Calculate the Weighted Expected Value of a Fuzzy Number

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Description

The calculation of the so-called weighted expected value is one of possible methods to deffuzify a fuzzy number.

For w=0.5 we get the ordinary expectedValue.

Usage

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## S4 method for signature 'FuzzyNumber'
weightedExpectedValue(object, w=0.5, ...)

Arguments

object

a fuzzy number

...

additional arguments passed to expectedInterval

w

a single numeric value in [0,1]

Details

The weighted expected value of A is defined as EV_w(A) := (1-w) EI_L(A) + w EI_U(A), where EI is the expectedInterval.

Value

Returns a single numeric value.

See Also

Other FuzzyNumber-method: *,PiecewiseLinearFuzzyNumber,FuzzyNumber-method, *,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method, *,PiecewiseLinearFuzzyNumber,numeric-method, *,TrapezoidalFuzzyNumber,numeric-method, *,numeric,FuzzyNumber-method, +,PiecewiseLinearFuzzyNumber,FuzzyNumber-method, +,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method, +,PiecewiseLinearFuzzyNumber,numeric-method, +,TrapezoidalFuzzyNumber,TrapezoidalFuzzyNumber-method, +,numeric,FuzzyNumber-method, -,FuzzyNumber,ANY-method, -,PiecewiseLinearFuzzyNumber,FuzzyNumber-method, -,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method, -,PiecewiseLinearFuzzyNumber,numeric-method, -,TrapezoidalFuzzyNumber,TrapezoidalFuzzyNumber-method, -,numeric,FuzzyNumber-method, /,PiecewiseLinearFuzzyNumber,FuzzyNumber-method, /,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method, /,PiecewiseLinearFuzzyNumber,numeric-method, Arithmetic; FuzzyNumber-class; FuzzyNumber; alphaInterval, alphaInterval,FuzzyNumber-method, alphaInterval,PiecewiseLinearFuzzyNumber-method, alphaInterval,PowerFuzzyNumber-method, alphaInterval,TrapezoidalFuzzyNumber-method; alphacut, alphacut,FuzzyNumber,numeric-method; ambiguity, ambiguity,FuzzyNumber-method; as.FuzzyNumber, as.FuzzyNumber,FuzzyNumber-method, as.FuzzyNumber,numeric-method; as.PiecewiseLinearFuzzyNumber, as.PiecewiseLinearFuzzyNumber,FuzzyNumber-method, as.PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method, as.PiecewiseLinearFuzzyNumber,TrapezoidalFuzzyNumber-method, as.PiecewiseLinearFuzzyNumber,numeric-method; as.PowerFuzzyNumber, as.PowerFuzzyNumber,FuzzyNumber-method, as.PowerFuzzyNumber,PiecewiseLinearFuzzyNumber-method, as.PowerFuzzyNumber,PowerFuzzyNumber-method, as.PowerFuzzyNumber,TrapezoidalFuzzyNumber-method, as.PowerFuzzyNumber,numeric-method; as.TrapezoidalFuzzyNumber, as.TrapezoidalFuzzyNumber,FuzzyNumber-method, as.TrapezoidalFuzzyNumber,PiecewiseLinearFuzzyNumber-method, as.TrapezoidalFuzzyNumber,PowerFuzzyNumber-method, as.TrapezoidalFuzzyNumber,TrapezoidalFuzzyNumber-method, as.TrapezoidalFuzzyNumber,numeric-method; as.character, as.character,FuzzyNumber-method, as.character,PiecewiseLinearFuzzyNumber-method, as.character,PowerFuzzyNumber-method, as.character,TrapezoidalFuzzyNumber-method; core, core,FuzzyNumber-method; distance, distance,DiscontinuousFuzzyNumber,DiscontinuousFuzzyNumber-method, distance,DiscontinuousFuzzyNumber,FuzzyNumber-method, distance,FuzzyNumber,DiscontinuousFuzzyNumber-method, distance,FuzzyNumber,FuzzyNumber-method; evaluate, evaluate,FuzzyNumber,numeric-method; expectedInterval, expectedInterval,FuzzyNumber-method, expectedInterval,PiecewiseLinearFuzzyNumber-method, expectedInterval,PowerFuzzyNumber-method, expectedInterval,TrapezoidalFuzzyNumber-method; expectedValue, expectedValue,FuzzyNumber-method; integrateAlpha, integrateAlpha,DiscontinuousFuzzyNumber,character,numeric,numeric-method, integrateAlpha,FuzzyNumber,character,numeric,numeric-method; piecewiseLinearApproximation, piecewiseLinearApproximation,FuzzyNumber-method; plot, plot,DiscontinuousFuzzyNumber,missing-method, plot,FuzzyNumber,missing-method, plot,PiecewiseLinearFuzzyNumber,missing-method, plot,TrapezoidalFuzzyNumber,missing-method; show, show,FuzzyNumber-method; supp, supp,FuzzyNumber-method; trapezoidalApproximation, trapezoidalApproximation,FuzzyNumber-method; value, value,FuzzyNumber-method; width, width,FuzzyNumber-method

Other characteristics: ambiguity, ambiguity,FuzzyNumber-method; expectedValue, expectedValue,FuzzyNumber-method; value, value,FuzzyNumber-method; width, width,FuzzyNumber-method

Other deffuzification: expectedValue, expectedValue,FuzzyNumber-method; value, value,FuzzyNumber-method

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