A Fuzzy Set Approach to Expressing Preferences in Spatial Reasoning

  • Hans W. Guesgen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9060)


The way we use spatial descriptions in many everyday situations is of a qualitative nature. This is often achieved by specifying spatial relations between objects or regions. The advantage of using qualitative descriptions is that we can be less precise and thereby less prone to making an error. For example, it is often easier to decide whether an object is inside another object than to specify exactly where the first object is with respect to the second one. In artificial intelligence, a variety of formalisms have been developed that deal with space on the basis of relations between objects or regions that objects might occupy. One of these formalisms is the RCC theory, which is based on a primitive relation, called connectedness, and uses a set of topological relations, defined on the basis of connectedness, to provide a framework for reasoning about regions. This paper discusses an extension of the RCC theory based on fuzzy logic, which enables us to express preferences among spatial descriptions.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Allen, J.: Maintaining knowledge about temporal intervals. Commun. ACM 26, 832–843 (1983)CrossRefMATHGoogle Scholar
  2. 2.
    Bloch, I.: Spatial representation of spatial relationship knowledge. In: Proc. KR 2000, pp. 247–258. Breckenridge, Colorado (2000)Google Scholar
  3. 3.
    Bloch, I.: Fuzzy spatial relationships for image processing and interpretation: A review. Image and Vision Computing 23, 89–110 (2005)CrossRefGoogle Scholar
  4. 4.
    Brewka, G.: Preferred subtheories: An extended logical framework for default reasoning. In: Proc. IJCAI 1989, pp. 1043–1048 (1989)Google Scholar
  5. 5.
    Cohn, A., Bennett, B., Gooday, J., Gotts, N.: Representing and reasoning with qualitative spatial relations about regions. In: Stock, O. (ed.) Spatial and Temporal Reasoning, pp. 97–134. Kluwer, Dordrecht (1997)CrossRefGoogle Scholar
  6. 6.
    Cohn, A., Gotts, N.: The ‘Egg-Yolk’ representation of regions with indeterminate boundaries. In: Burrough, P., Frank, A. (eds.) Geographical Objects with Undetermined Boundaries. GISDATA Series, vol. 2, pp. 171–187. Taylor and Francis, London (1996)Google Scholar
  7. 7.
    Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, London (1980)MATHGoogle Scholar
  8. 8.
    Egenhofer, M., Al-Taha, K.: Reasoning about gradual changes of topological relationships. In: Frank, A.U., Campari, I., Formentini, U. (eds.) GIS 1992. LNCS, vol. 639, pp. 196–219. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  9. 9.
    Freksa, C.: Temporal reasoning based on semi-intervals. Artificial Intelligence 54, 199–227 (1992)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Freuder, E., Wallace, R.: Partial constraint satisfaction. Artificial Intelligence 58, 21–70 (1992)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Guesgen, H.: Spatial reasoning based on Allen’s temporal logic. Technical Report TR-89-049, ICSI, Berkeley, California (1989)Google Scholar
  12. 12.
    Guesgen, H., Hertzberg, J.: Spatial persistence. Applied Intelligence (Special Issue on Spatial and Temporal Reasoning) 6, 11–28 (1996)Google Scholar
  13. 13.
    Guesgen, H., Hertzberg, J., Philpott, A.: Towards implementing fuzzy Allen relations. In: Proc. ECAI-94 Workshop on Spatial and Temporal Reasoning, Amsterdam, The Netherlands, pp. 49–55 (1994)Google Scholar
  14. 14.
    Klir, G., Folger, T.: Fuzzy Sets, Uncertainty, and Information. Prentice Hall, Englewood Cliffs (1988)Google Scholar
  15. 15.
    Lehmann, F., Cohn, A.: The EGG/YOLK reliability hierarchy: Semantic data integration using sorts with prototypes. In: Proc. 3rd International Conference on Information and Knowledge Management (CIKM 1994), pp. 272–279. Gaithersburg, Maryland (1994)Google Scholar
  16. 16.
    Ligozat, G. (ed.): Qualitative Spatial and Temporal Reasoning. Wiley-ISTE, Hoboken (2011)MATHGoogle Scholar
  17. 17.
    Randell, D., Cui, Z., Cohn, A.: A spatial logic based on regions and connection. In: Proc. KR 1992, pp. 165–176. Cambridge, Massachusetts (1992)Google Scholar
  18. 18.
    Renz, J.: A spatial odyssey of the interval algebra: 1. directed intervals. In: Proc. IJCAI 2001, pp. 51–56. Seattle, Washington (2001)Google Scholar
  19. 19.
    Schockaert, S., De Cock, M., Cornelis, C., Kerre, E.: Fuzzy region connection calculus: Representing vague topological information. Journal of Approximate Reasoning 48, 314–331 (2008)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Zadeh, L.: Fuzzy sets. Information and Control 8, 338–353 (1965)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Hans W. Guesgen
    • 1
  1. 1.Massey UniversityPalmerston NorthNew Zealand

Personalised recommendations