%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 }