Degrees of compatible L-subsets and compatible mappings

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.