17,765 research outputs found
The Gini index,the dual decomposition of aggregation functions, and the consistent measurement of inequality
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.Aggregation functions, dual decomposition, OWA operators, Gini index, consistent measures of achievement/shortfall inequality, Sen index, poverty measures.
A Fast Parallel Poisson Solver on Irregular Domains Applied to Beam Dynamic Simulations
We discuss the scalable parallel solution of the Poisson equation within a
Particle-In-Cell (PIC) code for the simulation of electron beams in particle
accelerators of irregular shape. The problem is discretized by Finite
Differences. Depending on the treatment of the Dirichlet boundary the resulting
system of equations is symmetric or `mildly' nonsymmetric positive definite. In
all cases, the system is solved by the preconditioned conjugate gradient
algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG)
preconditioning. We investigate variants of the implementation of SA-AMG that
lead to considerable improvements in the execution times. We demonstrate good
scalability of the solver on distributed memory parallel processor with up to
2048 processors. We also compare our SAAMG-PCG solver with an FFT-based solver
that is more commonly used for applications in beam dynamics
Meaningful aggregation functions mapping ordinal scales into an ordinal scale: a state of the art
We present an overview of the meaningful aggregation functions mapping
ordinal scales into an ordinal scale. Three main classes are discussed, namely
order invariant functions, comparison meaningful functions on a single ordinal
scale, and comparison meaningful functions on independent ordinal scales. It
appears that the most prominent meaningful aggregation functions are lattice
polynomial functions, that is, functions built only on projections and minimum
and maximum operations
Rationalizing Choice with Multi-Self Models
This paper studies a class of multi-self decision-making models proposed in economics, psychology, and marketing. In this class, choices arise from the set-dependent aggregation of a collection of utility functions, where the aggregation procedure satisfies some simple properties. We propose a method for characterizing the extent of irrationality in a choice behavior, and use this measure to provide a lower bound on the set of choice behaviors that can be rationalized with n utility functions. Under an additional assumption (scale-invariance), we show that generically at most five "reasons" are needed for every "mistake."Multi-self models, Index of irrationality, IIA violations, Rationalizability
On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts
Extensions of aggregation functions to Atanassov orthopairs (often referred to as intuitionistic fuzzy sets or AIFS) usually involve replacing the standard arithmetic operations with those defined for the membership and non-membership orthopairs. One problem with such constructions is that the usual choice of operations has led to formulas which do not generalize the aggregation of ordinary fuzzy sets (where the membership and non-membership values add to 1). Previous extensions of the weighted arithmetic mean and ordered weighted averaging operator also have the absorbent element 〈1,0〉, which becomes particularly problematic in the case of the Bonferroni mean, whose generalizations are useful for modeling mandatory requirements. As well as considering the consistency and interpretability of the operations used for their construction, we hold that it is also important for aggregation functions over higher order fuzzy sets to exhibit analogous behavior to their standard definitions. After highlighting the main drawbacks of existing Bonferroni means defined for Atanassov orthopairs and interval data, we present two alternative methods for extending the generalized Bonferroni mean. Both lead to functions with properties more consistent with the original Bonferroni mean, and which coincide in the case of ordinary fuzzy values.<br /
2D growth processes: SLE and Loewner chains
This review provides an introduction to two dimensional growth processes.
Although it covers a variety processes such as diffusion limited aggregation,
it is mostly devoted to a detailed presentation of stochastic Schramm-Loewner
evolutions (SLE) which are Markov processes describing interfaces in 2D
critical systems. It starts with an informal discussion, using numerical
simulations, of various examples of 2D growth processes and their connections
with statistical mechanics. SLE is then introduced and Schramm's argument
mapping conformally invariant interfaces to SLE is explained. A substantial
part of the review is devoted to reveal the deep connections between
statistical mechanics and processes, and more specifically to the present
context, between 2D critical systems and SLE. Some of the SLE remarkable
properties are explained, as well as the tools for computing with SLE. This
review has been written with the aim of filling the gap between the
mathematical and the physical literatures on the subject.Comment: A review on Stochastic Loewner evolutions for Physics Reports, 172
pages, low quality figures, better quality figures upon request to the
authors, comments welcom
The dual decomposition of aggregation functions and its application in welfare economics
Producción CientíficaIn this paper, we review the role of self-duality in the theory of aggregation
functions, the dual decomposition of aggregation functions into a self-dual core
and an anti-self-dual remainder, and some applications to welfare, inequality,
and poverty measures.Ministerio de Economía, Industria y Competitividad (ECO2012-32178)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA066U13
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