Fuzzy data treated as functional data: A one-way ANOVA test approach

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

doi:10.1016/j.csda.2010.06.013

Cited by 147 publications

(86 citation statements)

References 28 publications

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“…The α-cuts or α-levels of a fuzzy set U , denoted by U α , are the intervals determined by the set of values verifying U (x) ≥ α, for α ∈ [0, 1]. Two of the most typical shapes of fuzzy sets considered in the literature are trapezoidal and triangular, where the last one is a special case of the first one (see, for instance, [8,12]). …”

Section: Preliminariesmentioning

confidence: 99%

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Analysis of the reliability of the fuzzy scale for assessing the students’ learning styles in Mathematics

Guajardo¹,

López²,

Ruiz³

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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The reliability of the fuzzy scale for assessing the responses of a person in an opinion questionnaire (which is usually treated as a Likert-type questionnaire) is analyzed. Thus, a comparison between a classical Likert scale-based questionnaire and its fuzzy rating scale-based version in terms of their reliability is established. For this purpose, some questions of the Grasha-Riechmann student learning style scales have been answered by a group of students using both scales. Considering that the Likert version of this questionnaire is reliable, the aim is to check the reliability of its fuzzy version by comparing the corresponding Cronbach's alpha coefficients.

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Section: Preliminariesmentioning

confidence: 99%

“…To overcome these problems, a way for describing each individual opinion/perception/valuation by means of a fuzzy set capturing the subjectiveness or imprecision involved in the answer and without taking into account a pre-fixed enumeration of answers has been proposed in the literature [11,13,12,23].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the reliability of the fuzzy scale for assessing the students’ learning styles in Mathematics

Guajardo¹,

López²,

Ruiz³

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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show abstract

“…the Borel σ-field generated by the topology induced by D φ W (see, for instance, González-Rodríguez et al [15]). Consequently, one can trivially refer to the induced distribution of a random fuzzy number, the independence of two fuzzy numbers, and so on.…”

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

confidence: 99%

“…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

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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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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“…Wu [3] solved one-way fuzzy ANOVA using the h-level set and the notions of pessimistic degree and optimistic degree. ANOVA study was developed by Gonzalez-Rodriguez et al [4] and Montenegro et al [5]. They presented an exact one-way ANOVA testing procedure for the case with normal fuzzy random variables.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Variance for Fuzzy Data Based on Permutation Method

Lee

Jung

Lee

et al. 2017

IJFIS

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This paper deals with analysis of variance with fuzzy data (ANOVAF) based on permutation method. The permutation method is a nonparametric method introduced by Heap and Johnson for the data when the normal distribution cannot be assumed. We proposed two different approaches to test hypothesis of fuzzy means using the empirical distribution. To compare the results, several distances are considered especially using ρ-distance. Applying Monte Carlo simulation, it is confirmed through the numerical examples that the significant probability (p-value) get approached true parameter (p-value) regardless of distances or testing method based on proposed method. In addition, the number of permutation samples required is determined in the example to satisfy specified given accuracy.

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Fuzzy data treated as functional data: A one-way ANOVA test approach

Cited by 147 publications

References 28 publications

Analysis of the reliability of the fuzzy scale for assessing the students’ learning styles in Mathematics

Analysis of the reliability of the fuzzy scale for assessing the students’ learning styles in Mathematics

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

Analysis of Variance for Fuzzy Data Based on Permutation Method

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