distance-methods: Calculate the Distance Between Two Fuzzy Numbers

In gagolews/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

## 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.

See Also

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()

gagolews/FuzzyNumbers documentation built on Nov. 17, 2021, 6:44 a.m.