Currently, only Euclidean distance may be calculated. We have \(d_E^2(A,B) := \int_0^1 (A_L(\alpha)-B_L(\alpha))^2\,d\alpha,\int_0^1 + (A_U(\alpha)-B_U(\alpha))^2\,d\alpha \), see (Grzegorzewski, 1988).
# S4 method for FuzzyNumber,FuzzyNumber
distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...)# S4 method for FuzzyNumber,DiscontinuousFuzzyNumber
distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...)
# S4 method for DiscontinuousFuzzyNumber,FuzzyNumber
distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...)
# S4 method for DiscontinuousFuzzyNumber,DiscontinuousFuzzyNumber
distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...)
a fuzzy number
a fuzzy number
additional arguments passed to integrate
one of "Euclidean", "EuclideanSquared"
Returns the calculated distance, i.e. a single numeric value.
The calculation are done using numerical integration,
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