FuzzyNumbers (version 0.4-7)

alphaInterval: Compute the Alpha-Interval of a Fuzzy Number

Description

We have \(\alpha-Int(A) := [\int_0^1 \alpha A_L(\alpha)\,d\alpha, \int_0^1 \alpha A_U(\alpha)\,d\alpha] \).

Usage

# S4 method for FuzzyNumber
alphaInterval(object, ...)
# S4 method for TrapezoidalFuzzyNumber
alphaInterval(object)
# S4 method for PiecewiseLinearFuzzyNumber
alphaInterval(object)
# S4 method for PowerFuzzyNumber
alphaInterval(object)

Arguments

object

a fuzzy number

...

for FuzzyNumber and DiscontinuousFuzzyNumber - additional arguments passed to integrateAlpha

Value

Returns numeric vector of length 2.

Details

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.

See Also

Other FuzzyNumber-method: Arithmetic, Extract, 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, Extract, 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: Extract, PowerFuzzyNumber-class, PowerFuzzyNumber, as.PowerFuzzyNumber(), as.TrapezoidalFuzzyNumber(), as.character(), expectedInterval()