The self-dual core and the anti-self-dual remainder of an aggregation operator
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Cited by (30)
A note on the orness classification of the rank-dependent welfare functions and rank-dependent poverty measures
2023, Fuzzy Sets and SystemsStability properties of aggregation functions under inversion of scales. Some characterisations
2019, Fuzzy Sets and SystemsCitation Excerpt :In these results each self-dual aggregation function is obtained by a particular way of combining an aggregation function with its corresponding dual. Of all the possible ways of combining an arbitrary aggregation function with its dual, leading to self-dual aggregation functions, the construction generated following the approach proposed by García-Lapresta and Marques Pereira [14] is in fact the only one which preserves invariance under admissible transformations of the corresponding scale. This latter characterisation result is a generalisation of those in Maes et al. [24, Lemma 2 and Theorem 4] and Puerta and Urrutia [26, Proposition 6].
k-additive aggregation functions and their characterization
2018, European Journal of Operational ResearchSome characterisations of self-dual aggregation functions when relative shortfalls are considered
2018, Fuzzy Sets and SystemsCitation Excerpt :We offer two characterisations of self-duality for aggregation functions by considering relative shortfalls, which are the logarithmic transformations of absolute shortfalls. The two characterisations take their cues from the papers by Calvo et al. [6] and García-Lapresta and Marques Pereira [11] respectively. Pointing out that in both characterisations each self-dual function is obtained by a particular way of combining an aggregation function with its dual and following Maes et al. [18], we provide a characterisation of self-dual aggregation functions which preserve homogeneity of degree 1.
The orness value for rank-dependent welfare functions and rank-dependent poverty measures
2017, Fuzzy Sets and SystemsCitation Excerpt :The OWA operators were first introduced in decision theory by Yager [30] as a new aggregation technique that collects the multiple criteria to form an overall decision function. In recent years, OWA operators have received great attention and scholars have applied them in different contexts, such as decision making under uncertainty, fuzzy system, welfare and so on (see Yager and Kreinovich [32], Fodor and Roubens [14], Yager [31], García-Lapresta et al. [16], Aristondo et al. [2] and [3] and Aristondo and Ciommi [4]). As mentioned, every OWA operator has assigned to it a numerical value called orness.