Characterization of homogeneous and quasi-homogeneous binary aggregation functions

In this paper, we explore the use of aggregation functions in the construction of coherent upper previsions. Sub-additivity is one of the defining properties of a coherent upper prevision defined on a linear space of random variables and thus we introduce a new sub-additive transformation of aggregation functions, called a revenue transformation, whose output is a sub-additive aggregation function bounded below by the transformed aggregation function, if it exists. Method of constructing coherent upper previsions by means of shift-invariant, positively homogeneous and sub-additive aggregation functions is given and a full characterization of shift-invariant, positively homogeneous and idempotent aggregation functions on [0,∞[n is presented. Lastly, some concluding remarks are added.

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Additive Aggregation Functions: Generalizations and Modifications of Additivity

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488519400026 ◽

2019 ◽

Vol 27 (Supp01) ◽

pp. 39-58

Author(s):

Anna Kolesárová ◽

Fateme Kouchakinejad ◽

Radko Mesiar

Keyword(s):

Unit Interval ◽

Aggregation Functions

In this paper we study some modifications and generalizations of additivity in the case of aggregation functions on the unit interval [0, 1]. We prove that some common properties of aggregation functions can be viewed as modifications of additivity — additivity with constraints.We also generalize additivity into pseudo-additivity and k-pseudo-additivity, and provide characterization of pseudo-additive and k-pseudo-additive aggregation functions, including maxitive and k-maxitive aggregation functions.

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LOCALLY INTERNAL AGGREGATION FUNCTIONS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488599000179 ◽

1999 ◽

Vol 07 (03) ◽

pp. 235-241 ◽

Cited By ~ 5

Author(s):

G. MAYOR ◽

J. MARTIN

Keyword(s):

Aggregation Function ◽

Aggregation Functions

We introduce the concept of locally internal aggregation function with domain ℝn and values in ℝ, and demonstrate some results which lead to the characterization of such functions.

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Characterization of Quadratic Aggregation Functions

IEEE Transactions on Fuzzy Systems ◽

10.1109/tfuzz.2019.2900850 ◽

2019 ◽

Vol 27 (4) ◽

pp. 824-829

Author(s):

Santi Tasena

Keyword(s):

Aggregation Functions

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Parametric characterization of aggregation functions

Fuzzy Sets and Systems ◽

10.1016/j.fss.2008.08.002 ◽

2009 ◽

Vol 160 (6) ◽

pp. 816-831 ◽

Cited By ~ 14

Author(s):

Anna Kolesárová ◽

Radko Mesiar

Keyword(s):

Aggregation Functions

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Morphological Characterization of Mycobacteriophage R1

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100051281 ◽

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.

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AEM analysis of crystallization in Ti-based amorphous alloys

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100075142 ◽

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.

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