Representation and construction of self-dual aggregation operators

Maes, Koen; Saminger, Susanne; Baets, Bernard De

doi:10.1016/j.ejor.2005.10.056

Cited by 22 publications

(15 citation statements)

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“…Each binary aggregation function in that family corresponds to a particular way of combining an aggregation function A with its dual A * for the construction of the self-dual core A. As particular cases of the general framework proposed in Maes et al [19], one obtains García-Lapresta and Marques Pereira's construction, based on the arithmetic mean, and Silvert's construction, based on the symmetric sums formula (see Silvert [26]). However, the dual decomposition framework introduced in García-Lapresta and Marques Pereira [12] remains the only one which preserves stability under translations, a crucial requirement in the present construction of poverty measures.…”

Section: If a Is Stable For Translations Then A Is Invariant For Tramentioning

confidence: 99%

“…In Maes et al [19], the authors propose a generalization of the dual decomposition framework introduced in García-Lapresta and Marques Pereira [12], based on a family of binary aggregation functions satisfying a form of twisted self-duality condition. Each binary aggregation function in that family corresponds to a particular way of combining an aggregation function A with its dual A * for the construction of the self-dual core A.…”

Section: If a Is Stable For Translations Then A Is Invariant For Tramentioning

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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Section: If a Is Stable For Translations Then A Is Invariant For Tramentioning

confidence: 99%

Section: If a Is Stable For Translations Then A Is Invariant For Tramentioning

confidence: 99%

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.

View full text Add to dashboard Cite

show abstract

“…Maes et al [20] provide a characterization of self-dual aggregation functions which generalizes those given by Silvert [24] and García-Lapresta and Marques Pereira [14]. In turn, Maes and De Baets [19] merge self-dual and commutative binary aggregation functions in a single functional equation.…”

Section: ])mentioning

confidence: 95%

“…Each binary aggregation function in that family corresponds to a particular way of combining an aggregation function A with its dual A * for the construction of the self-dual core A. As particular cases of the general framework proposed in Maes et al [20], one obtains García-Lapresta and Marques Pereira's construction, based on the arithmetic mean, and Silvert's construction, based on the symmetric sums formula (see Silvert [24]). However, the dual decomposition framework introduced in García-Lapresta and Marques Pereira [14] remains the only one which preserves stability under translations.…”

Section: The Anti-self-dual Remainder Of An Aggregation Functionmentioning

confidence: 99%

“…In Maes et al [20], the authors propose a generalization of the dual decomposition framework introduced in García-Lapresta and Marques Pereira [14], based on a family of binary aggregation functions satisfying a form of twisted self-duality condition. Each binary aggregation function in that family corresponds to a particular way of combining an aggregation function A with its dual A * for the construction of the self-dual core A.…”

Section: The Anti-self-dual Remainder Of An Aggregation Functionmentioning

confidence: 99%

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