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,
Extract,
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,
Extract,
integrateAlpha(),
plot()