Skip to main content
SpringerLink
Log in

Geospatial Uncertainty Representation: Fuzzy and Rough Set Approaches

  • Chapter
  • First Online:
Fifty Years of Fuzzy Logic and its Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 326))

Abstract

Uncertainty in geospatial data is often considered in the context of geographical information systems which enable a variety of operations and manipulation of spatial data. Here we consider how both fuzzy set and rough set theory has been used to represent geospatial data with uncertainty. Terrain modeling and triangulated irregular networks techniques utilizing fuzzy sets are presented. Rough set theory is overviewed and its application to spatial data is described. Issues of uncertainty in the representation of spatial relationships such as topological and directional relationships are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Longley, P., Goodchild, M., Maguire, D., Rhind, D.: Geographic Information Systems and Science, 3rd edn. Wiley, Chichestere (2010)

    Google Scholar 

  2. Rigaux, P., Scholl, M., Voisard, A.: Spatial Databases with Application to GIS. Morgan Kaufmann San Francisco (2002)

    Google Scholar 

  3. Shekar, S., Chawla, S.: Spatial Databases: A Tour. Prentice Hall, Upper Saddle River (2003)

    Google Scholar 

  4. Boyd, D., Crawford, K.: Critical questions for big data. Inf. Commun. Soc. 15(5), 662–679 (2012)

    Article  Google Scholar 

  5. Michael, K., Miller, K.: Big Data: New opportunities and new challenges. IEEE Comput. 46(6), 22–24 (2013)

    Article  Google Scholar 

  6. Shekar, S., Gunturi, V., Evans, M., Yang, K.: Spatial big-data challenges—intersecting mobility and cloud computing. In: Proceedings of 11th ACM International Workshop on Data Engineering for Wireless and Mobile Access, New York, pp. 1–6 (2012)

    Google Scholar 

  7. Overpeck, J., Meehl, G., Bony, S., Easterling, D.: Climate data challenges in the 21st century. Science 331, 700–702 (2011)

    Article  Google Scholar 

  8. Vatsavai, R., Chandola, V., Klasky, S., Ganguly, A., Stefandidis, A., Shekhar, S.: Spatiotemporal data mining in the era of big data. In: Proceedings of ACM Sigspatial: Bigspatial ‘12, Redondo Beach, CA, pp. 1–10 (2012)

    Google Scholar 

  9. Burrough, P., Frank, A. (eds.): Geographic Objects with Indeterminate Boundaries, GISDATA Series, vol. 2. Taylor and Francis, London (1996)

    Google Scholar 

  10. Zhang, J., Goodchild, M .: Uncertainty in Geographical Information. Taylor and Francis, London (2002)

    Google Scholar 

  11. Varsi, A.: Philosophical issues in geography—an introduction. Topoi 20, 119–130 (2001)

    Article  Google Scholar 

  12. Varsi, A.: Vagueness in geography. Philos. Geogr. 4, 49–65 (2001)

    Article  Google Scholar 

  13. Couclelis, H.: The certainty of uncertainty: GIS and the limits of geographic knowledge. Trans. GIS 7(2), 165–175 (2003)

    Article  Google Scholar 

  14. Worboys, M., Clementini, E.: Integration of imperfect spatial information. J. Vis. Lang. Comput. 12, 61–80 (2001)

    Article  Google Scholar 

  15. Beaubouef, T., Petry, F., Breckenridge, J.: Rough set based uncertainty management for spatial databases and geographical information systems. In: Suzuki, Y. (ed.) Soft Computing in Industrial Applications, pp. 471–479. Chap 6a. Springer, London (2000)

    Google Scholar 

  16. Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  17. Gale, S.: Inexactness, fuzzy sets, and the foundations of behavioral geography. Geogr. Anal. 4, 337–349 (1972)

    Article  Google Scholar 

  18. Fisher, P.: Boolean and fuzzy regions. In: Burrough, P.A., Frank, A. (eds.) Geographic Objects with Indeterminate Boundaries, 87–94. Taylor and Francis, London (1996)

