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1

Bootstrapped tests for epistemic fuzzy data

Grzegorzewski Przemyslaw, Romaniuk Maciej

International Journal of Applied Mathematics and Computer Science

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2024

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Vol. 34, no. 2

277--289

EN

Epistemic bootstrap is a resampling algorithm that generates bootstrap real-valued samples based on some epistemic fuzzy data input. We apply this method as a universal basis for various statistical tests which can be then directly used for fuzzy random variables. Two classical goodness-of-fit tests are considered as an example to examine the suggested methodology for both synthetic and real data. The proposed approach is also compared with two other goodness-of-fit tests dedicated directly to fuzzy data.

2

Bootstrap methods for epistemic fuzzy data

Grzegorzewski Przemyslaw, Romaniuk Maciej

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 2

285--297

EN

Fuzzy numbers are often used for modeling imprecise perceptions of the real-valued observations. Such epistemic fuzzy data may cause problems in statistical reasoning and data analysis. We propose a universal nonparametric technique, called the epistemic bootstrap, which could be helpful when the existing methods do not work or do not give satisfactory results. Besides the simple epistemic bootstrap, we develop its several refinements that aim to reduce the variance in statistical inference. We also perform an extended simulation study to examine statistical properties of the approaches considered. The discussion of the results is supplemented by some hints for practical use.

3

Forecasting the confidence interval of efficiency in fuzzy DEA

Kafi Azarnoosh, Daneshian Behrouz, Rostamy-Malkhalifeh Mohsen

Operations Research and Decisions

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2021

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Vol. 31, No. 1

41--59

EN

Data envelopment analysis (DEA) is a well-known method that based on inputs and outputs calculates the efficiency of decision-making units (DMUs). Comparing the efficiency and ranking of DMUs in different periods lets the decision-makers prevent any loss in the productivity of units and improve the production planning. Despite the merits of DEA models, they are not able to forecast the efficiency of future periods with known input/output records of the DMUs. With this end in view, this study aims at proposing a forecasting algorithm with a 95% confidence interval to generate fuzzy data sets for future periods. Moreover, managers’ opinions are inserted in the proposed forecasting model. Equipped with the forecasted data sets and concerning the data sets from earlier periods, this model can rightly forecast the efficiency of the future periods. The proposed procedure also employs the simple geometric mean to discriminate between efficient units. Examples from a real case including 20 automobile firms show the applicability of the proposed algorithm.

4

Flexible resampling for fuzzy data

Grzegorzewski Przemyslaw, Hryniewicz Olgierd, Romaniuk Maciej

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 2

281--297

EN

In this paper, a new methodology for simulating bootstrap samples of fuzzy numbers is proposed. Unlike the classical bootstrap, it allows enriching a resampling scheme with values from outside the initial sample. Although a secondary sample may contain results beyond members of the primary set, they are generated smartly so that the crucial characteristics of the original observations remain invariant. Two methods for generating bootstrap samples preserving the representation (i.e., the value and the ambiguity or the expected value and the width) of fuzzy numbers belonging to the primary sample are suggested and numerically examined with respect to other approaches and various statistical properties.

5

A fuzzy nonparametric Shewhart chart based on the bootstrap approach

Wang D., Hryniewicz O.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 2

389--401

EN

In this paper, we consider a nonparametric Shewhart chart for fuzzy data. We utilize the fuzzy data without transforming them into a real-valued scalar (a representative value). Usually fuzzy data (described by fuzzy random variables) do not have a distributional model available, and also the size of the fuzzy sample data is small. Based on the bootstrap methodology, we design a nonparametric Shewhart control chart in the space of fuzzy random variables equipped with some L2 metric, in which a novel approach for generating the control limits is proposed. The control limits are determined by the necessity index of strict dominance combined with the bootstrap quantile of the test statistic. An in-control bootstrap ARL of the proposed chart is also considered.

6

Bayes statistical decisions with random fuzzy data – an application for the Weibull distribution

Hryniewicz O., Kaczmarek K., Nowak P.

Eksploatacja i Niezawodność

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2015

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Vol. 17, no. 4

610--616

EN

In the majority of decision models used in practice all input data are assumed to be precise. This assumption is made both for random results of measurements, and for constant parameters such as, e.g. costs related to decisions. In reality many of these values are reported in an imprecise way. When this imprecision cannot be related to randomness the fuzzy set theory yields tools for its description. It seems to be important to retain both types of uncertainty, random and fuzzy, while building mathematical models for making decisions. In the paper we propose a fuzzy-Bayesian model for making statistical decisions. In the proposed model the randomness of data is reflected in related risks, and fuzziness is described by possibility measures of dominance such as PSD (Possibility of Strict Dominance) and NSD (Necessity of Strict Dominance). The proposed model allows a decision-maker to reflect in his/hers decisions different types of uncertainty. The theoretical results have been applied in the case of reliability data described by the Weibull distribution.

PL

W większości stosowanych w praktyce modeli decyzyjnych zakłada się, że wszystkie występujące w nich dane wejściowe są podane w sposób precyzyjny. Założenie to dotyczy zarówno losowych wyników pomiarów jak też i stałych parametrów, takich jak np. koszty podjętych decyzji. W rzeczywistości wiele z tych wartości jest podawanych w sposób nieprecyzyjny. Jeżeli taki brak precyzji nie ma charakteru losowego, to teoria zbiorów rozmytych dostarcza narzędzi do opisu tego zjawiska. Wydaje się rzeczą istotną, by przy tworzeniu matematycznych modeli podejmowania decyzji zachować oba typy niepewności: losowość i rozmytość. W pracy proponujemy rozmyto-bayesowski model podejmowania decyzji statystycznych. W proponowanym modelu losowość odpowiada za związane z podjęciem decyzji ryzyko, zaś rozmytość jest opisana przez miary możliwości dominacji, takie jak PSD (Możliwość Ścisłej Dominacji) oraz NSD (Konieczność Ścisłej Dominacji). Zaproponowany model pozwala decydentowi ująć w procesie podejmowania decyzji różne rodzaje niepewności. Rozważania teoretyczne zostały w pracy zastosowane do analizy danych niezawodnościowych opisanych rozkładem Weibulla.

7

Statistical analysis of interval and imprecise data : applications in the analysis of reliability field data

Hryniewicz O.

Journal of Polish Safety and Reliability Association

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2007

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Vol. 1

181--192

EN

The analysis of field lifetime data is much more complicated than the analysis of the results of reliability laboratory tests. In the paper we present an overview of the most important problems of the statistical analysis of field lifetime data, and present their solutions known from literature. When the input information is partial or imprecise, we propose to use interval arithmetics for the calculation of bounds on reliability characteristics of interest. When this information can be described in a more informative fuzzy form, we can generalize our interval-valued results to their fuzzy equivalents.

8

Rozmyty model związków encji.

Biedrzycka B., Mazur Z.

Prace Naukowe Wydziałowego Zakładu Informatyki Politechniki Wrocławskiej

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2002

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z. 3

43-57

PL

W pracy przedstawiono tematykę związaną z rozmytym modelowaniem konceptualnym. Opisano w jaki sposób logika rozmyta może zostać użyta w modelu związków encji. Przedstawiono rozmyte rozszerzenie pojęć klasycznego modelu związków encji takich jak: encje, związki, atrybuty na trzech poziomach - poziomach typów i ich instancji. Dostarczono szerszego spojrzenia na związki pomiędzy encjami w kontekście uczestnictwa i liczebności.

EN

Fuzzy entity-relationship model and representation of various forms of fuzzy data in relational model addressing extensions of classical model with fuzzy elements hale been presented.