alphaInterval {FuzzyNumbers}

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 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)

Arguments

object

a fuzzy number

...

for FuzzyNumber and DiscontinuousFuzzyNumber - additional arguments passed to integrateAlpha

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.

Value

Returns numeric vector of length 2.

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()