Fuzzy Voronoi Diagram

  • Mohammadreza Jooyandeh
  • Ali Mohades Khorasani
Part of the Communications in Computer and Information Science book series (CCIS, volume 6)


In this paper, with first introduce a new extension of Voronoi diagram. We assume Voronoi sites to be fuzzy sets and then define Voronoi diagram for this kind of sites, and provide an algorithm for computing this diagram for fuzzy sites. In the next part of the paper we change sites from set of points to set of fuzzy circles. Then we define the fuzzy Voronoi diagram for such sets and introduce an algorithm for computing it.


Fuzzy Voronoi Diagram Voronoi Diagram Fuzzy Voronoi Cell Fuzzy Geometry Fuzzy Set 


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  1. 1.
    Leibon, G., Letscher, D.: Delaunay triangulations and Voronoi diagrams for Riemannian manifolds. In: 16th Annual Symp. Foundations on Computational Geometry, pp. 341–349. ACM Press, Hong Kong (2000)Google Scholar
  2. 2.
    Alt, H., Cheong, O., Vigneron, A.: The Voronoi diagram of curved objects. Discrete Comput. Geom. 34, 439–453 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Gavriloa, M.L., Rokne, J.: Updating the topology of the dynamic Voronoi diagram for spheres in Euclidean d-dimensional space. Discrete Compu. Geom. 20, 231–242 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Aurenhammer, F., Edelsbrunner, H.: An optimal algorithm for constructing the weighted Voronoi diagram in the plane. Pattern Recognition 17, 251–257 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Arya, S., Malamatos, T.: Linear-size approximate voronoi diagrams. In: 13th Annual ACM-SIAM Symp. on Discrete algorithms, pp. 147–155. Society for Industrial and Applied Mathematics, San Francisco (2002)Google Scholar
  6. 6.
    Fortune, S.: A sweepline algorithm for Voronoi diagrams. Algorithmica 2, 153–174 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kim, D.S., Kim, D., Sugihara, K.: Voronoi diagram of a circle set from Voronoi diagram of a point set. Comput. Aided Geom. Des. 18, 563–585 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kavka, C., Schoenauer, M.: Evolution of Voronoi-Based Fuzzy Controllers. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 541–550. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Mohammadreza Jooyandeh
    • 1
  • Ali Mohades Khorasani
    • 1
  1. 1.Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran

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