Calculate the Expected Interval of a Fuzzy Number
We have EI(A) := [int_0^1 A_L(α) dα, int_0^1 A_U(α) dα], see (Duboid, Prade, 1987).
## S4 method for signature 'FuzzyNumber' expectedInterval(object, ...) ## S4 method for signature 'TrapezoidalFuzzyNumber' expectedInterval(object) ## S4 method for signature 'PiecewiseLinearFuzzyNumber' expectedInterval(object) ## S4 method for signature 'PowerFuzzyNumber' expectedInterval(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 a numeric vector of length 2.
Dubois D., Prade H. (1987), The mean value of a fuzzy number, Fuzzy Sets and Systems 24, pp. 279-300.
Other FuzzyNumber-method: Arithmetic,
FuzzyNumber-class,
FuzzyNumber, alphaInterval,
alphacut, ambiguity,
as.FuzzyNumber,
as.PiecewiseLinearFuzzyNumber,
as.PowerFuzzyNumber,
as.TrapezoidalFuzzyNumber,
as.character, core,
distance, evaluate,
expectedValue,
integrateAlpha,
piecewiseLinearApproximation,
plot, show,
supp,
trapezoidalApproximation,
value, weightedExpectedValue,
width
Other TrapezoidalFuzzyNumber-method: Arithmetic,
TrapezoidalFuzzyNumber-class,
TrapezoidalFuzzyNumber,
TriangularFuzzyNumber,
alphaInterval,
as.PiecewiseLinearFuzzyNumber,
as.PowerFuzzyNumber,
as.TrapezoidalFuzzyNumber,
plot
Other PiecewiseLinearFuzzyNumber-method: Arithmetic,
PiecewiseLinearFuzzyNumber-class,
PiecewiseLinearFuzzyNumber,
^,PiecewiseLinearFuzzyNumber,numeric-method,
alphaInterval, arctan2,
as.PiecewiseLinearFuzzyNumber,
as.PowerFuzzyNumber,
as.TrapezoidalFuzzyNumber,
as.character, fapply,
maximum, minimum,
necessityExceedance,
necessityStrictExceedance,
necessityStrictUndervaluation,
necessityUndervaluation,
plot, possibilityExceedance,
possibilityStrictExceedance,
possibilityStrictUndervaluation,
possibilityUndervaluation
Other PowerFuzzyNumber-method: PowerFuzzyNumber-class,
PowerFuzzyNumber,
alphaInterval,
as.PowerFuzzyNumber,
as.TrapezoidalFuzzyNumber,
as.character
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