An Introduction to Fuzzy Logic and Fuzzy Sets pp 175-183 | Cite as

# Fuzzy Plane Geometry

## Abstract

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.

## Keywords

Membership Function Fuzzy Number Plane Geometry Fuzzy Subset Degree Angle## Preview

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