A Characterization of the 2-Additive Symmetric Choquet Integral Using Trinary Alternatives

2014 ◽  
pp. 266-275
Author(s):  
Brice Mayag
Keyword(s):  
Choquet Integral

scholarly journals A characterization of the 2-additive Choquet integral through cardinal information

2011 ◽  
Vol 184 (1) ◽  
pp. 84-105 ◽  
Author(s):  
Brice Mayag ◽  
Michel Grabisch ◽  
Christophe Labreuche
Keyword(s):  
Choquet Integral

Cardinal-Probabilistic Interaction Indices and their Applications: A Survey

2003 ◽  
Vol 7 (2) ◽  
pp. 79-85 ◽  
Author(s):  
Katsushige Fujimoto ◽  
Keyword(s):  
Choquet Integral ◽  
Axiomatic Characterization ◽  
Probability Measures ◽  
Choice Probability ◽  
Hierarchical Decomposition ◽  
Möbius Transform

The class of cardinal probabilistic interaction indices obtained as expected marginal interactions includes the Shapley, Banzhaf, and chaining interaction indices and the Möbius and co-Möbius transform so. We will survey cardinal-probabilistic interaction indices and their applications, focusing on axiomatic characterization of the class of cardinal-probabilistic interaction indices. We show that these typical cardinal-probabilistic interaction indices can be represented as the Stieltjes integrals with respect to choice-probability measures on [0,1]. We introduce a method for hierarchical decomposition of systems represented by the Choquet integral using interaction indices.

AN ITERATIVITY CONDITION FOR THE MEAN-VALUE PRINCIPLE UNDER CUMULATIVE PROSPECT THEORY

2013 ◽  
Vol 43 (1) ◽  
pp. 61-71
Author(s):  
Marek Kaluszka ◽  
Michał Krzeszowiec
Keyword(s):  
Prospect Theory ◽  
Choquet Integral ◽  
Cumulative Prospect Theory ◽  
Mean Value ◽  
Full Characterization ◽  
Distortion Functions ◽  
Random Loss ◽  
The Mean

AbstractIn this paper, we present the full characterization of the iterativity condition for the mean-value principle under the cumulative prospect theory. It turns out that the premium principle is iterative for exactly six pairs of probability distortion functions. Some of the corresponding premium principles are the classical mean-value principle, essential infimum or essential supremum of the random loss. Moreover, from the proof of the main theorem of this paper, it follows that the iterativity of the mean-value principle is equivalent to the iterativity of the generalized Choquet integral.

scholarly journals A note on comonotonic additivity

1996 ◽  
Vol 38 (2) ◽  
pp. 199-205 ◽  
Author(s):  
June M. Parker
Keyword(s):  
Choquet Integral ◽  
Preference Ordering ◽  
Choquet Integrals ◽  
Comonotonic Additivity

AbstractThe axiom of comonotonic independence for a preference ordering was introduced by Schmeidler [9]. It leads to the comonotonic additivity for the functional representing the preference ordering, which is necessarily a Choquet integral.The aim of this paper is to illuminate the concepts of comonotonicity, comonotonic independence and comonotonic additivity. For example the seemingly weaker condition of weak comonotonic independence used by Chateauneuf in [2] is seen to be equivalent to comonotonic independence. Comonotonic additivity is characterized as additivity on chains of sets. From this the characterization of Choquet integrals in [4], [1], [8] follows easily.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

Characterization of Coherent, Ordered Precipitates in Nickel-Base Alloys

1973 ◽  
Vol 31 ◽  
pp. 144-145
Author(s):  
B. H. Kear ◽  
J. M. Oblak
Keyword(s):  
Stable Phase ◽  
Nickel Base Superalloy ◽  
Alloy 718 ◽  
Commercial Alloy ◽  
Precipitate Morphology ◽  
Continuous Precipitation ◽  
Nickel Base ◽  
Base Superalloy ◽  
Strengthening Precipitate

A nickel-base superalloy is essentially a Ni/Cr solid solution hardened by additions of Al (Ti, Nb, etc.) to precipitate a coherent, ordered phase. In most commercial alloy systems, e.g. B-1900, IN-100 and Mar-M200, the stable precipitate is Ni3 (Al,Ti) γ′, with an LI2structure. In A lloy 901 the normal precipitate is metastable Nis Ti3 γ′ ; the stable phase is a hexagonal Do2 4 structure. In Alloy 718 the strengthening precipitate is metastable γ″, which has a body-centered tetragonal D022 structure.Precipitate MorphologyIn most systems the ordered γ′ phase forms by a continuous precipitation re-action, which gives rise to a uniform intragranular dispersion of precipitate particles. For zero γ/γ′ misfit, the γ′ precipitates assume a spheroidal.

The Use of Advanced Analytical Techniques for Characterization of the Chemical, Physical, and Crystallographic Nature of a Surface

1973 ◽  
Vol 31 ◽  
pp. 132-133 ◽  
Author(s):  
R. E. Herfert
Keyword(s):  
Surface Characterization ◽  
Analytical Techniques ◽  
X Ray Diffraction ◽  
Depth Of Penetration ◽  
X Ray ◽  
The Past ◽  
Transmission Electron ◽  
Scanning Electron

Studies of the nature of a surface, either metallic or nonmetallic, in the past, have been limited to the instrumentation available for these measurements. In the past, optical microscopy, replica transmission electron microscopy, electron or X-ray diffraction and optical or X-ray spectroscopy have provided the means of surface characterization. Actually, some of these techniques are not purely surface; the depth of penetration may be a few thousands of an inch. Within the last five years, instrumentation has been made available which now makes it practical for use to study the outer few 100A of layers and characterize it completely from a chemical, physical, and crystallographic standpoint. The scanning electron microscope (SEM) provides a means of viewing the surface of a material in situ to magnifications as high as 250,000X.

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