The self-dual core and the anti-self-dual remainder of an aggregation operator

García-Lapresta, José Luis; Pereira, Ricardo Alberto Marques

doi:10.1016/j.fss.2007.06.012

Cited by 32 publications

(66 citation statements)

References 29 publications

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“…[14], plus also García-Lapresta and Marques Pereira [12]. It is easy to see that every aggregation function is compensative.…”

Section: Definition 1 Letmentioning

confidence: 91%

“…Pereira [12]. First we introduce the concepts of self-dual core and anti-self-dual remainder of an aggregation function, establishing which properties are inherited in each case from the original aggregation function.…”

Section: Dual Decompositionmentioning

confidence: 99%

“…The following result concerns two more properties of the anti-self-dual remainder based directly on the definition A = A − A and the corresponding properties of the self-dual core (see García-Lapresta and Marques Pereira [12]). …”

Section: Definition 9 Letmentioning

confidence: 99%

“…We show that the Sen poverty index may be interpreted as an OWA operator (Yager [30]). Consequently, the dual decomposition of aggregation functions into a self-dual core and anti-self-dual remainder proposed by García-Lapresta and Marques Pereira [12] may be used. We show that these two terms can be interpreted as measures of the intensity and the inequality among the poor respectively.…”

Section: Introductionmentioning

confidence: 99%

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The gini index, the dual decomposition of aggregation functions, and the consistent measurement of inequality

Aristondo

García-Lapresta

Vega

et al. 2011

Int. J. Intell. Syst.

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In several economic fields, such as those related to health, education or poverty, the individuals' characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A difficulty arises when inequality needs to be assessed. One may focus either on achievements or on shortfalls but the respective inequality rankings may lead to contradictory results. Specifically, this paper concentrates on the poverty measure proposed by Sen. According to this measure the inequality among the poor is captured by the Gini index. However, the rankings obtained by the Gini index applied to either the achievements or the shortfalls do not coincide in general. To overcome this drawback, we show that an OWA operator is underlying in the definition of the Sen measure. The dual decomposition of the OWA operators into a self-dual core and anti-self-dual remainder allows us to propose an inequality component which measures consistently the achievement and shortfall inequality among the poor. Keywords AbstractIn several economic fields, such as those related to health, education or poverty, the individuals' characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A difficulty arises when inequality needs to be assessed. One may focus either on achievements or on shortfalls but the respective inequality rankings may lead to contradictory results. Specifically, this paper concentrates on the poverty measure proposed by Sen. According to this measure the inequality among the poor is captured by the Gini index. However, the rankings obtained by the Gini index applied to either the achievements or the shortfalls do not coincide in general. To overcome this drawback, we show that an OWA operator is underlying in the definition of the Sen measure. The dual decomposition of the OWA operators into a self-dual core and anti-self-dual remainder allows us to propose an inequality component which measures consistently the achievement and shortfall inequality among the poor.

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“…[14], plus also García-Lapresta and Marques Pereira [12]. It is easy to see that every aggregation function is compensative.…”

Section: Definition 1 Letmentioning

confidence: 91%

Section: Dual Decompositionmentioning

confidence: 99%

Section: Definition 9 Letmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The gini index, the dual decomposition of aggregation functions, and the consistent measurement of inequality

Aristondo

García-Lapresta

Vega

et al. 2011

Int. J. Intell. Syst.

Self Cite

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show abstract

“…, x n ) represents the 1 income distribution of a population of n ≥ 2 individuals. Recently, the extended interpretation of this formula in terms of the dual decomposition [19] of aggregation functions has been discussed in [20,1].…”

Section: Introductionmentioning

confidence: 99%

The Generalized Gini Welfare Function in the Framework of Symmetric Choquet Integration

Bortot

Pereira

2013

Multicriteria and Multiagent Decision Making With Applications to Economics and Social Sciences

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In the context of Social Welfare and Choquet integration, we briefly review the classical Gini inequality index for populations of n ≥ 2 individuals, including the associated Lorenz area formula, plus the k-additivity framework for Choquet integration introduced by Grabisch, particularly in the additive and 2-additive symmetric cases. We then show that any 2-additive symmetric Choquet integral can be written as the difference between the arithmetic mean and a multiple of the classical Gini inequality index, with a given interval constraint on the multiplicative parameter. In the special case of positive parameter values, this result corresponds to the well-known Ben Porath and Gilboa's formula for Weymark's generalized Gini welfare functions, with linearly decreasing (inequality averse) weight distributions.

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Multidistances and Dispersion Measures

Martínez-Panero

García-Lapresta

Meneses

2016

Fuzzy Logic and Information Fusion

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In this paper, we provide a formal notion of absolute dispersion measure that is satisfied by some classical dispersion measures used in Statistics, such as the range, the variance, the mean deviation and the standard deviation, among others, and also by the absolute Gini index, used in Welfare Economics for measuring inequality. The notion of absolute dispersion measure shares some properties with the notion of multidistance introduced and analyzed by Martín and Mayor in several recent papers. We compare absolute dispersion measures and multidistances and we establish that these two notions are compatible by showing some functions that are simultaneously absolute dispersion measures and multidistances. We also establish that remainders obtained through the dual decomposition of exponential means, introduced by García-Lapresta and Marques Pereira, are absolute dispersion measures up to sign.

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The self-dual core and the anti-self-dual remainder of an aggregation operator

Cited by 32 publications

References 29 publications

The gini index, the dual decomposition of aggregation functions, and the consistent measurement of inequality

The gini index, the dual decomposition of aggregation functions, and the consistent measurement of inequality

The Generalized Gini Welfare Function in the Framework of Symmetric Choquet Integration

Multidistances and Dispersion Measures

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