| distance {FuzzyNumbers} | R Documentation |
Calculate the Distance Between Two Fuzzy Numbers
Description
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).
Usage
## 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"), ...)
Arguments
e1 |
a fuzzy number |
e2 |
a fuzzy number |
... |
additional arguments passed to |
type |
one of |
Details
The calculation are done using numerical integration,
Value
Returns the calculated distance, i.e. a single numeric value.
References
Grzegorzewski P., Metrics and orders in space of fuzzy numbers, Fuzzy Sets and Systems 97, 1998, pp. 83-94.
See Also
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()