We have \(EI(A) := [\int_0^1 A_L(\alpha)\,d\alpha,\int_0^1 A_U(\alpha)\,d\alpha] \), see (Duboid, Prade, 1987).
# S4 method for FuzzyNumber
expectedInterval(object, ...)# S4 method for TrapezoidalFuzzyNumber
expectedInterval(object)
# S4 method for PiecewiseLinearFuzzyNumber
expectedInterval(object)
# S4 method for PowerFuzzyNumber
expectedInterval(object)
a fuzzy number
for FuzzyNumber and DiscontinuousFuzzyNumber - additional arguments passed to integrateAlpha
Returns a numeric vector of length 2.
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.
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