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Integration of the Biot-Gassmann Fluid Substitution Method and Machine Learning-Based Velocity-Stress Relationship for Estimating In Situ Stresses. [PDF]

ACS Omega
Mustafa A, Lu G, Bunger AP.
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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).
Daróczy, Zoltán, Hajdu, Gabriella
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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
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Some results of weighted quasi-arithmetic mean of continuous triangular norms

Information Sciences, 2008
Let \(T_1\) and \(T_2\) be two continuous t-norms, \(f:[0,1]\to[-\infty,\infty]\) be strictly monotone. Then the function \(T(x,y)=f^{-1}(pf(T_1(x,y))+(1-p)f(T_2(x,y)))\), where \(p\in(0,1)\), is called the weighted quasi-arithmetic mean of \(T_1\) and \(T_2\) with respect to \(f\). This function satisfies all properties of t-norms except associativity.
Ouyang, Yao, Fang, Jinxuan
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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
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A functional equation involving comparable weighted quasi-arithmetic means

Acta Mathematica Hungarica, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daróczy, Z., Maksa, Gy.
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