Fuzzifying Spatial Relations

  • Hans W. Guesgen
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 106)


Reasoning about space plays an essential role in many cultures. Not only is space, like time, one of the most fundamental categories of human cognition, but also does it structure all our activities and relationships with the external world. Space serves as the basis for many metaphors, including temporal metaphors. It is inherently more complex than time, because it is multidimensional and epistemologically multiple.

The way humans often deal with space in everyday situations is on a qualitative basis, allowing for imprecision in spatial descriptions when interacting with each other. Instead of using an absolute space (i.e., space viewed as a “container”, which exists independently of the objects that are located in it), it seems that they prefer a relative space, which is a construct induced by spatial relations over non-purely spatial entities.

In artificial intelligence, a variety of formalisms have been developed that deal with space on the basis of relations between objects. Although most approaches provide some algorithms to reason about such relations, they usually do not make any attempt to address questions like how to handle imprecision in spatial relations or how to combine qualitative spatial relations with quantitative information. Although these questions seem to be unrelated to each other, we show in this chapter that fuzzy logic can provide an answer to both of them.


Spatial Relation Linguistic Variable Constraint Satisfaction Constraint Satisfaction Problem Fuzzy Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Allen J.F. (1983), Maintaining knowledge about temporal intervals, Communications of the ACM, 26, pp. 832–843.MATHCrossRefGoogle Scholar
  2. 2.
    Dechter R. and Meiri I. (1994), Experimental evaluation of preprocessing algorithms for constraint satisfaction problems, Artificial Intelligence, 68, pp. 211241.Google Scholar
  3. 3.
    Dechter R. and Pearl J. (1987), Network-based heuristics for constraint-satisfaction problems, Artificial Intelligence, 34, pp. 1–38.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Dubois D., Fargier H., and Prade H. (1993), Propagation et satisfaction de constraintes flexibles, in Fuzzy Sets, Neural Networks and Soft Computing, Yager R.R. and Zadeh L. (Eds.), Kluwer, Dordrecht, The Netherlands.Google Scholar
  5. 5.
    Frank A.U. (1998), Formal models for cognition: taxonomy of spatial location description and frames of reference, in Spatial Cognition: An Interdisciplinary Approach to Representation and Processing Spatial Knowledge, Freksa C., Ha-bel C., and Wender K.F. (Eds.), Lecture Notes in Artificial Intelligence 1404, Springer, Berlin, Germany, pp. 293–312.Google Scholar
  6. 6.
    Freksa C. (1990), Qualitative spatial reasoning, Proc. Workshop RAUM, Koblenz, Germany, pp. 21–36.Google Scholar
  7. 7.
    Freksa C. (1992), Temporal reasoning based on semi-intervals, Artificial Intelligence, 54, pp. 199–227.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Freuder E.C. (1982), A sufficient condition for backtrack-free search, Journal of the ACM, 29, pp. 24–32.MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Freuder E.C. (1994), Using metalevel constraint knowledge to reduce constraint checking, Proc. ECAI-94 Workshop on Constraint Processing, Amsterdam, The Netherlands, pp. 27–33.Google Scholar
  10. 10.
    Freuder E.C. and Wallace R.J. (1992), Partial constraint satisfaction. Artificial Intelligence, 58, pp. 21–70.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Guesgen H.W. (1994), A formal framework for weak constraint satisfaction based on fuzzy sets, Proc. ANZIIS-94, Brisbane, Australia, pp. 199–203.Google Scholar
  12. 12.
    Guesgen H.W. (1996), Attacking the complexity of fuzzy constraint satisfaction problems, Proc. International Discourse on Fuzzy Logic and the Management of Complexity (FLAMOC-96), Sydney, Australia, pp. 66–72.Google Scholar
  13. 13.
    Guesgen H.W. and Albrecht J. (2000), Imprecise reasoning in geographic information systems, Fuzzy Sets and Systems (Special Issue on Uncertainty Management in Spatial Data and GIS), 113, pp. 121–131.MATHGoogle Scholar
  14. 14.
    Guesgen H.W. and Hertzberg J. (1993), A constraint-based approach to spatiotemporal reasoning, Applied Intelligence (Special Issue on Applications of Temporal Models), 3, pp. 71–90.Google Scholar
  15. 15.
    Guesgen H.W. and Hertzberg J. (1996), Spatial persistence, Applied Intelligence (Special Issue on Spatial and Temporal Reasoning), 6, pp. 11–28.Google Scholar
  16. 16.
    Guesgen H.W. and Hertzberg J. (2001), Algorithms for buffering fuzzy raster maps, Proc. FLAIRS-01, Key West, Florida, pp. 542–546.Google Scholar
  17. 17.
    Guesgen H.W., Hertzberg J., and Philpott A. (1994), Towards implementing fuzzy Allen relations, Proc. ECAI-94 Workshop on Spatial and Temporal Reasoning, Amsterdam, The Netherlands, pp. 49–55.Google Scholar
  18. 18.
    Guesgen H.W. and Philpott A. (1995), Heuristics for solving fuzzy constraint satisfaction problems, Proc. ANNES-95, Dunedin, New Zealand, pp. 132–135.Google Scholar
  19. 19.
    Haralick R.M. and Elliott G.L. (1980), Increasing tree search efficiency for constraint satisfaction problems, Artificial Intelligence, 14, pp. 263–313.CrossRefGoogle Scholar
  20. 20.
    Hernandez D. (1991), Relative representation of spatial knowledge: the 2-D case, in Cognitive and Linguistic Aspects of Geographic Space, Mark D.M. and Frank A.U. (Eds.), Kluwer, Dordrecht, The Netherlands, pp. 373–385.CrossRefGoogle Scholar
  21. 21.
    Mackworth A.K. (1977), Consistency in networks of relations, Artificial Intelligence, 8, pp. 99–118.MATHCrossRefGoogle Scholar
  22. 22.
    Mukerjee A. and Joe G. (1990), A qualitative model for space, Proc. AAAI-90, Boston, Massachusetts, pp. 721–727.Google Scholar
  23. 23.
    Prosser P. (1993), Hybrid algorithms for the constraint satisfaction problem, Computational Intelligence, 9, pp. 268–299.CrossRefGoogle Scholar
  24. 24.
    Ruttkay Z. (1994), Fuzzy constraint satisfaction, Proc. FUZZ-IEEE’94, Orlando, Florida.Google Scholar
  25. 25.
    Stone H.S. and Stone J.M. (1986), Efficient search techniques: an empirical study of the n-queens problem, Technical Report RC 12057 (#54343), IBM T.J. Watson Research Center, Yorktown Heights, New York.Google Scholar
  26. 26.
    Vieu L. (1997), Spatial representation and reasoning in artificial intelligence, in Spatial and Temporal Reasoning, Stock O. (Ed.), Kluwer, Dordrecht, The Netherlands, pp. 5–41.CrossRefGoogle Scholar
  27. 27.
    Zadeh L.A. (1975), The concept of a linguistic variable and its application to approximate reasoning—I, Information Sciences, 8, pp. 199–249.MathSciNetMATHCrossRefGoogle Scholar

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© Physica-Verlag Heidelberg 2002

Authors and Affiliations

  • Hans W. Guesgen
    • 1
  1. 1.Computer Science DepartmentUniversity of AucklandAucklandNew Zealand

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