    Google Scholar 

  19. Robinson, V., Frank, A.: About different kinds of uncertainty in geographic information systems. In: Proceedings AUTOCARTO 7 Conference, pp. 440–449. American Society for Photogrammetry and Remote Sensing, Falls Church (1985)

    Google Scholar 

  20. Wang, F.: A fuzzy grammar and possibility theory-based natural language user interface for spatial queries. Int. J. Fuzzy Sets Syst. 113, 147–159 (2000)

    Article  MATH  Google Scholar 

  21. Cobb, M., Petry, F.: Modeling Spatial data within a fuzzy framework. J. Am. Soc. Inf. Sci. 49(3), 253–266 (1998)

    Article  Google Scholar 

  22. Cross, V., Firat, A.: Fuzzy objects for geographical information systems. Fuzzy Sets Syst. 113, 19–36 (2000)

    Article  MATH  Google Scholar 

  23. De Tré, G., De Caluwe, R.: A generalized object-oriented database model with generalized constraints. In: Proceedings of NAFIPS 1999, New York, pp. 381–386 (1999)

    Google Scholar 

  24. Morris, A.: A framework for modeling uncertainty in spatial databases. Trans. GIS 7, 83–101 (2003)

    Article  Google Scholar 

  25. Skidmore, A.: Terrain position as mapped from a gridded digital elevation model. Int. J. Geogr. Inf. Syst. 4, 33–49 (1990)

    Article  Google Scholar 

  26. Irvin, B., Ventura, S., Slater, B.: Fuzzy and isodata classification of landform elements from digital terrain data in Pleasant Valley, Wisconsin. Geoderma 77, 137–154 (1996)

    Article  Google Scholar 

  27. MacMillan, R., Pettapiece, W., Nolan, S., Goddard, T.: A generic procedure for automatically segmenting landforms into landform elements using DEMs, heuristic rules and fuzzy logic. Fuzzy Sets Syst. 113, 81–109 (2000)

    Article  MATH  Google Scholar 

  28. Shi, X., Xing, A., Zhu, A., Wang, R.: Fuzzy representation of special terrain features using a similarity-based approach. In: Petry, F., Robinson, V., Cobb, M. (eds.) Fuzzy Modeling with Spatial Information for Geographic Problems, pp. 233–252. Springer, Heidelberg (2005)

    Google Scholar 

  29. Verstraete, J., De Tré, G., De Caluwe, R., Hallez, A.: Field based methods for the modeling of fuzzy spatial data. In: Petry, F., Robinson, V., Cobb, M. (eds.) Fuzzy Modeling with Spatial Information for Geographic Problems, pp. 41–70. Springer, Heidelberg (2005)

    Google Scholar 

  30. Schneider, M.: Spatial data types for database systems. Doctoral Thesis, Fern Universität Hagen, GR

    Google Scholar 

  31. Worboys, M.: Imprecision in finite resolution spatial data. Geoinformatica 2(3), 257–280 (1998)

    Article  Google Scholar 

  32. Worboys, M.: Computation with imprecise geospatial data. Comput. Environ. Urban Syst. 22(2), 85–106 (1998)

    Article  Google Scholar 

  33. Ahlqvist, O., Keukelaar, J., Oukbir, K.: Rough classification and accuracy assessment. Int. J. Geogr. Inf. Sci. 14(5), 475–496 (2000)

    Article  Google Scholar 

  34. Wang, S., Yuan, H., Chen, G., Li, D., Shi, W.: Rough spatial interpretation. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 435–444. Springer, Heidelberg (2004)

    Google Scholar 

  35. Bittner, T., Stell, J.: Stratified rough sets and vagueness. In: Kuhn, W., Worboys, M.F., Timpf, S. (eds.) COSIT 2003. LNCS, vol. 2825, pp. 286–303. Springer, Heidelberg (2003)

    Google Scholar 

  36. Pawlak, Z.: Rough sets. Int. J. Man-Mach. Stud. 21, 127–134 (1984)

    Article  MATH  Google Scholar 

  37. Egenhofer, M., Franzosa, R.: Point set topological spatial relations. Int. J. Geogr. Inf. Syst. 5(2), 161–174 (1991)

    Article  Google Scholar 

  38. Papadias, D., Karacapilidis, N., Arkoumnais, D.: Processing fuzzy spatial queries: a configuration similarity approach. Int. J. Geogr. Inf. Sci. 13, 93–128 (1999)

