore, we show that dismantling intervals can be identified directly in the formal context utilizing a characterization via arrow relations and provide an algorithm to compute all dismantling intervals.
@article{FELDE2023108931,
abstract = {Dismantling allows for the removal of elements from a poset, or in our case lattice, without disturbing the remaining structure. In this paper we have extended the notion of dismantling by single elements to the dismantling by intervals in a lattice. We utilize theory from Formal Concept Analysis (FCA) to show that lattices dismantled by intervals correspond to closed subrelations in the respective formal context, and that there exists a unique core with respect to dismantling by intervals. Furthermore, we show that dismantling intervals can be identified directly in the formal context utilizing a characterization via arrow relations and provide an algorithm to compute all dismantling intervals.},
added-at = {2023-12-12T12:51:11.000+0100},
author = {Felde, Maximilian and Koyda, Maren},
biburl = {https://www.bibsonomy.org/bibtex/25a88357f3c6b8e71274c65f04cc41cc7/kde-alumni},
doi = {10.1016/j.ijar.2023.108931},
interhash = {7d216a5386cc9229dbf6ef5bcb8c24ed},
intrahash = {5a88357f3c6b8e71274c65f04cc41cc7},
issn = {0888-613X},
journal = {International Journal of Approximate Reasoning},
keywords = {Arrow_relations Closed_subrelations Concept_lattice Dismantling_intervals Formal_concept_analysis myown},
pages = 108931,
timestamp = {2023-12-12T12:51:11.000+0100},
title = {Interval-dismantling for lattices},
url = {https://www.sciencedirect.com/science/article/pii/S0888613X23000622},
volume = 159,
year = 2023
}