Increasing Solutions of the Homogeneity Equation and of Similar Equations

Aczel, J.; Gronau, Detlef; Schwaiger, Jens

doi:10.1006/jmaa.1994.1097

Cited by 14 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…See also, e.g., [11,12]. A monotone measure [13] is any set function µ : A → [0, ∞[ that is non-decreasing, i.e., A ⊆ B ⊆ Ω implies µ(A) ≤ µ(B); and grounded, i.e., µ(∅) = 0.…”

Section: Preliminariesmentioning

confidence: 99%

Sub-Additive Aggregation Functions and Their Applications in Construction of Coherent Upper Previsions

2020

View full text Add to dashboard Cite

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.

show abstract

Section: Preliminariesmentioning

confidence: 99%

Sub-Additive Aggregation Functions and Their Applications in Construction of Coherent Upper Previsions

2020

View full text Add to dashboard Cite

show abstract

“…The restriction of these families to nondecreasing functions and strictly increasing functions is discussed in Aczél et al [7].…”

Section: Aggregation On Ratio and Interval Scalesmentioning

confidence: 99%

Aggregation Functions for Decision Making

Marichal

2009

Decision‐making Process

View full text Add to dashboard Cite

show abstract

“…Equations (1) and (2) were completely solved in the eighties for ratio scale variables, with domain R + := [0, ∞), and interval scale variables, with domain R, even under some further assumptions such as symmetry, continuity, and nondecreasing monotonicity (in each argument); see [1,2,3,4,19].…”

Section: Introductionmentioning

confidence: 99%

Meaningful aggregation functions mapping ordinal scales into an ordinal scale: a state of the art

Mesiar

2009

Aequ. math.

View full text Add to dashboard Cite

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.

show abstract

Increasing Solutions of the Homogeneity Equation and of Similar Equations

Cited by 14 publications

References 0 publications

Sub-Additive Aggregation Functions and Their Applications in Construction of Coherent Upper Previsions

Sub-Additive Aggregation Functions and Their Applications in Construction of Coherent Upper Previsions

Aggregation Functions for Decision Making

Meaningful aggregation functions mapping ordinal scales into an ordinal scale: a state of the art

Contact Info

Product

Resources

About