Abstract
One of the relations used with granularity is indistinguishability, where distinguishable entities in a finer-grained granule are indistinguishable in a coarser-grained granule. This relation is a subtype of equivalence relation, which is used in the other direction to create finer-grained granules. Together with the notion of similarity, we formally prove some intuitive properties of the indistinguishability relation for both qualitative and quantitative granularity, that with a given granulation there must be at least two granules (levels of granularity) for it to be granular, and derive a strict order between finer and coarser granules. Based on these results, granulation hierarchy is defined as extra assisting structure to augment implementations.
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References found in this work BETA

Mereology.Achille C. Varzi - 2016 - Stanford Encyclopedia of Philosophy.
Granularity as a Parameter of Context.Hedda R. Schmidtke - 2005 - In B. Kokinov A. Dey (ed.), Modeling and Using Context. Springer. pp. 450--463.

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