Results 241 to 250 of about 52,246 (269)

An Orness Measure for Quasi-Arithmetic Means

IEEE Transactions on Fuzzy Systems, 2006
In this paper, an orness measure to reflect the or-like degree of the quasi-arithmetic mean operator is proposed. With the generating function representation method, some properties of a quasi-arithmetic mean, associated with its orness measure, are analyzed.
Xinwang Liu
exaly   +2 more sources

Limit properties of quasi-arithmetic means

Fuzzy Sets and Systems, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anna Kolesárová
exaly   +2 more sources

Generalized weighted quasi-arithmetic means

Aequationes Mathematicae, 2010
Let \(I\subseteq \mathbb R\) be an interval. A function \(M:\;I^2\to \mathbb R\) is called a mean on \(I^2\), if \[ \min (x,y)\leq M(x,y)\leq \max (x,y),\quad x,y\in I. \] The author considers means of the form \[ M_{f,g}(x,y)=(f+g)^{-1}(f(x)+g(y)) \] where \(f\) and \(g\) are real functions on \(I\), and studies conditions on \(f,g\), under which ...
Janusz Matkowski, Matkowski Janusz
exaly   +2 more sources

Parameterized defuzzification with continuous weighted quasi-arithmetic means – An extension☆

Information Sciences, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xinwang Liu
exaly   +3 more sources

On linear combinations of weighted quasi-arithmetic means

Aequationes Mathematicae, 2005
Let \(CM(I)\) denote the set of all continuous and strictly monotone real functions on the interval \(I\). A mean \(M\) on \(I\) is called a weighted quasi--arithmetic mean if there exists \(\phi \in CM(I)\) such that \[ M(x,y)=\phi^{-1}(\lambda\phi(x)+(1-\lambda)\phi(y))=:A_{\phi}(x,y;\lambda) \qquad (x,y \in I).
Zoltan Daróczy
exaly   +2 more sources

Quasi-Arithmetic Type Mean Generated by the Generalized Choquet Integral

Symmetry, 2020
It is known that the quasi-arithmetic means can be characterized in various ways, with an essential role of a symmetry property. In the expected utility theory, the quasi-arithmetic mean is called the certainty equivalent and it is applied, e.g., in a ...
Sebastian Wójcik
exaly   +2 more sources

The orness measures for two compound quasi-arithmetic mean aggregation operators

International Journal of Approximate Reasoning, 2010
The paper first summarizes the orness measures and their common characteristics of some averaging operators: the quasi-arithmetic mean, the ordered weighted averaging (OWA) operator, the regular increasing monotone (RIM) quantifier and the weighted ...
Xinwang Liu
exaly   +2 more sources

The invariance of the arithmetic mean with respect to generalized quasi-arithmetic means

Journal of Mathematical Analysis and Applications, 2009
The aim of this paper is to find those pairs of generalized quasi-arithmetic means on an open real interval I for which the arithmetic mean is invariant, i.e., to characterize those continuous strictly monotone functions φ,ψ:I→R and Borel probability ...
Zsolt Pales
exaly   +2 more sources

WEIGHTED QUASI-ARITHMETIC MEANS AND A RISK INDEX FOR STOCHASTIC ENVIRONMENTS

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2011
In this paper, the weighted quasi-arithmetic means are discussed from the viewpoint of utility functions and downward risks in economics. Representing the weighting functions by probability density functions and the conditional expectations, an index for downward risks in stochastic environments is derived.
YUJI YOSHIDA
openaire   +2 more sources

An invariance of geometric mean with respect to generalized quasi-arithmetic means

Journal of Mathematical Analysis and Applications, 2011
In this paper, we study the invariance of the geometric mean with respect to some generalized quasi-arithmetic means, namely, we present some results concerning the functional equationφ−1(∫01φ(tx+(1−t)y)dμ(t))⋅ψ−1(∫01ψ(tx+(1−t)y)dν(t))=xy,x,y∈I, where I ...
Qian Zhang
exaly   +2 more sources