CalculateExpValue {FuzzyResampling}

Calculation of the expected value for triangular and trapezoidal fuzzy numbers

Description

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

Usage

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

Other characteristics of fuzzy numbers functions: CalculateAmbiguityL(), CalculateAmbiguityR(), CalculateAmbiguity(), 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 expected value of the first fuzzy number

CalculateExpValue(fuzzyValues[1,])

# calculate the expected value for the whole matrix

CalculateExpValue(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 expected value of the first fuzzy number

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