Kybernetika 60 no. 2, 172-196, 2024

Degrees of compatible L-subsets and compatible mappings

Fu-Gui Shi and Yan SunDOI: 10.14736/kyb-2024-2-0172

Abstract:

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.

Keywords:

$L$-approximation spaces, compatible $L$-subsets, compatible mappings, complete $L$-sublattices

Classification:

06B75, 06D10, 06D72

paper.pdf

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