# expectedInterval-methods: Calculate the Expected Interval of a Fuzzy Number In FuzzyNumbers: Tools to Deal with Fuzzy Numbers

## Description

We have EI(A) := [int_0^1 A_L(α) dα, int_0^1 A_U(α) dα], see (Duboid, Prade, 1987).

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## 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) ```

## 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 a numeric vector of length 2.

## References

Dubois D., Prade H. (1987), The mean value of a fuzzy number, Fuzzy Sets and Systems 24, pp. 279-300.

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