Compute the Alpha-Interval of a Fuzzy Number
We have α-Int(A) := [int_0^1 α A_L(α) dα, int_0^1 α A_U(α) dα].
## S4 method for signature 'FuzzyNumber' alphaInterval(object, ...) ## S4 method for signature 'TrapezoidalFuzzyNumber' alphaInterval(object) ## S4 method for signature 'PiecewiseLinearFuzzyNumber' alphaInterval(object) ## S4 method for signature 'PowerFuzzyNumber' alphaInterval(object)
object |
a fuzzy number |
... |
for |
Note that if an instance of the FuzzyNumber or
DiscontinuousFuzzyNumber class
is given, the calculation is performed via numerical integration.
Otherwise, the computation is exact.
Returns numeric vector of length 2.
Other FuzzyNumber-method: Arithmetic,
FuzzyNumber-class,
FuzzyNumber, alphacut,
ambiguity, as.FuzzyNumber,
as.PiecewiseLinearFuzzyNumber,
as.PowerFuzzyNumber,
as.TrapezoidalFuzzyNumber,
as.character, core,
distance, evaluate,
expectedInterval,
expectedValue,
integrateAlpha,
piecewiseLinearApproximation,
plot, show,
supp,
trapezoidalApproximation,
value, weightedExpectedValue,
width
Other TrapezoidalFuzzyNumber-method: Arithmetic,
TrapezoidalFuzzyNumber-class,
TrapezoidalFuzzyNumber,
TriangularFuzzyNumber,
as.PiecewiseLinearFuzzyNumber,
as.PowerFuzzyNumber,
as.TrapezoidalFuzzyNumber,
expectedInterval, plot
Other PiecewiseLinearFuzzyNumber-method: Arithmetic,
PiecewiseLinearFuzzyNumber-class,
PiecewiseLinearFuzzyNumber,
^,PiecewiseLinearFuzzyNumber,numeric-method,
arctan2,
as.PiecewiseLinearFuzzyNumber,
as.PowerFuzzyNumber,
as.TrapezoidalFuzzyNumber,
as.character,
expectedInterval, fapply,
maximum, minimum,
necessityExceedance,
necessityStrictExceedance,
necessityStrictUndervaluation,
necessityUndervaluation,
plot, possibilityExceedance,
possibilityStrictExceedance,
possibilityStrictUndervaluation,
possibilityUndervaluation
Other PowerFuzzyNumber-method: PowerFuzzyNumber-class,
PowerFuzzyNumber,
as.PowerFuzzyNumber,
as.TrapezoidalFuzzyNumber,
as.character,
expectedInterval
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