A generalized L1-type metric between fuzzy numbers for an approach to central tendency of fuzzy data

Random fuzzy numbers are becoming a valuable tool to model and handle fuzzyvalued data generated through a random process. Recent studies have been devoted to introduce measures of the central tendency of random fuzzy numbers showing a more robust behaviour than the so-called Aumann-type mean value. This paper aims to deepen in the (rather comparative) analysis of these centrality measures and the Aumann-type mean by examining the situation of symmetric random fuzzy numbers. Similarities and differences with the real-valued case are pointed out and theoretical conclusions are accompanied with some illustrative examples.

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“…The two sample medians have shown a more robust behaviour than the Aumanntype sample mean (see Sinova et al [23,24]). …”

Section: And Where In Case the Involved Median Of A Real-valued Randomentioning

confidence: 98%

Central tendency for symmetric random fuzzy numbers

Sinova

Casals

Alvarez

2014

Information Sciences

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“…Hence, for each wabl/ldev/rdev representation of a fuzzy number in Definition 2.1 there is a corresponding representation as introduced in Sinova et al [40]. Bertoluzza et al's L 2 metric can be expressed in terms of the mid/spread representation for fuzzy numbers (see, for instance, Gil et al [50]).…”

Section: Functions Satifying Coditions I) and Ii) Then There Exists mentioning

confidence: 99%

“…Recently (Sinova et al [40]) introduced a new parametric family of L 1 metrics with the goal of defining a robust centrality measure for fuzzy data. These metrics are based on a new representation of fuzzy numbers that coincides with the mid/spread representation in case of symmetric fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

“…However, no discussion has been carried out regarding the interpretation of the involved parameter, which makes it difficult to make a suitable choice for this parameter in practice. This paper introduces a new parametric family of L 2 metrics between fuzzy numbers that is based on a modification of the fuzzy number representation in [40]. This new parametric family of metrics aims to allow an intuitive interpretation of the involved parameter which facilitates the selection of its value in practice.…”

Section: Introductionmentioning

confidence: 99%

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A parameterized metric between fuzzy numbers and its parameter interpretation

Sinova

Alvarez

López

et al. 2014

Fuzzy Sets and Systems

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When handling fuzzy number data, it is common practice to make use of a metric to quantify distances between fuzzy numbers. Several metrics have been suggested in the literature for this purpose. When statistically analyzing fuzzy number-valued data, L 2 metrics become especially useful. This paper introduces a new family of generalized L 2 metrics which take into account key features of the involved fuzzy numbers, namely, a measure of central location and two measures associated with the shape of the fuzzy numbers are used. A crucial property related to these three measures is that necessary and sufficient conditions can be established for them to characterize fuzzy numbers. Furthermore, the family of generalized L 2 metrics depends on one parameter. A discussion is provided regarding the interpretation of this parameter which can guide selection of its value in practice. * corresponding author: magil@uniovi.es, Fax: (+34) 985103354. Preprint submitted to Fuzzy Sets and SystemsJune 7, 2013 AbstractWhen handling fuzzy number data, it is common practice to make use of a metric to quantify distances between fuzzy numbers. Several metrics have been suggested in the literature for this purpose. When statistically analyzing fuzzy number-valued data, L 2 metrics become especially useful. This paper introduces a new family of generalized L 2 metrics which take into account key features of the involved fuzzy numbers, namely, a measure of central location and two measures associated with the shape of the fuzzy numbers are used. A crucial property related to these three measures is that necessary and sufficient conditions can be established for them to characterize fuzzy numbers. Furthermore, the family of generalized L 2 metrics depends on one parameter. A discussion is provided regarding the interpretation of this parameter which can guide selection of its value in practice.Keywords: fuzzy number, L 2 -metric, wabl/ldev/rdev representation of fuzzy numbers, L 2 wabl/ldev/rdev metric, weighting parameter

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“…Other relevant summary measures of the distribution of a random fuzzy number are the Fréchet variance based on D φ W (see, for instance, Lubiano et al [23], Blanco-Fernández et al [2]), and the L 1 -medians by Sinova et al [30,31]. 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.…”

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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A generalized L1-type metric between fuzzy numbers for an approach to central tendency of fuzzy data

Cited by 26 publications

References 25 publications

Central tendency for symmetric random fuzzy numbers

Central tendency for symmetric random fuzzy numbers

A parameterized metric between fuzzy numbers and its parameter interpretation

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

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