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FuzzyNumbers (version 0.4-7)

distance: Calculate the Distance Between Two Fuzzy Numbers

Description

Currently, only Euclidean distance may be calculated. We have dE2(A,B):=01(AL(α)BL(α))2dα,01+(AU(α)BU(α))2dα, see (Grzegorzewski, 1988).

Usage

# S4 method for FuzzyNumber,FuzzyNumber
distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...)

# S4 method for FuzzyNumber,DiscontinuousFuzzyNumber distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...)

# S4 method for DiscontinuousFuzzyNumber,FuzzyNumber distance(e1, e2, type=c("Euclidean", "EuclideanSquared"), ...)

# S4 method for 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"

Value

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

Details

The calculation are done using numerical integration,

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()