FuzzyResampling (version 0.6.4)

BertoluzzaDistance: Calculate Bertoluzza's (mid/spread) distance for triangular and trapezoidal fuzzy numbers

Description

BertoluzzaDistance returns the Bertoulzza et al.'s (aka mid/spread) distance with the given weight theta between two triangular or trapezoidal fuzzy numbers.

Usage

BertoluzzaDistance(fuzzyNumber1, fuzzyNumber2, theta = 1/3, increases = FALSE)

Value

This function returns vector of doubles related to the calculated distances.

Arguments

fuzzyNumber1

The first triangular or trapezoidal fuzzy number. More than one value can be given in the form of matrix.

fuzzyNumber2

The second triangular or trapezoidal fuzzy number. More than one value can be given in the form of matrix.

theta

The weighting parameter for the mid/spread distance.

increases

If TRUE is used, then the fuzzy numbers should be given in the form: left increment of the support, left end of the core, right end of the core, right increment of the support. Otherwise, the default value FALSE is used and the fuzzy numbers should be given in the form: left end of the support, left end of the core, right end of the core, right end of the support.

Details

The input fuzzy values should be triangular or trapezoidal fuzzy numbers, given as a single vector or a whole matrix. In each row, there should be a single fuzzy number in one of the forms:

1. left end of the support, left end of the core, right end of the core, right end of the support, or

2. left increment of the support, left end of the core, right end of the core, right increment of the support.

In this second case, the parameter increases=TRUE has to be used.

The procedure calculates the mid/spread distance between two fuzzy values based on the weight theta, usually we have theta = 1/3 or theta = 1. The output is given as vector of distances.

References

Bertoluzza, C., Corral, N., Salas, A. (1995) On a new class of distances between fuzzy numbers Mathware and Soft Computing, 2 (2), pp. 71-84

Examples

# prepare some fuzzy numbers (first type of the initial sample)

fuzzyValues <- matrix(c(0.25,0.5,1,1.25,0.75,1,1.5,2.2,-1,0,0,2),ncol = 4,byrow = TRUE)

# calculate the mid/spread distance between the first value
# (from the first row) and the second one (from the second row)

BertoluzzaDistance(fuzzyValues[1,],fuzzyValues[2,])

# calculate the mid/spread distance between the first value
# (from the first row) and all of the values (from the first to the third row)

BertoluzzaDistance(fuzzyValues[1,],fuzzyValues)