Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data

González‐Rodríguez, Gil; Montenegro, Manuel; Colubi, Ana; Gil, María Ángeles

doi:10.1016/j.fss.2003.11.021

Cited by 88 publications

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“…The covariance of two random fuzzy numbers can be also introduced (see González-Rodríguez et al [13], Blanco-Fernández et al [2]) in connection with the simple linear regression analysis between random fuzzy sets, although in this case it does not involve D Another statistical problem involving Bertoluzza et al's metric is that of testing about the population fuzzy-valued Aumann-type mean of one or more random fuzzy numbers on the basis of a sample of independent observations from it or them. More concretely (see Körner [20], Montenegro et al [25,26], González-Rodríguez et al [16,15], Gil et al [10], and Blanco-Fernández et al [2] …”

Section: Definition 3 Given a Probability Space (ω A P ) A Random mentioning

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Bertoluzza et al.’s metric as a basis for analyzing fuzzy data

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Gil

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Since Bertoluzza et al. 's metric between fuzzy numbers has been introduced, several studies involving it have been developed. Some of these studies concern equivalent expressions for the metric which are useful for either theoretical, practical or simulation purposes. Other studies refer to the potentiality of Bertoluzza et al.'s metric to establish statistical methods for the analysis of fuzzy data. This paper shortly reviews such studies and examine part of the scientific impact of the metric.

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Section: Definition 3 Given a Probability Space (ω A P ) A Random mentioning

confidence: 99%

Bertoluzza et al.’s metric as a basis for analyzing fuzzy data

Casals

Corral

Gil

et al. 2013

METRON

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“…Classical methods are not always successful dealing with uncertain data, because the uncertainties appearing in these domains may be of various types, such as probability theory [4], fuzzy set theory [36], intuitionistic fuzzy set theory [2], vague set theory [10], interval mathematics [14], and other mathematical tools are well know and often useful approaches to describing uncertainty. Therefore, in the studies proposed by Montenegro et al [25], González-Rodríguez et al [13], and Gil et al [11] it has been stated that the well-known bootstrap techniques are a valuable tool in testing statistical hypotheses about the means and variances of fuzzy random variables, when these…”

Section: Introductionmentioning

confidence: 99%

Bootstrap Approach to the One-Sample and Two- Sample Test of Variances of a Fuzzy Random Variable

Chachi

2017

Stat., optim. inf. comput.

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The aim of this paper is to present in a concise and integrated way of the bootstrap approach to statistical testing of hypotheses about the variance of fuzzy random variable. In this approach, first a notion of fuzzy random variables is recalled. Then, we will consider hypothesis-tests for the (crisp-valued) variance of fuzzy data in a population. For this purpose, the α-pessimistic values of the imprecise observations are used for defining a new notion of distance measure between fuzzy data, which is then used to make a procedure for testing the statistical hypotheses. Based on this argument, the application of bootstrap techniques in dealing with these testing problems will be introduced. The procedure develops a non-parametric approach to testing statistical hypotheses based on one-sample and two-sample fuzzy data.

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“…Montenegro et al (2001Montenegro et al ( , 2004, using a generalized metric for fuzzy numbers, proposed a method to test hypotheses about the fuzzy mean of a FRV in one and two populations settings. Gonzalez-Rodríguez et al (2006) extended a one-sample bootstrap method of testing about the mean of a general fuzzy random variable. Gil et al (2006) introduced a bootstrap approach to the multiple-sample test of means for imprecisely valued sample data.…”

Section: Introductionmentioning

confidence: 99%

Parametric testing statistical hypotheses for fuzzy random variables

Hesamian

Shams

2015

Soft Comput

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In this paper, a method is proposed for testing statistical hypotheses about the fuzzy parameter of the underlying parametric population. In this approach, using definition of fuzzy random variables, the concept of the power of test and p value is extended to the fuzzy power and fuzzy p value. To do this, the concepts of fuzzy p value have been defined using the α-optimistic values of the fuzzy observations and fuzzy parameters. This paper also develop the concepts of fuzzy type-I, fuzzy type-II errors and fuzzy power for the proposed hypothesis tests. To make decision as a fuzzy test, a well-known index is employed to compare the observed fuzzy p value and a given significance value. The result provides a fuzzy test function which leads to some degrees to accept or to reject the null hypothesis. As an application of the proposed method, we focus on the normal fuzzy random variable to investigate hypotheses about the related fuzzy parameters. An applied example is provided throughout the paper clarifying the discussions made in this paper.

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Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data

Cited by 88 publications

References 12 publications

Bertoluzza et al.’s metric as a basis for analyzing fuzzy data

Bertoluzza et al.’s metric as a basis for analyzing fuzzy data

Bootstrap Approach to the One-Sample and Two- Sample Test of Variances of a Fuzzy Random Variable

Parametric testing statistical hypotheses for fuzzy random variables

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