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Fuzzy regions: adding subregions and the impact on surface and distance calculation

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Abstract
In the concept of fuzzy regions we introduced before, a region was considered to be a fuzzy set of points, each having its own membership grade. While this allows the modelling of regions in which points only partly belong to the region, it has the downside that all the points are considered independently, which is too loose a restriction for some situations. The model is not able to support the fact that some points may be linked together. In this contribution, we propose an extension to the model, so that points can be made related to one another. It will permit the user to, for instance, specify points or even (sub)regions within the fuzzy region that are linked together: they all belong to the region to the same extent at the same time. By letting the user specify such subregions, the accuracy Of the model can be increased: the model can match the real situation better; while at the same time decreasing the fuzziness: if points are known to be related, there is no need to consider them independently. As an example, the use of such a fuzzy region to represent a lake with a variable water level can be considered: as the water level rises, a set of points will become flooded; it is interesting to represent this set of points as a. subset of the region, as these points are somewhat related (the same can be done for different water levels). The impact of this extension to the model on both surface area calculation an distance measurement are considered, and new appropriate definitions are introduced.

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Citation

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MLA
Verstraete, Jörg. “Fuzzy Regions: Adding Subregions and the Impact on Surface and Distance Calculation.” Communications in Computer and Information Science. Ed. E Hüllermeier, R Kruse, & F Hoffman. Vol. 80. New York, NY, USA: Springer, 2010. 561–570. Print.
APA
Verstraete, Jörg. (2010). Fuzzy regions: adding subregions and the impact on surface and distance calculation. In E Hüllermeier, R. Kruse, & F. Hoffman (Eds.), Communications in Computer and Information Science (Vol. 80, pp. 561–570). Presented at the 13th International conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2010), New York, NY, USA: Springer.
Chicago author-date
Verstraete, Jörg. 2010. “Fuzzy Regions: Adding Subregions and the Impact on Surface and Distance Calculation.” In Communications in Computer and Information Science, ed. E Hüllermeier, R Kruse, and F Hoffman, 80:561–570. New York, NY, USA: Springer.
Chicago author-date (all authors)
Verstraete, Jörg. 2010. “Fuzzy Regions: Adding Subregions and the Impact on Surface and Distance Calculation.” In Communications in Computer and Information Science, ed. E Hüllermeier, R Kruse, and F Hoffman, 80:561–570. New York, NY, USA: Springer.
Vancouver
1.
Verstraete J. Fuzzy regions: adding subregions and the impact on surface and distance calculation. In: Hüllermeier E, Kruse R, Hoffman F, editors. Communications in Computer and Information Science. New York, NY, USA: Springer; 2010. p. 561–70.
IEEE
[1]
J. Verstraete, “Fuzzy regions: adding subregions and the impact on surface and distance calculation,” in Communications in Computer and Information Science, Dortmund, Germany, 2010, vol. 80, pp. 561–570.
@inproceedings{1944952,
  abstract     = {In the concept of fuzzy regions we introduced before, a region was considered to be a fuzzy set of points, each having its own membership grade. While this allows the modelling of regions in which points only partly belong to the region, it has the downside that all the points are considered independently, which is too loose a restriction for some situations. The model is not able to support the fact that some points may be linked together. In this contribution, we propose an extension to the model, so that points can be made related to one another. It will permit the user to, for instance, specify points or even (sub)regions within the fuzzy region that are linked together: they all belong to the region to the same extent at the same time. By letting the user specify such subregions, the accuracy Of the model can be increased: the model can match the real situation better; while at the same time decreasing the fuzziness: if points are known to be related, there is no need to consider them independently. As an example, the use of such a fuzzy region to represent a lake with a variable water level can be considered: as the water level rises, a set of points will become flooded; it is interesting to represent this set of points as a. subset of the region, as these points are somewhat related (the same can be done for different water levels). The impact of this extension to the model on both surface area calculation an distance measurement are considered, and new appropriate definitions are introduced.},
  author       = {Verstraete, Jörg},
  booktitle    = {Communications in Computer and Information Science},
  editor       = {Hüllermeier, E and Kruse, R and Hoffman, F},
  isbn         = {9783642140549},
  issn         = {1865-0929},
  language     = {eng},
  location     = {Dortmund, Germany},
  pages        = {561--570},
  publisher    = {Springer},
  title        = {Fuzzy regions: adding subregions and the impact on surface and distance calculation},
  url          = {http://dx.doi.org/10.1007/978-3-642-14055-6_59},
  volume       = {80},
  year         = {2010},
}

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