# distance-methods: Calculate the Distance Between Two Fuzzy Numbers In FuzzyNumbers: Tools to Deal with Fuzzy Numbers

## Description

Currently, only Euclidean distance may be calculated. We have d_E^2(A,B) := int_0^1 (A_L(α)-B_L(α))^2 dα + int_0^1 (A_U(α)-B_U(α))^2 dα, see (Grzegorzewski, 1988).

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## S4 method for signature 'FuzzyNumber,FuzzyNumber' distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...) ## S4 method for signature 'FuzzyNumber,DiscontinuousFuzzyNumber' distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...) ## S4 method for signature 'DiscontinuousFuzzyNumber,FuzzyNumber' distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...) ## S4 method for signature 'DiscontinuousFuzzyNumber,DiscontinuousFuzzyNumber' distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...) ```

## Arguments

 `e1` a fuzzy number `e2` a fuzzy number `...` additional arguments passed to `integrate` `type` one of `"Euclidean"`, `"EuclideanSquared"`

## Details

The calculation are done using numerical integration,

## Value

Returns the calculated distance, i.e. a single numeric value.

## References

Grzegorzewski P., Metrics and orders in space of fuzzy numbers, Fuzzy Sets and Systems 97, 1998, pp. 83-94.

Other FuzzyNumber-method: `Arithmetic`, `Extract`, `FuzzyNumber-class`, `FuzzyNumber`, `alphaInterval()`, `alphacut()`, `ambiguity()`, `as.FuzzyNumber()`, `as.PiecewiseLinearFuzzyNumber()`, `as.PowerFuzzyNumber()`, `as.TrapezoidalFuzzyNumber()`, `as.character()`, `core()`, `evaluate()`, `expectedInterval()`, `expectedValue()`, `integrateAlpha()`, `piecewiseLinearApproximation()`, `plot()`, `show()`, `supp()`, `trapezoidalApproximation()`, `value()`, `weightedExpectedValue()`, `width()`
Other DiscontinuousFuzzyNumber-method: `DiscontinuousFuzzyNumber-class`, `DiscontinuousFuzzyNumber`, `Extract`, `integrateAlpha()`, `plot()`