CalculateAmbiguity {FuzzyResampling}

Calculation of the ambiguity for triangular and trapezoidal fuzzy numbers

Description

CalculateAmbiguity returns the ambiguity of the triangular or trapezoidal fuzzy number (see, e.g., (Ban et al., 2015), (Grzegorzewski and Romaniuk, 2022)).

Usage

CalculateAmbiguity(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 ambiguity of fuzzy number, is calculated. For the respective formulas, see, e.g., (Ban et al., 2015), (Grzegorzewski and Romaniuk, 2022).

Value

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

References

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

Grzegorzewski, P., Romaniuk, M. (2022) Bootstrap methods for fuzzy data Uncertainty and Imprecision in Decision Making and Decision Support: New Advances, Challenges, and Perspectives, pp. 28-47 Springer

See Also

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

Other characteristics of fuzzy numbers functions: CalculateAmbiguityL(), CalculateAmbiguityR(), CalculateExpValue(), CalculateFuzziness(), 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 ambiguity of the first fuzzy number

CalculateAmbiguity(fuzzyValues[1,])

# calculate the ambiguity for the whole matrix

CalculateAmbiguity(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 ambiguity of the first fuzzy number

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