CalculateFuzziness {FuzzyResampling}

Calculation of the fuzziness for triangular and trapezoidal fuzzy numbers

Description

CalculateFuzziness returns the fuzziness of the triangular or trapezoidal fuzzy number (see, e.g., (Ban et al., 2015), (Grzegorzewski et al., 2020)).

Usage

CalculateFuzziness(fuzzyNumber, increases = FALSE)

Arguments

fuzzyNumber

Input data consist of triangular or trapezoidal fuzzy numbers.

increases

If TRUE is used, then the initial data should consist of the fuzzy numbers 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 data should consist of 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.

Then for each fuzzy number, its characteristics, known as the fuzziness of fuzzy number, is calculated. For the respective formulas, see, e.g., (Ban et al., 2015), (Grzegorzewski et al., 2020)).

Value

This function returns vector of double values. Each output value is equal to the fuzziness of the respective fuzzy number.

References

Ban, A.I., Coroianu, L., Grzegorzewski, P. (2015) Fuzy Numbers: Approximations, Ranking and Applications Institute of Computer Sciences, Polish Academy of Sciences

Grzegorzewski, P., Hryniewicz, O., Romaniuk, M. (2020) Flexible resampling for fuzzy data based on the canonical representation International Journal of Computational Intelligence Systems, 13 (1), pp. 1650-1662

See Also

CalculateValue for calculation of the value, CalculateAmbiguityL for calculation of the left-hand ambiguity, CalculateAmbiguityR for calculation of the right-hand ambiguity, CalculateAmbiguity for calculation of the ambiguity, CalculateExpValue for calculation of the expected value, CalculateWidth for calculation of the width

Other characteristics of fuzzy numbers functions: CalculateAmbiguityL(), CalculateAmbiguityR(), CalculateAmbiguity(), CalculateExpValue(), CalculateValue(), CalculateWidth()

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 fuzziness of the first fuzzy number

CalculateFuzziness(fuzzyValues[1,])

# calculate the fuzziness for the whole matrix

CalculateFuzziness(fuzzyValues)

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

fuzzyValuesInc <- matrix(c(0.25,0.5,1,0.25,0.25,1,1.5,0.7,1,0,0,2),
ncol = 4,byrow = TRUE)

# calculate the fuzziness of the first fuzzy number

CalculateFuzziness(fuzzyValuesInc[1,], increases = TRUE)