Rejoinder on “A distance-based statistical analysis of fuzzy number-valued data”

Blanco-Fernández, Angela; Casals, María Rosa; Colubi, Ana; Corral, Norberto; García-Bárzana, Marta; Alvarez, María Ángeles Gil; González‐Rodríguez, Gil; López, María Teresa; Lubiano, María Asunción; Montenegro, Manuel; Ramos-Guajardo, Ana Belén; Sáa, Sara de la Rosa de; Sinova, Beatriz

doi:10.1016/j.ijar.2014.04.003

Cited by 21 publications

(6 citation statements)

References 18 publications

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“…A predominant approach to handle interval‐valued data as an entire entity, which can be found in the literature, especially associated with the linear regression analysis for interval‐valued data, classification or hypotheses testing, is sometimes called the distance‐based methodology . Its usefulness results from many theoretical and practical reasons summarized in . The idea goes back to a suitable metric that can be used in

K_{c} (R)

.…”

Section: Nonparametric Tests In the Ontic Perspectivementioning

confidence: 99%

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The sign test and the signed‐rank test for interval‐valued data

Grzegorzewski

Śpiewak

2019

Int J Intell Syst

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Two versions of the generalized sign test and the signed‐rank test for interval‐valued data (both for one‐sample and paired two‐sample problem) are proposed. These two versions correspond to different possible views on the interval outcomes of the experiment—either the epistemic or the ontic one. Each view yields its own approach to data analysis which results in different test construction and the way of carrying on the statistical inference.

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K_{c} (R)

.…”

Section: Nonparametric Tests In the Ontic Perspectivementioning

confidence: 99%

“…Its usefulness results from many theoretical and practical reasons summarized in. 49,50 The idea goes back to a suitable metric that can be used in  ( ) c . Recently, a generalized family of L 2 -type metrics between intervals was introduced by Trutschnig et al 51 and is given by…”

Section: Random Intervalmentioning

confidence: 99%

The sign test and the signed‐rank test for interval‐valued data

Grzegorzewski

Śpiewak

2019

Int J Intell Syst

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“…It should be remarked that the space (F c (R), +, •) is not linear, so there is no "difference operation" between fuzzy numbers that is well-defined and, at the same time, keeps the main properties of the difference between real values in connection with the sum. For that reason, differences involved in statistical developments for real numbers are often replaced by distances between fuzzy numbers whenever this is possible (see [9] and [10] for more details about the distance-based analysis of fuzzy number-valued data).…”

Section: Preliminaries On the Space Of Fuzzy Numbersmentioning

confidence: 99%

Advantages of M-estimators of location for fuzzy numbers based on Tukey's biweight loss function

Sinova

Aelst

2018

International Journal of Approximate Reasoning

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M-estimators of location have been adapted to summarize the central tendency of random fuzzy numbers in a robust way. Under mild conditions on the loss function, which include the well-known Huber and Hampel families of loss functions, fuzzy number-valued location M-estimators exist and can be expressed as weighted means of the observations. Huber and Hampel loss functions depend on one and three tuning parameters, respectively. Some empirical analyses have been developed to compare the finite-sample behavior of the corresponding location M-estimators when these tuning parameters are well-chosen quantiles of the distribution of distances from an initial estimate to each observation. In that sense, it has been shown that the flexibility of the three tuning parameters in the Hampel loss function makes the corresponding M-estimator more accurate than the M-estimator based on the Huber loss function in many situations. More recently, Tukey's biweight (or bisquare) loss function has also been used to compute M-estimators of location for random fuzzy numbers. The robustness of all these estimators has been proven by their finite sample breakdown point, but a simulation study to compare the finite-sample behavior of the M-estimators defined in terms of Hampel and Tukey loss functions is still lacking. This paper aims to develop such simulation results and analyze the advantages of choosing

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“…For instance, González-Rodríguez et al [2] provides a detailed explanation of an approach to ANOVA with fuzzy data based on the functional data identification. The recent reviews of Blanco-Fernández et al [12], [13], [14], [15] and Gil et al [16] summarize most of these statistical developments.…”

Section: A Distances Between Fuzzy Datamentioning

confidence: 99%

M-Estimates of Location for the Robust Central Tendency of Fuzzy Data

Sinova

Alvarez

Aelst

2016

IEEE Trans. Fuzzy Syst.

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The Aumann-type mean has been shown to possess valuable properties as a measure of the location or central tendency of fuzzy data associated with a random experiment. However, concerning robustness its behaviour is not appropriate. The Aumann-type mean is highly affected by slight changes in the fuzzy data or when outliers arise in the sample. Robust estimators of location, on the other hand, avoid such adverse effects. For this purpose, this paper considers the M-estimation approach and discusses conditions under which this alternative yields valid fuzzy-valued M-estimators. The resulting M-estimators are applied to a real-life example. Finally, some simulation studies show empirically the suitability of the introduced estimators. Index Terms-fuzzy number-valued data, M-estimators, random fuzzy numbers, robust location of fuzzy data.

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Rejoinder on “A distance-based statistical analysis of fuzzy number-valued data”

Cited by 21 publications

References 18 publications

The sign test and the signed‐rank test for interval‐valued data

The sign test and the signed‐rank test for interval‐valued data

Advantages of M-estimators of location for fuzzy numbers based on Tukey's biweight loss function

M-Estimates of Location for the Robust Central Tendency of Fuzzy Data

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