Subsethood, which is to measure the degree of set inclusion relation, is
predominant in fuzzy set theory. This paper introduces some basic concepts of
spatial granules, coarse-fine relation, and operations like meet, join,
quotient meet and quotient join. All the atomic granules can be hierarchized by
set-inclusion relation and all the granules can be hierarchized by coarse-fine
relation. Viewing an information system from the micro and the macro
perspectives, we can get a micro knowledge space and a micro knowledge space,
from which a rough set model and a spatial rough granule model are respectively
obtained. The classical rough set model is the special case of the rough set
model induced from the micro knowledge space, while the spatial rough granule
model will be play a pivotal role in the problem-solving of structures. We
discuss twelve axioms of monotone increasing subsethood and twelve
corresponding axioms of monotone decreasing supsethood, and generalize
subsethood and supsethood to conditional granularity and conditional fineness
respectively. We develop five conditional granularity measures and five
conditional fineness measures and prove that each conditional granularity or
fineness measure satisfies its corresponding twelve axioms although its
subsethood or supsethood measure only hold one of the two boundary conditions.
We further define five conditional granularity entropies and five conditional
fineness entropies respectively, and each entropy only satisfies part of the
boundary conditions but all the ten monotone conditions