# maximum: Maximum of fuzzy nubmers In FuzzyNumbers: Tools to Deal with Fuzzy Numbers

## Description

Determines maximum fuzzy number based on two inputs.

## Usage

 1 2 3 ## S4 method for signature ## 'PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber' maximum(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.

Other min_max-operators: minimum()

## 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)) maxFN = maximum(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(maxFN, 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) maxFN = maximum(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(maxFN, col="green", add=TRUE)

### Example output

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