Calculate the Distance Between Two Fuzzy Numbers
Currently, only Euclidean distance may be calculated. We have d_E^2(A,B) := int_0^1 (A_L(α)-B_L(α))^2 dα + int_0^1 (A_U(α)-B_U(α))^2 dα, see (Grzegorzewski, 1988).
## S4 method for signature 'FuzzyNumber,FuzzyNumber'
distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...)
## S4 method for signature 'FuzzyNumber,DiscontinuousFuzzyNumber'
distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...)
## S4 method for signature 'DiscontinuousFuzzyNumber,FuzzyNumber'
distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...)
## S4 method for signature 'DiscontinuousFuzzyNumber,DiscontinuousFuzzyNumber'
distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...)e1 |
a fuzzy number |
e2 |
a fuzzy number |
... |
additional arguments passed to |
type |
one of |
The calculation are done using numerical integration,
Returns the calculated distance, i.e. a single numeric value.
Grzegorzewski P., Metrics and orders in space of fuzzy numbers, Fuzzy Sets and Systems 97, 1998, pp. 83-94.
Other FuzzyNumber-method: Arithmetic,
FuzzyNumber-class,
FuzzyNumber, alphaInterval,
alphacut, ambiguity,
as.FuzzyNumber,
as.PiecewiseLinearFuzzyNumber,
as.PowerFuzzyNumber,
as.TrapezoidalFuzzyNumber,
as.character, core,
evaluate, expectedInterval,
expectedValue,
integrateAlpha,
piecewiseLinearApproximation,
plot, show,
supp,
trapezoidalApproximation,
value, weightedExpectedValue,
width
Other DiscontinuousFuzzyNumber-method: DiscontinuousFuzzyNumber-class,
DiscontinuousFuzzyNumber,
integrateAlpha, plot
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