Fuzzy Plane Geometry: Triangles
Fuzzy Plane Geometry: Triangles
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Date
1998-10-15
Authors
Rosenfeld, Azriel
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Abstract
(Also cross-referenced as CAR-TR-694)
A fuzzy triangle T (with a discrete-valued membership function)
can be regarded as a nest of parallel-sided triangles Ti with successively
higher membership values. Such a nest is determined by its max projections
on any two of its "sides". The area (per imeter) of T is a weighted sum of
the areas (perimeters) of the Ti's. The side lengths and altitudes of T
can also be defined as weighted sums obtained from projections; using
these definitions, the perimeter of T is the sum of the side lengths, and
the s ide lengths are related to the vertex angles by the Law of Sines,
but there is no simple relationship between the area of T and the products
of the side lengths and altitudes.