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

Casals, María Rosa; Corral, Norberto; Gil, María Ángeles; López, María Teresa; Lubiano, María Asunción; Montenegro, Manuel; Naval, Gloria; Salas, Antonia

doi:10.1007/s40300-013-0023-y

Cited by 6 publications

(5 citation statements)

References 34 publications

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“…In the case of trapezoidal fuzzy numbers, the C-test is applied to compare the empirical sizes for this test using the classical bootstrap, the VA method and the VAF method with the same values of n, b as in the previous analyses. As an essential part of the C-test, the mid-spread distance (or Bertoluzza et al 's distance [32]) with the weighting parameter 𝜃 = 1/3 is used, which leads to weighing uniformly the squared distances between the convex linear combinations of the end points of the different level intervals [9].…”

Section: Results Given In Tablesmentioning

confidence: 99%

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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Section: Results Given In Tablesmentioning

confidence: 99%

Flexible Bootstrap for Fuzzy Data Based on the Canonical Representation

Grzegorzewski¹,

Hryniewicz²,

Romaniuk³

2020

IJCIS

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“…where D θ is the mid/spread distance with θ = 1 (Casals et al, 2013), θ * i is an estimator of θ based on the i-th boostrap replication, and θ * = b i=1 θ * i , was applied. Some experimental results can be found in Tables 2-5 (others are available upon request).…”

Section: Fn Typementioning

confidence: 99%

Flexible resampling for fuzzy data

Grzegorzewski¹,

Hryniewicz²,

Romaniuk³

2020

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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.

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“…In this paper, a parameterized and versatile family of distances has been chosen, although a few other distances will occasionally be mentioned. This family of distances has been introduced by Bertoluzza et al [9] (see Casals et al [10] for a recent review, and Trutschnig et al [11] for its generalization to fuzzy vector-valued data). It is formalized as follows:…”

Section: A Distances Between Fuzzy Datamentioning

confidence: 99%

“…Another interesting choice is associated with the value θ = 1/3, since (see Casals et al [10]) it can be equivalently expressed as…”

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

Cited by 6 publications

References 34 publications

Flexible Bootstrap for Fuzzy Data Based on the Canonical Representation

Flexible Bootstrap for Fuzzy Data Based on the Canonical Representation

Flexible resampling for fuzzy data

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

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