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