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Approximation

  • Reference work entry
  • First Online:
Encyclopedia of GIS

  • 95 Accesses

Synonyms

Rough approximation; Rough set theory

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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Author information

Authors and Affiliations

  1. Department of Philosophy; Department of Geography, State University of New York at Buffalo, Buffalo, NY, USA

    Thomas Bittner

  2. School of Computing, University of Leeds, Leeds, UK

    John G. Stell

Authors
  1. Thomas Bittner
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  2. John G. Stell
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Editor information

Editors and Affiliations

  1. University of Minnesota, Minneapolis, MN, USA

    Shashi Shekhar

  2. Management Science and Information Systems Department, Rutgers Business School, Rutgers, The State University of New Jersey, Newark, NJ, USA

    Hui Xiong

  3. Department of Management Sciences, Tippie College of Business, University of Iowa, Iowa City, IA, USA

    Xun Zhou

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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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