On Some Applications of Simulations in Estimation of Maintenance Costs and in Statistical Tests for Fuzzy Settings

Romaniuk, Maciej

doi:10.1007/978-3-030-28665-1_33

Cited by 8 publications

(8 citation statements)

References 36 publications

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“…Because of the previously mentioned shortcomings of Efron's approach, several modifications were proposed in the case of real-valued data. New resampling methods for fuzzy data were introduced recently in Grzegorzewski et al (2019Grzegorzewski et al ( , 2020b; Romaniuk (2019); . All of them are implemented in FuzzyResampling package.…”

Section: Resampling Approaches For Fuzzy Datamentioning

confidence: 99%

“…For the second group, we are interested in the preservation of some basic characteristics of the initial values, like their canonical representation (Delgado et al, 1998). Both approaches seem to be fruitful in many aspects of the statistical inference (see Grzegorzewski et al (2019Grzegorzewski et al ( , 2020b; Grzegorzewski and Romaniuk (2022b); Romaniuk (2019); ) and may be helpful in improving the results of some real-life data analyses.…”

Section: Introductionmentioning

confidence: 99%

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Resampling Fuzzy Numbers with Statistical Applications: FuzzyResampling Package

Romaniuk,

Grzegorzewski

2023

The R Journal

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The classical bootstrap has proven its usefulness in many areas of statistical inference. However, some shortcomings of this method are also known. Therefore, various bootstrap modifications and other resampling algorithms have been introduced, especially for real-valued data. Recently, bootstrap methods have become popular in statistical reasoning based on imprecise data often modeled by fuzzy numbers. One of the challenges faced there is to create bootstrap samples of fuzzy numbers which are similar to initial fuzzy samples but different in some way at the same time. These methods are implemented in FuzzyResampling package and applied in different statistical functions like single-sample or two-sample tests for the mean. Besides describing the aforementioned functions, some examples of their applications as well as numerical comparisons of the classical bootstrap with the new resampling algorithms are provided in this contribution.

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Section: Resampling Approaches For Fuzzy Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Resampling Fuzzy Numbers with Statistical Applications: FuzzyResampling Package

Romaniuk,

Grzegorzewski

2023

The R Journal

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“…To avoid undesired repetitions which often appear in bootstrap Romaniuk and Hryniewicz [17][18][19] proposed a resampling method which enrich secondary samples with fuzzy observations imitating those from the primary sample but containing some incremental spreads on their 𝛼-cuts. Then Grzegorzewski et al [21,28] suggested another approach for generating bootstrap samples which may differ from the primary one but preserve the two-parameter canonical representation of each fuzzy observation, i.e., its value and ambiguity or the expected value and the width.…”

Section: Value-ambiguity (Va) Bootstrap Algorithmmentioning

confidence: 99%

“…Summing up the aforementioned considerations as well as the restrictions specified in ( 15), ( 16) and (17), we obtain the following bootstrap algorithm for generating a secondary sample of trapezoidal fuzzy numbers.…”

Section: Value-ambiguity-fuzziness (Vaf) Bootstrap Algorithmmentioning

confidence: 99%

“…To increase the diversity of simulated results some new approaches were proposed. Romaniuk and Hryniewicz [17,18] introduced two resampling methods in which new triangular fuzzy numbers were generated from the primary sample by adding some incremental spreads for 𝛼-cuts. The resampling algorithms for interval-valued fuzzy numbers were considered in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Flexible Bootstrap for Fuzzy Data Based on the Canonical Representation

Grzegorzewski¹,

Hryniewicz²,

Romaniuk³

2020

IJCIS

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Several new resampling methods for generating bootstrap samples of fuzzy numbers are proposed. To avoid undesired repetitions in the secondary samples we do not draw randomly directly observations from the primary samples but construct them allowing for some modifications in their membership functions, however only such which do not disturb the canonical representation of the initial fuzzy numbers. We consider both two-parameter and three-parameter canonical representations, as well as the triangular and trapezoidal outputs in the secondary samples. Numerical experiments concerning some statistical tests based on fuzzy samples show that the suggested methods may appear helpful in statistical reasoning with imprecise data.

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Imprecise Approaches to Analysis of Insurance Portfolio with Catastrophe Bond

Romaniuk

2020

Information Processing and Management of Uncertainty in Knowledge-Based Systems

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On Some Applications of Simulations in Estimation of Maintenance Costs and in Statistical Tests for Fuzzy Settings

Cited by 8 publications

References 36 publications

Resampling Fuzzy Numbers with Statistical Applications: FuzzyResampling Package

Resampling Fuzzy Numbers with Statistical Applications: FuzzyResampling Package

Flexible Bootstrap for Fuzzy Data Based on the Canonical Representation

Imprecise Approaches to Analysis of Insurance Portfolio with Catastrophe Bond

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