An axiomatic approach to the definition of the entropy of a discrete Choquet capacity

in Information Sciences (2005), 172(1-2), 131-153

To extend the classical Shannon entropy to non-additive measures, Marichal recently introduced the concept of generalized entropy for discrete Choquet capacities. We provide a first axiomatization of this ... [more ▼]

To extend the classical Shannon entropy to non-additive measures, Marichal recently introduced the concept of generalized entropy for discrete Choquet capacities. We provide a first axiomatization of this new concept on the basis of three axioms: the symmetry property, a boundary condition for which the entropy reduces to the Shannon entropy, and a generalized version of the well-known recursivity property. We also show that this generalized entropy fulfills several properties considered as requisites for defining an entropy-like measure. Lastly, we provide an interpretation of it in the framework of aggregation by the discrete Choquet integral. [less ▲]

An Axiomatic Approach to the Measurement of Comparative Female Disadvantage

in Social Indicators Research (2022), 164

Female comparative disadvantage refers to the mismatch of the female with respect to achievements in different dimensions of human well-being in comparison with the corresponding achievements of the male ... [more ▼]

Female comparative disadvantage refers to the mismatch of the female with respect to achievements in different dimensions of human well-being in comparison with the corresponding achievements of the male. This paper axiomatically derives a general family of female comparative disadvantage indicators which has very important policy implications. The axioms employed are shown to be ‘independent’. An empirical illustration of the general index is provided using the UNDP data on mean years of schooling, life expectancy at birth and gross national income per capita in 2018. Results show that female comparative disadvantage is not necessarily related to standard measures of human development, such as the HDI, and is present even in countries reaching very high human development. The factor where policy intervention is needed the most is income. [less ▲]

Axiomatic characterizations of generalized values

in Discrete Applied Mathematics (2007), 155(1), 26-43

In the framework of cooperative game theory, the concept of generalized value, which is an extension of that of value, has been recently proposed to measure the overall influence of coalitions in games ... [more ▼]

In the framework of cooperative game theory, the concept of generalized value, which is an extension of that of value, has been recently proposed to measure the overall influence of coalitions in games. Axiomatizations of two classes of generalized values, namely probabilistic generalized values and generalized semivalues, which extend probabilistic values and semivalues, respectively, are first proposed. The axioms we utilize are based on natural extensions of axioms involved in the axiomatizations of values. In the second half of the paper, special instances of generalized semivalues are also axiomatized. [less ▲]

Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices

in Proc. 10th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2004), Perugia, Italy, July 4-9, 2004 (2004, July)

In the framework of cooperative game theory and multicriteria decision making, the concept of interaction index, which can be regarded as an extension of that of value, has been recently proposed to ... [more ▼]

In the framework of cooperative game theory and multicriteria decision making, the concept of interaction index, which can be regarded as an extension of that of value, has been recently proposed to measure the interaction phenomena among players or criteria. Axiomatizations of two classes of interaction indices, namely probabilistic interaction indices and cardinal-probabilistic interaction indices, generalizing probabilistic values and semivalues, respectively, are first proposed. Three existing instances of cardinal-probabilistic interaction indices encountered thus far in the literature are also axiomatized. [less ▲]

Axiomatizations of quasi-Lovász extensions of pseudo-Boolean functions

in Aequationes Mathematicae (2011), 82(3), 213-231

We introduce the concept of quasi-Lov\'asz extension as being a mapping $f\colon I^n\to\R$ defined on a nonempty real interval $I$ containing the origin and which can be factorized as $f(x_1,\ldots,x_n)=L ... [more ▼]

We introduce the concept of quasi-Lov\'asz extension as being a mapping $f\colon I^n\to\R$ defined on a nonempty real interval $I$ containing the origin and which can be factorized as $f(x_1,\ldots,x_n)=L(\varphi(x_1),\ldots,\varphi(x_n))$, where $L$ is the Lov\'asz extension of a pseudo-Boolean function $\psi\colon\{0,1\}^n\to\R$ (i.e., the function $L\colon\R^n\to\R$ whose restriction to each simplex of the standard triangulation of $[0,1]^n$ is the unique affine function which agrees with $\psi$ at the vertices of this simplex) and $\varphi\colon I\to\R$ is a nondecreasing function vanishing at the origin. These functions appear naturally within the scope of decision making under uncertainty since they subsume overall preference functionals associated with discrete Choquet integrals whose variables are transformed by a given utility function. To axiomatize the class of quasi-Lov\'asz extensions, we propose generalizations of properties used to characterize the Lov\'asz extensions, including a comonotonic version of modularity and a natural relaxation of homogeneity. A variant of the latter property enables us to axiomatize also the class of symmetric quasi-Lov\'asz extensions, which are compositions of symmetric Lov\'asz extensions with $1$-place nondecreasing odd functions. [less ▲]

Axiomatizations of signed discrete Choquet integrals

in International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems (2011), 19(2), 193-199

We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lovász extension of a pseudo-Boolean function which vanishes at the origin. We ... [more ▼]

We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lovász extension of a pseudo-Boolean function which vanishes at the origin. We present axiomatizations of this generalized Choquet integral, given in terms of certain functional equations, as well as by necessary and sufficient conditions which reveal desirable properties in aggregation theory. [less ▲]

The axisymetric failure mechanism of circular shallow foundations and pile foundations in non-cohesive soils

in Computations and Materials in Civil Engineering (2017), 2(1), 1-15

In 1920 Prandtl published an analytical solution for the bearing capacity of a centric loaded strip footing on a weightless in-finite half-space, based on a so-called Prandtl-wedge failure mechanism ... [more ▼]

In 1920 Prandtl published an analytical solution for the bearing capacity of a centric loaded strip footing on a weightless in-finite half-space, based on a so-called Prandtl-wedge failure mechanism. Reissner extended this solution for a surrounding surcharge and Keverling Buisman and Terzaghi for the soil weight. Meyerhof and other researchers presented correction factors for the shape of the shallow foundation, which would suggest that, the failure mechanism of circular shallow foundations, is related to the Prandtl-wedge failure mechanism. Meyerhof and Koppejan adapted this Prandtl-wedge failure mechanism also for pile foundations. The numerical calculations made in this article show that the Prandtl-wedge cannot be applied to circular shallow foundations and pile foundations in non-cohesive soils. The failure zone (plastic zone) below a loaded circular plate or pile tip, is far wider and deeper than the Prandtl-wedge. The calculations also show that there is, for these axisymmetric cases, failure both in and out of the standard x-y plane, but most of the failure is due to out-of-plane (tangential) failure. Therefore, this failure mechanism is different from the Prandtl-wedge failure mechanism. Also interesting are the circular and diagonal thin zones below the plate and around the pile tip, where there is no out-of-plane failure, although there is still in-plane failure. In these thin zones without out-of-plane failure, the tangential (out-of-plane) stresses are relatively high due to large shear strains, formed during previous shearing or sliding of the soil. [less ▲]

Az Európai Közösség büntetőjoga

in Állam- és Jogtudomány (1998)

Az-Atlanti-óceán (és a Pacifica-ügy) mint vízválasztó

in Medias Res (2013)

Das ‚A‘ und ‚J‘ der Ähnlichkeit. Variationen zu Kleists Griffel

in Patrut, Iulia-Karin; Rössler, Reto (Eds.) Ähnlichkeit um 1800. Konturen eines literatur- und kulturtheoretischen Paradigmas am Beginn der Moderne (2019)