Resampling Methods for Triangular and Trapezoidal Fuzzy Numbers
// 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,
Grzegorzewski and Romaniuk (2022)
doi:10.1007/978-3-030-95929-6_3, 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.