Resampling Methods for Triangular and Trapezoidal Fuzzy Numbers
c(
person("Maciej", "Romaniuk", email = "mroman@ibspan.waw.pl", role = "cre"),
person("Przemyslaw", "Grzegorzewski", email = "przemyslaw.grzegorzewski@ibspan.waw.pl", role = "aut"),
person("Olgierd", "Hryniewicz", email = "hryniewi@ibspan.waw.pl", role = "aut"))
The classical (i.e. Efron's, see Efron and Tibshirani (1994, ISBN:978-0412042317)  "An Introduction to the Bootstrap") bootstrap is widely used for both the real (i.e. "crisp") and fuzzy data.
The main aim of the algorithms implemented in this package  is to overcome a problem with repetition of a few distinct values and to create fuzzy numbers, which are "similar" (but not the same) to values from the initial sample.
To do this, different characteristics of triangular/trapezoidal numbers are kept (like the value, the ambiguity, etc., see Grzegorzewski et al. <doi:10.2991/eusflat-19.2019.68>, Grzegorzewski et al. (2020) <doi:10.2991/ijcis.d.201012.003>, Grzegorzewski et al. (2020) <doi:10.34768/amcs-2020-0022>,  Romaniuk and Hryniewicz (2019) <doi:10.1007/s00500-018-3251-5>).
Maciej Romaniuk [cre],
Przemyslaw Grzegorzewski [aut],
Olgierd Hryniewicz [aut]

The classical (i.e. Efron's, see Efron and Tibshirani (1994, ISBN:978-0412042317)  "An Introduction to the Bootstrap") bootstrap is widely used for both the real (i.e. "crisp") and fuzzy data.
The main aim of the algorithms implemented in this package  is to overcome a problem with repetition of a few distinct values and to create fuzzy numbers, which are "similar" (but not the same) to values from the initial sample.
To do this, different characteristics of triangular/trapezoidal numbers are kept (like the value, the ambiguity, etc., see Grzegorzewski et al. <doi:10.2991/eusflat-19.2019.68>, Grzegorzewski et al. (2020) <doi:10.2991/ijcis.d.201012.003>, Grzegorzewski et al. (2020) <doi:10.34768/amcs-2020-0022>,  Romaniuk and Hryniewicz (2019) <doi:10.1007/s00500-018-3251-5>).
Some additional procedures related to these resampling methods are also provided,
like calculation of the Bertoluzza et al.'s distance (aka the mid/spread distance, see Bertoluzza et al. (1995) "On a new class of distances between fuzzy numbers")
and estimation of the p-value of the one-sample bootstrapped test for the mean (see Lubiano et al. (2016, <doi:10.1016/j.ejor.2015.11.016>)).
Additionally, there are procedures which randomly generate trapezoidal fuzzy numbers using some well-known statistical distributions.