Results 131 to 140 of about 30,930 (154)

Matkowski–Sutô Type Equation on Symmetrized Weighted Quasi-Arithmetic Means

Results in Mathematics, 2011
Given \(\varphi \in \mathcal{CM}(I)\) (\(\mathcal{CM}(I)\) is the class of continuous and strictly monotone real valued functions defined on the open interval \(I\)), \(A_{\varphi}(x,y;\alpha)\) denotes the weighted quasi-arithmetic mean generated by \(\varphi\) with weight \(\alpha ...
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Square iterative roots of generalized weighted quasi-arithmetic mean-type mappings

Acta Mathematica Hungarica, 2021
Let functions \(f\) and \(g\) of a single variable be of the same type monotonicity, continuous and \(f+g\) be strictly monotonic. The function of two variables \(A_{f,g}(x, y) := (f + g)^{-1} (f(x) + g(y))\) is called the bivariable strict mean. The authors solve the functional equation \((A_{f,g}, A_{g,h})\circ (A_{f,g}, A_{g,h}) = (A_{F,G}, A_{G,H})\
Li, L., Matkowski, J., Zhang, Q.
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The Matkowski–Sutő problem for weighted quasi-arithmetic means

Acta Mathematica Hungarica, 2003
Let \(I\subset\mathbb{R}\) be a non-void open interval and let \(\mathcal{CM}(I)\) denote the class of all continuous and strictly monotone real-valued functions defined on the interval \(I\). A function \(M:I\times I \to I\) is called a weighted quasi-arithmetic mean on \(I\) if there exist a number ...
Daróczy, Z., Páles, Zs.
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On an equation involving weighted quasi-arithmetic means

Acta Mathematica Hungarica, 2010
The main theorem of this paper gives a full solution of the Matkowski-Sutô type functional equation \[ \kappa x+(1-\kappa)y=\lambda \varphi^{-1}(\mu\varphi(x)+(1-\mu)\varphi(y)) +(1-\lambda)\psi^{-1}(\nu\psi(x)+(1-\nu)\psi(y)). \] The unknown functions \(\varphi\) and \(\psi\) are assumed to be continuous and strictly monotone on an interval (these are
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Invariance of weighted quasi-arithmetic means with continuous generators

Publicationes Mathematicae Debrecen, 2007
The paper is a significant contribution to the theory of the invariance equation \[ M_0\big(M_1(x,y),M_2(x,y)\big)=M_0(x,y),\qquad(x,y\in I), \] where \(M_0,M_1,M_2:I^2\to I\) are two-variable means on the interval \(I\). The main result of the paper completely solves this equation in the class of weighted two-variable quasiarithmetic means (i.e, when,
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Weighted Quasi-arithmetic Means and Conditional Expectations

2010
In this paper, the weighted quasi-arithmetic means are discussed from the viewpoint of utility functions and background risks in economics, and they are represented by weighting functions and conditional expectations. Using these representations, an index for background risks in stochastic environments is derived through the weighted quasi-arithmetic ...
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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.
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Clustering Methods Based on Weighted Quasi-Arithmetic Means of T-Transitive Fuzzy Relations

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2015
In this paper we propose clustering methods based on weighted quasiarithmetic means of T-transitive fuzzy relations. We first generate a T-transitive closure RT from a proximity relation R based on a max-T composition and produce a T-transitive lower approximation or opening RT from the proximity relation R through the residuation operator.
Miin-Shen Yang, Ching-Nan Wang
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Weighted Quasi-Arithmetic Means: Utility Functions and Weighting Functions

2013
This paper discusses weighted quasi-arithmetic means from viewpoint of a combined index of utility functions and weighting functions, which represent stochastic risk in economics. The combined index characterizes decision maker's attitude and background risks in stochastic environments by conditional expectation representations of weighted quasi ...
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Quasi-arithmetic means and ratios of an interval induced from weighted aggregation operations

Soft Computing, 2009
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