# minimum: Minimum of fuzzy nubmers In FuzzyNumbers: Tools to Deal with Fuzzy Numbers

## Description

Determines minimum fuzzy number based on two inputs.

## Usage

 ```1 2 3``` ```## S4 method for signature ## 'PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber' minimum(e1, e2) ```

## Arguments

 `e1` a PiecewiseLinearFuzzyNumber `e2` a PiecewiseLinearFuzzyNumber

## Details

The resulting PiecewiseLinearFuzzyNumber is only an approximation of the result it might not be very precise for small number of knots (see examples).

## Value

Returns a PiecewiseLinearFuzzyNumber representing maximal value of the inputs.

## References

KAUFMANN, A., GUPTA, M. M. (1985) Introduction to Fuzzy Arithmetic. New York : Van Nostrand Reinhold Company. ISBN 044230079.

## See Also

Other min_max-operators: `maximum()`

Other PiecewiseLinearFuzzyNumber-method: `Arithmetic`, `Extract`, `PiecewiseLinearFuzzyNumber-class`, `PiecewiseLinearFuzzyNumber`, `^,PiecewiseLinearFuzzyNumber,numeric-method`, `alphaInterval()`, `arctan2()`, `as.PiecewiseLinearFuzzyNumber()`, `as.PowerFuzzyNumber()`, `as.TrapezoidalFuzzyNumber()`, `as.character()`, `expectedInterval()`, `fapply()`, `maximum()`, `necessityExceedance()`, `necessityStrictExceedance()`, `necessityStrictUndervaluation()`, `necessityUndervaluation()`, `plot()`, `possibilityExceedance()`, `possibilityStrictExceedance()`, `possibilityStrictUndervaluation()`, `possibilityUndervaluation()`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```# example with low number of knots, showing the approximate nature # of the result x = as.PiecewiseLinearFuzzyNumber(TriangularFuzzyNumber(-4.8, -3 , -1.5)) y = as.PiecewiseLinearFuzzyNumber(TriangularFuzzyNumber(-5.5, -2.5, -1.1)) minFN = minimum(x,y) min = min(alphacut(x,0)[1],alphacut(y,0)[1]) max = max(alphacut(x,0)[2],alphacut(y,0)[2]) plot(x, col="red", xlim=c(min,max)) plot(y, col="blue", add=TRUE) plot(minFN, col="green", add=TRUE) # example with high number of knots, that does not suffer # from the approximate nature of the result x = as.PiecewiseLinearFuzzyNumber(TriangularFuzzyNumber(-4.8, -3 , -1.5), knot.n = 9) y = as.PiecewiseLinearFuzzyNumber(TriangularFuzzyNumber(-5.5, -2.5, -1.1), knot.n = 9) minFN = minimum(x,y) min = min(alphacut(x,0)[1],alphacut(y,0)[1]) max = max(alphacut(x,0)[2],alphacut(y,0)[2]) plot(x, col="red", xlim=c(min,max)) plot(y, col="blue", add=TRUE) plot(minFN, col="green", add=TRUE) ```

### Example output

```
```

FuzzyNumbers documentation built on Nov. 15, 2021, 5:09 p.m.