Geodesic
Degrees of compatible $L$-subsets and compatible mappings
Kybernetika, Tome 60 (2024) no. 2, pp. 172-196 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Based on a completely distributive lattice $L$, degrees of compatible $L$-subsets and compatible mappings are introduced in an $L$-approximation space and their characterizations are given by four kinds of cut sets of $L$-subsets and $L$-equivalences, respectively. Besides, some characterizations of compatible mappings and compatible degrees of mappings are given by compatible $L$-subsets and compatible degrees of $L$-subsets. Finally, the notion of complete $L$-sublattices is introduced and it is shown that the product of complete $L$-sublattices is still a complete $L$-sublattice and the compatible degree of an $L$-subset is a complete $L$-sublattice.
Based on a completely distributive lattice $L$, degrees of compatible $L$-subsets and compatible mappings are introduced in an $L$-approximation space and their characterizations are given by four kinds of cut sets of $L$-subsets and $L$-equivalences, respectively. Besides, some characterizations of compatible mappings and compatible degrees of mappings are given by compatible $L$-subsets and compatible degrees of $L$-subsets. Finally, the notion of complete $L$-sublattices is introduced and it is shown that the product of complete $L$-sublattices is still a complete $L$-sublattice and the compatible degree of an $L$-subset is a complete $L$-sublattice.
DOI : 10.14736/kyb-2024-2-0172
Classification : 06B75, 06D10, 06D72
Keywords: $L$-approximation spaces; compatible $L$-subsets; compatible mappings; complete $L$-sublattices 
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Shi, Fu-Gui; Sun, Yan. Degrees of compatible $L$-subsets and compatible mappings. Kybernetika, Tome 60 (2024) no. 2, pp. 172-196. doi: 10.14736/kyb-2024-2-0172

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