The aim of the package is to provide some basic functions
 for doing statistics with trapezoidal fuzzy numbers. In particular,
  the package contains several functions for simulating trapezoidal 
  fuzzy numbers, as well as for calculating some central tendency 
  measures (mean and two types of median), some scale measures 
  (variance, ADD, MDD, Sn, Qn, Tn and some M-estimators) and 
  one diversity index and one inequality index. Moreover, 
  functions for calculating the 1-norm distance, the mid/spr 
  distance and the (phi,theta)-wabl/ldev/rdev distance between 
  fuzzy numbers are included, and a function to calculate the 
  value phi-wabl given a sample of trapezoidal fuzzy numbers.

The aim of the package is to contain the package 'FuzzyStatTra' in 
    Encapsulated Object Oriented Programming using R6. 'FuzzyStatTra' contains Statistical 
    Methods for Trapezoidal Fuzzy Numbers, whose aim is to provide some basic functions 
    for doing statistical analysis with trapezoidal fuzzy numbers. For more details, you 
    can visit the website of the SMIRE+CoDiRE (Statistical Methods with Imprecise Random 
    Elements and Comparison of Distributions of Random Elements) Research Group 
    (<https://bellman.ciencias.uniovi.es/smire+codire/>). The most related paper can be 
    found in References. Now, those functions are organized in specific classes and methods. 
    This object-based approach is an important step in making statistical computing more 
    accessible to users.

The main goal of this package is to present various fuzzy statistical tools. It intends to provide an implementation of the theoretical and empirical approaches presented in the book entitled "The signed distance measure in fuzzy statistical analysis. Some theoretical, empirical and programming advances" <doi: 10.1007/978-3-030-76916-1>. For the theoretical approaches, see Berkachy R. and Donze L. (2019) <doi:10.1007/978-3-030-03368-2_1>. For the empirical approaches, see Berkachy R. and Donze L. (2016) <ISBN: 978-989-758-201-1>). Important (non-exhaustive) implementation highlights of this package are as follows: (1) a numerical procedure to estimate the fuzzy difference and the fuzzy square. (2) two numerical methods of fuzzification. (3) a function performing different possibilities of distances, including the signed distance and the generalized signed distance for instance with all its properties. (4) numerical estimations of fuzzy statistical measures such as the variance, the moment, etc. (5) two methods of estimation of the bootstrap distribution of the likelihood ratio in the fuzzy context. (6) an estimation of a fuzzy confidence interval by the likelihood ratio method. (7) testing fuzzy hypotheses and/or fuzzy data by fuzzy confidence intervals in the Kwakernaak - Kruse and Meyer sense. (8) a general method to estimate the fuzzy p-value with fuzzy hypotheses and/or fuzzy data. (9) a method of estimation of global and individual evaluations of linguistic questionnaires. (10) numerical estimations of multi-ways analysis of variance models in the fuzzy context. The unbalance in the considered designs are also foreseen.