Synonyms
Definition
Approximations are representations that describe entities in terms of relations to cells in a partition which serves as a frame of reference. Approximations give raise to an indiscernibility relation: in the “approximation space” two entities are indiscernible if and only if they have identical approximations. Approximations are used as tools for the representation of objects with indeterminate boundaries and multi-resolution spatial, temporal, and attribute data.
Example
At every moment in time, your body axes create a partition of space consisting of the cells front-left (fl), back-left (bl), front-right (fr), and back-right (br) as depicted in Fig. 1. Every object, including your-brother (yb), your-sister1 (ys1), your-sister2 (ys1), and your-house(yh), can be characterized in terms of their relations to the cells of the partition. For example, part-of(ys1,fl), disjoint(ys1,fr), disjoint(ys1,br), disjoint(ys1,bl),...
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Recommended Reading
Pawlak Z, Grzymala-Busse J, Slowinski R, Ziarko RA (1995) Rough sets Commun ACM 38(11):89–95
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Bittner, T., Stell, J.G. (2017). Approximation. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-17885-1_65
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