"The connection between distortion risk measures and ordered weighted averaging operators"

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and nite random variables is presented. This connection oers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.Fuzzy systems; Degree of orness; Risk quantification; Discrete random variable JEL classification:C02,C60

Indicators for the characterization of discrete Choquet integrals

Ordered weighted averaging (OWA) operators and their extensions are powerful tools used in numerous decision-making problems. This class of operator belongs to a more general family of aggregation operators, understood as discrete Choquet integrals. Aggregation operators are usually characterized by indicators. In this article four indicators usually associated with the OWA operator are extended to discrete Choquet integrals: namely, the degree of balance, the divergence, the variance indicator and Renyi entropies. All of these indicators are considered from a local and a global perspective. Linearity of indicators for linear combinations of capacities is investigated and, to illustrate the application of results, indicators of the probabilistic ordered weighted averaging -POWA- operator are derived. Finally, an example is provided to show the application to a specific context

The connection between distortion risk measures and ordered weighted averaging operators [WP]

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and finite random variables is presented. This connection offers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed

The connection between distortion risk measures and ordered weighted averaging operators

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and finite random variables is presented. This connection offers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed

Symmetry Breakdown in Franckeite: Spontaneous Strain, Rippling, and Interlayer Moire

Franckeite is a naturally occurring layered mineral with a structure composed of alternating stacks of SnS2-like and PbS-like layers. Although this superlattice is composed of a sequence of isotropic two-dimensional layers, it exhibits a spontaneous rippling that makes the material structurally anisotropic. We demonstrate that this rippling comes hand in hand with an inhomogeneous in-plane strain profile and anisotropic electrical, vibrational, and optical properties. We argue that this symmetry breakdown results from a spatial modulation of the van der Waals interaction between layers due to the SnS2-like and PbS-like lattices incommensurability

Formation of titanium monoxide (001) single-crystalline thin film induced by ion bombardment of titanium dioxide (110)

© 2015 Macmillan Publishers Limited. All rights reserved. A plethora of technological applications justify why titanium dioxide is probably the most studied oxide, and an optimal exploitation of its properties quite frequently requires a controlled modification of the surface. Low-energy ion bombardment is one of the most extended techniques for this purpose and has been recently used in titanium oxides, among other applications, to favour resistive switching mechanisms or to form transparent conductive layers. Surfaces modified in this way are frequently described as reduced and defective, with a high density of oxygen vacancies. Here we show, at variance with this view, that high ion doses on rutile titanium dioxide (110) induce its transformation into a nanometric and single-crystalline titanium monoxide (001) thin film with rocksalt structure. The discovery of this ability may pave the way to new technical applications of ion bombardment not previously reported, which can be used to fabricate heterostructures and interfaces.Peer Reviewe

Direct transformation of crystalline MoO3_3 into few-layers MoS2_2

We fabricate large-area atomically thin MoS$_2$ layers through the direct transformation of crystalline molybdenum MoS$_2$ (MoO$_3$) by sulfurization at relatively low temperatures. The obtained MoS2 sheets are polycrystalline (~10-20 nm single-crystal domain size) with areas of up to 300x300 um$^2$ with 2-4 layers in thickness and show a marked p-type behaviour. The synthesized films are characterized by a combination of complementary techniques: Raman spectroscopy, X-ray diffraction, transmission electron microscopy and electronic transport measurements.Comment: 6 figures in main text, 2 figures in supp. inf

Hexagonal Hybrid Bismuthene by Molecular Interface Engineering

High-quality devices based on layered heterostructures are typically built from materials obtained by complex solid-state physical approaches or laborious mechanical exfoliation and transfer. Meanwhile, wet-chemically synthesized materials commonly suffer from surface residuals and intrinsic defects. Here, we synthesize using an unprecedented colloidal photocatalyzed, one-pot redox reaction a few-layers bismuth hybrid of “electronic grade” structural quality. Intriguingly, the material presents a sulfur-alkyl-functionalized reconstructed surface that prevents it from oxidation and leads to a tuned electronic structure that results from the altered arrangement of the surface. The metallic behavior of the hybrid is supported by ab initio predictions and room temperature transport measurements of individual nanoflakes. Our findings indicate how surface reconstructions in two-dimensional (2D) systems can promote unexpected properties that can pave the way to new functionalities and devices. Moreover, this scalable synthetic process opens new avenues for applications in plasmonics or electronic (and spintronic) device fabrication. Beyond electronics, this 2D hybrid material may be of interest in organic catalysis, biomedicine, or energy storage and conversion