The goal of FuzzyImputationTest is to impute (i.e., replace missing values given by NAs) dataset that consists of triangular or trapezoidal fuzzy numbers, and check quality of such an imputation. To impute fuzzy values, various imputation methods - both general (like miceRanger, missingForest, knn), and specific ones (d-imputation method, abbreviated as DIMP, see (Romaniuk and Grzegorzewski 2023)) - can be used. To check the quality of the imputation process, the dataset without missing values can be specified, and then it is tested with the whole set of procedures. These procedures are related to calculation of various sample statistics like the mean, standard deviation, and some special distance measures for fuzzy numbers, together with obtaining different error values, and conduction of statistical tests based on the epistemic bootstrap (see (P. Grzegorzewski and Romaniuk 2021, 2024; Przemyslaw Grzegorzewski and Romaniuk 2022)) from package (see (Romaniuk, Grzegorzewski, and Parchami 2024)). There are also special procedures to fuzzify the input and introduce some NAs when necessary.

The following procedures are available in the library:

- Imputation procedures:
*FuzzyImputation*- The main method to impute fuzzy values.*ImputationDimp*- The DIMP (d-imputation) method for fuzzy numbers.

- Testing procedures:
*ImputationTests*- The main benchmark function to check the quality of the imputed fuzzy values.*MethodsComparison*- The benchmark function for the built-in imputation methods with many repetitions.*ErrorMatrix*- Calculation of the various errors between two datasets - the true and the imputed one.*StatisticalMeasures*- Calculation of the various statistical measures between the real and imputed data.*ApplyStatisticalTests*- Statistical epistemic tests the imputed values.

- Conversion procedures:
*FuzzyNumbersToMatrix*- Conversion of a list of fuzzy numbers into a matrix.*MatrixToFuzzyNumbers*- Conversion of a matrix to a list of fuzzy numbers.

- Calculation of the distance measures:
*MeasureAHD*- Calculation of the AHD (Area Hight Distance) measure between two trapezoidal or triangular fuzzy numbers.*MeasureHSD*- Calculation of the HSD (Hight Source Distance) measure between two trapezoidal or triangular fuzzy numbers.*MeasureEuclidean*- Calculation of the Euclidean measure between two trapezoidal or triangular fuzzy numbers.

- Additional procedures:
*IntroducingNA*- Introducing NAs to the specified matrix.*RemoveNotFuzzy*- Removing values that are not fuzzy numbers.*FuzzifyMatrix*- Fuzzify the real-valued variables and construct trapezoidal or triangular fuzzy numbers.

You can install the development version of FuzzyImputationTest from GitHub with:

```
library(devtools)
install_github("mroman-ibs/FuzzyImputationTest")
```

```
# seed PRNG
set.seed(1234)
# load the necessary library
library(FuzzySimRes)
# generate sample of trapezoidal fuzzy numbers with FuzzySimRes library
<-SimulateSample(20,originalPD="rnorm",parOriginalPD=list(mean=0,sd=1),
list1incrCorePD="rexp", parIncrCorePD=list(rate=2),
suppLeftPD="runif",parSuppLeftPD=list(min=0,max=0.6),
suppRightPD="runif", parSuppRightPD=list(min=0,max=0.6),
type="trapezoidal")
# convert fuzzy data into a matrix
<- FuzzyNumbersToMatrix(list1$value)
matrix1
# check starting values
head(matrix1)
# add some NAs to the matrix
<- IntroducingNA(matrix1,percentage = 0.1)
matrix1NA
head(matrix1NA)
# impute missing values with the DIMP method
set.seed(12345)
FuzzyImputation(matrix1NA)
# impute missing values with the miceRanger method
set.seed(12345)
FuzzyImputation(matrix1NA,method = "miceRanger")
# compare imputation methods
set.seed(123456)
MethodsComparison(matrix1,iterations=10,matrix1Mask,trapezoidal=TRUE)
```

For additional examples check the help files please.

Grzegorzewski, P., and M. Romaniuk. 2021. “Epistemic Bootstrap for Fuzzy
Data.” In *Joint Proceedings of IFSA-EUSFLAT-AGOP 2021
Conferences*, 538–45. Atlantis Press.

———. 2024. “Bootstrapped Tests for Epistemic Fuzzy Data.”
*International Journal of Applied Mathematics and Computer
Science* 34 (2): 277–89. https://doi.org/10.61822/amcs-2024-0020.

Grzegorzewski, Przemyslaw, and Maciej Romaniuk. 2022. “Bootstrap Methods
for Epistemic Fuzzy Data.” *International Journal of Applied
Mathematics and Computer Science* 32 (2): 285–97.

Romaniuk, M., and P. Grzegorzewski. 2023. “Fuzzy Data Imputation with
DIMP and FGAIN.” RB/23/2023. Systems Research Institute, PAS.

Romaniuk, M., P. Grzegorzewski, and A. Parchami. 2024. “FuzzySimRes:
Epistemic Bootstrap – the Efficient Tool for Statistical Inference Based
on Imprecise Data.” *R Journal*.