    Article  Google Scholar 

  39. Kulik, L., Eschenbach, C., Habel, C., Schmidtke, H.: A graded approach to directions between extended objects. In: Egenhofer, M.J., Mark, D.M. (eds.) GIScience 2002. LNCS, vol. 2478, pp. 119–131. Springer, Heidelberg (2002)

    Google Scholar 

  40. Vazirgiannis, M.: Uncertainty handling in spatial relationships. In: ACM-SAC 2000 Proceedings, Como Italy, pp. 215–221 (2000)

    Google Scholar 

  41. Matsakis, P.: Understanding the spatial organization of image regions by force histograms. In: Matsakis, P., Sztandra, L. (eds.) Applying Soft Computing in Defining Spatial Relations, 1–16. Physica Verlag, Heidelberg (2002)

    Chapter  Google Scholar 

  42. Guesgen, H.: Fuzzifying Spatial Relations. In: Matsakis, P., Sztandra, L. (eds.) Applying Soft Computing in Defining Spatial Relations, GR 99-122. Physica Verlag, Heidelberg (2002)

    Google Scholar 

  43. Dutta, S.: Approximate spatial reasoning: integrating qualitative and quantitative constraints. Int. J. Approx. Reason. 5(3), 307–331 (1991)

    Article  Google Scholar 

  44. Allen, J.: Maintaining knowledge about temporal intervals. Commun. ACM 26(11), 832–843 (1983)

    Article  MATH  Google Scholar 

  45. Cobb, M., Petry, F.: Geometric approximations of spatial boundaries and assessment of fuzzy spatial relationships. Fuzzy Sets Syst. 113, 111–120 (2000)

    Article  MATH  Google Scholar 

  46. Petry, F., Cobb, M., Wen, L., Yang, H.: Design of system for managing fuzzy relationships for integration of spatial data in querying. Fuzzy Sets Syst. 140, 51–73 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  47. Mendel, J., John, R.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Sets 10, 117–127 (2002)

    Google Scholar 

  48. Verstraete, J.: Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions. In: Mugellini, E., Szczepaniak, P., Pettenati, M., Sokhn, M. (eds.) Advances in Intelligent Web Mastering, vol. 3, pp. 163–172 (2011)

    Google Scholar 

  49. Verstraete, J.: Surface area of level-2 fuzzy regions unifying possibilistic and versitic interpretations of regions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds.) Artifical Intellgience and Soft Computing, pp. 342–349. Springer (2012)

    Google Scholar 

  50. Atanassov, K.: Intuitionstic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

We would like to thank the Naval Research Laboratory’s Base Program, Program Element No. 0602435 N for sponsoring this research.

Author information

Authors and Affiliations

  1. Marine Geosciences Division, Geospatial Science and Technology Branch, Bldg. 1005, Raleigh, USA

    Frederick Petry

  2. Naval Research Laboratory, Stennis Space Center, MS 39529, Washington, USA

    Paul Elmore

Authors
  1. Frederick Petry
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul Elmore
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Frederick Petry .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Texas State University, San Marcos, Texas, USA

    Dan E. Tamir

  2. School of Computing and Information Sciences, Florida International University, Miami, Florida, USA

    Naphtali D. Rishe

  3. School of Computing and Information Sciences, The University of South Florida, Tampa, Florida, USA, and Florida International University, Miami, Florida, USA

    Abraham Kandel

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Petry, F., Elmore, P. (2015). Geospatial Uncertainty Representation: Fuzzy and Rough Set Approaches. In: Tamir, D., Rishe, N., Kandel, A. (eds) Fifty Years of Fuzzy Logic and its Applications. Studies in Fuzziness and Soft Computing, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-319-19683-1_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19683-1_24

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19682-4

  • Online ISBN: 978-3-319-19683-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation