DSGD

Calculates a distance by the SGD between fuzzy numbers

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.

Redina Berkachy

FuzzySTs

Fuzzy Statistical Tools

DSGD function

<dl><dt>X</dt>
<dd>a fuzzy number.</dd>
<dt>Y</dt>
<dd>a fuzzy number.</dd>
<dt>i</dt>
<dd>parameter of the density function of the Beta distribution, fixed by default to i = 1.</dd>
<dt>j</dt>
<dd>parameter of the density function of the Beta distribution, fixed by default to j = 1.</dd>
<dt>breakpoints</dt>
<dd>a positive arbitrary integer representing the number of breaks chosen to build the numerical alpha-cuts. It is fixed to 100 by default.</dd>
<dt>theta</dt>
<dd>a numerical value between 0 and 1, representing a weighting parameter. By default, theta is fixed to 1/3 referring to the Lebesgue space. This measure is used in the calculations of the following distances: d_Bertoluzza, d_mid/spr and d_phi-wabl/ldev/rdev.</dd></dl>

Arguments

Calculates a distance by the SGD between fuzzy numbers — DSGD

<dl>

<dt>X</dt>
<dd>a fuzzy number.</dd>


<dt>Y</dt>
<dd>a fuzzy number.</dd>


<dt>i</dt>
<dd>parameter of the density function of the Beta distribution, fixed by default to i = 1.</dd>


<dt>j</dt>
<dd>parameter of the density function of the Beta distribution, fixed by default to j = 1.</dd>


<dt>breakpoints</dt>
<dd>a positive arbitrary integer representing the number of breaks chosen to build the numerical alpha-cuts. It is fixed to 100 by default.</dd>


<dt>theta</dt>
<dd>a numerical value between 0 and 1, representing a weighting parameter. By default, theta is fixed to 1/3 referring to the Lebesgue space. This measure is used in the calculations of the following distances: d_Bertoluzza, d_mid/spr and d_phi-wabl/ldev/rdev.</dd>

</dl>

DSGD: Calculates a distance by the SGD between fuzzy numbers

Description

Usage

Value

Arguments