Fuzzy Plane Geometry

  • James J. Buckley
  • Esfandiar Eslami
Part of the Advances in Soft Computing book series (AINSC, volume 13)


Crisp plane geometry starts with points, then lines and parallel lines, circles, triangles, rectangles, etc. In fuzzy plane geometry we will do the same. Our fuzzy points, lines, circles, etc. will all be fuzzy subsets of R × R. We assume the standard xy— rectangular coordinate system in the plane. Since fuzzy subsets of R × R will be surfaces in R 3 we can not easily present graphs of their membership functions. However, α-cuts of fuzzy subsets of R × R will be crisp subsets of the plane. Using an xy-coordinate system we may draw pictures of α-cuts of fuzzy points in R × R, also for fuzzy lines, etc. In this way we can see what the membership functions of fuzzy subsets of R × R look like.


Membership Function Fuzzy Number Plane Geometry Fuzzy Subset Degree Angle 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • James J. Buckley
    • 1
  • Esfandiar Eslami
    • 2
  1. 1.Mathematics DepartmentUniversity of Alabama at BirminghamBirminghamUSA
  2. 2.Department of MathematicsShahid Bahonar UniversityKermanIran

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