FuzzyImputationTest (version 0.4.0)

MeasureAHD: Function to calculate the AHD distance between two fuzzy numbers.

Description

`MeasureAHD` calculates the AHD (Area Hight Distance) measure between two trapezoidal or triangular fuzzy numbers.

Usage

MeasureAHD(value1, value2, trapezoidal = TRUE, ...)

Value

The output is given as a numerical value.

Arguments

value1

The first input triangular or trapezoidal fuzzy number.

value2

The second input triangular or trapezoidal fuzzy number.

trapezoidal

Logical value depending on the type of input fuzzy values (triangular or trapezoidal ones).

...

Additional parameters passed to other functions.

Details

The procedure calculates the AHD (Area Hight Distance) measure of the distance between two trapezoidal or triangular fuzzy numbers. The input values can be given as triangular/trapezoidal fuzzy numbers using the objects defined in FuzzyNumbers package or vectors with three (in the case of triangular fuzzy numbers) or four (for trapezoidal fuzzy numbers) values related to left end of the support, the core (or its interval, respectively), and the right end of the support. The parameter trapezoidal is used to indicate if the input values are trapezoidal fuzzy numbers or triangular ones.

References

M. Amirfakhrian, S. Yeganehmanesh, and P. Grzegorzewski, “A new distance on fuzzy semi-numbers", Soft Computing, vol. 22, no. 14, pp. 4511–4524, 2018

See Also

MeasureHSD, MeasureEuclidean for other procedures to calculate distance measures.

Examples

# let's define two trapezoidal fuzzy numbers

tpfn1 <- c(1,2,3,4)

tpfn2 <- c(2,6,8,10)

# calculate the distance

MeasureAHD(tpfn1,tpfn2)

# now we use objects from the FuzzyNumbers package

# load the necessary library

library(FuzzyNumbers)

tpfn1 <- TrapezoidalFuzzyNumber(1,2,3,4)

tpfn2 <- TrapezoidalFuzzyNumber(2,6,8,10)

MeasureAHD(tpfn1,tpfn2)