FuzzyNumbers (version 0.4-6)

distance: Calculate the Distance Between Two Fuzzy Numbers

Description

Currently, only Euclidean distance may be calculated. We have \(d_E^2(A,B) := \int_0^1 (A_L(\alpha)-B_L(\alpha))^2\,d\alpha,\int_0^1 + (A_U(\alpha)-B_U(\alpha))^2\,d\alpha \), 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, 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, integrateAlpha, plot