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.2013.09.020

Cited by 72 publications

(46 citation statements)

References 35 publications

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“…Nevertheless, for computations, simulations, theoretical developments and the extension to higher dimensionality spaces, some equivalences become more appropriate. These 'definitional' equivalences has been also described in Blanco-Fernández et al [3].…”

Section: Definitional and Topological Equivalencessupporting

confidence: 66%

“…As it has been detailed in previous studies (see, for instance, Blanco-Fernández et al [3]), the metric D φ W can be alternatively expressed in some different ways. The expression as it was introduced by Bertoluzza et al is definitely the easiest version to interpret as it involves the choice of the weighting measure W .…”

Section: Definitional and Topological Equivalencesmentioning

confidence: 99%

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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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Section: Definitional and Topological Equivalencessupporting

confidence: 66%

Section: Definitional and Topological Equivalencesmentioning

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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“…Although it is not possible to establish a universally acceptable complete order between fuzzy Table 2: Sample means of the Likert answers numbers [3] (since it is not straightforward to order, for instance, the trapezoidal fuzzy numbers T ra (1,3,5,7) and T ra(2, 2.5, 5.5, 6)), some considerations about the fuzzy-type and Likert-type sample means above should be remarked, mainly:…”

Section: Resultsmentioning

confidence: 99%

“…• The use of the fuzzy scale entails higher diversity of responses than the Likert scale-based one, allowing the respondents to collect the subjectivity of their opinions in an more flexible way; • the flexibility of the fuzzy scale implies that two different people can provide different fuzzy responses to two different questions whereas their Likert-based answers to both questions coincide; • in the last years some statistical methods to deal with the descriptive and inferential analysis of fuzzy data have been developed (most of them have been summarized in [2,3]). …”

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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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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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“…These results may be used in the development of statistical methods for IFV-sets which, as for now, are practically non-existent. In the development of such methods, one can use approaches, already developed for random fuzzy sets, and described in an overview paper by Gil and Hryniewicz (2009) or in a recent paper by Blanco-Fernández et al (2014).…”

Section: Introductionmentioning

confidence: 99%

On central limit theorems for IV-events

Nowak

Hryniewicz

2017

Soft Comput

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Interval-valued fuzzy sets were introduced in 1970s as an extension of Zadeh's fuzzy sets. For intervalvalued fuzzy events, (IV-events for short) IV-probability theory has been developed. In this paper, we prove central limit theorems for triangular arrays of IV-observables within this theory. We prove the Lindeberg CLT and the Lyapunov CLT, assuming that IV-observables are not necessary identically distributed. We also prove the Feller theorem for null arrays of IV-observables. Furthermore, we present examples of applications of the aforementioned theorems. In particular, we study the convergence in distribution of scaled sums of identically distributed IV-observables.

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A distance-based statistical analysis of fuzzy number-valued data

Cited by 72 publications

References 35 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

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

On central limit theorems for IV-events

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