# alphacut-methods: Calculate Alpha-Cuts In FuzzyNumbers: Tools to Deal with Fuzzy Numbers

## Description

If A is a fuzzy numbers, then its α-cuts are always in form of intervals. Moreover, the α-cuts form a nonincreasing chain w.r.t. alpha.

## Usage

 ```1 2``` ```## S4 method for signature 'FuzzyNumber,numeric' alphacut(object, alpha) ```

## Arguments

 `object` a fuzzy numbers `alpha` numeric vector with elements in [0,1]

## Value

Returns a matrix with two columns (left and right alha cut bounds). if some elements in `alpha` are not in [0,1], then `NA` is set.

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`; `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`; `weightedExpectedValue`, `weightedExpectedValue,FuzzyNumber-method`; `width`, `width,FuzzyNumber-method`

Other alpha_cuts: `core`, `core,FuzzyNumber-method`; `supp`, `supp,FuzzyNumber-method`

## Examples

 ```1 2``` ```A <- TrapezoidalFuzzyNumber(1, 2, 3, 4) alphacut(A, c(-1, 0.4, 0.2)) ```

### Example output

```       L   U
-1.0  NA  NA
0.4 1.4 3.6
0.2 1.2 3.8
```

FuzzyNumbers documentation built on May 30, 2017, 3:47 a.m.