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Weighted quasi-arithmetic mean based score level fusion for multi-biometric systems
IET Biometrics, 2020Biometrics is now being principally employed in many daily applications ranging from the border crossing to mobile user authentication. In the high-security scenarios, biometrics require stringent accuracy and performance criteria.
Herbadji Abderrahmane +4 more
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The Invariance of the Arithmetic Mean With Respect to Generalized Quasi-Arithmetic Means
Journal of Mathematical Analysis and Applications, 2009 Given a continuous strictly monotone function \(\phi: I\to {\mathbb R}\) and a probability measure \(\mu\) on the Borel subjects of \([0,1],\) the two variable mean \({\mathcal M}_{\phi, \mu}: I^2\to I\) is defined by \[ {\mathcal M}_{\phi, \mu}(x,y)=\phi^{-1}\left(\int_0^1 \phi(tx+(1-t)y)d\mu(t)\right), \quad (x,y)\in I. \] The aim of this paper is to
Zsolt Páles
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A Characterization of Weighted Arithmetic Means
SIAM Journal on Algebraic Discrete Methods, 1980We prove, among other things, that the set of weighted arithmetic means is identical with the set of functions $f:R^n \to R$ satisfying (i) $\min \{ x_j \}\leqq f ( x_1 ,x_2 , \cdots ,x_n )\leqq \max \{ x_j \}$ and (ii) for $k = 2,3:\sum _{i = 1}^k x_{ij} = s( j = 1,2, \cdots ,n ) \Rightarrow \sum _{i = 1}^k f( x_{i1} ,x_{i2} , \cdots ,x_{in} ) = s$.
J. Aczél, C. Wagner
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Intuitionistic Fuzzy Hybrid Weighted Arithmetic Mean and Its Application in Decision Making
Int. J. Uncertain. Fuzziness Knowl. Based Syst., 2019Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a non-membership function, and a hesitancy function, is a generalization of a fuzzy set.
Weize Wang, J. Mendel
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On Means That are Both Quasi-Arithmetic and Conjugate Arithmetic
Acta Mathematica Hungarica, 2001The authors determine all means of two variables that are simultaneously of the form \[ \psi^{-1}\biggl({\psi(x)+\psi(y)\over 2}\biggr)\quad\text{and}\quad \varphi^{-1}(\varphi(x)+\varphi(y)-\varphi\Bigl({x+y\over 2}\Bigl)). \] The functions \(\psi\) and \(\varphi\) are strictly monotonic, continuous, defined on an open real interval, and one of them ...
Daróczy, Z., Páles, Zs.
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Visualizing the Arithmetic Mean
Mathematics Teacher: Learning and Teaching PK-12, 2021The two provided activities are geared for students in middle school to facilitate and deepen their understanding of the arithmetic mean. Through these activities, students analyze visual representations and use a special type of statistical thinking called transnumerative thinking.
Michael Daiga, Shannon Driskell
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THE MEAN-VALUES OF ARITHMETICAL FUNCTIONS
The Quarterly Journal of Mathematics, 1949Es wird zunächst folgender Satz bewiesen: Es seien \(\{a_n\}\), \(\{A_n\}\) zwei Folgen, verknüpft durch \[ A_n = \sum_{m\mid n} a_m,\quad a_n = \sum_{m\mid n} \mu(n) A_m, \] dann gilt \[ \lim_{N\to\infty} N^{-1} \sum_{n=1}^N A_n \rightarrow \lim_{N\to\infty} N^{-1} \sum_{n=1}^N a_nn^{-1}, \qquad (N\to\infty), \] wenn es eine positive nichtabnehmende ...
Atkinson, F. V., Lord Cherwell
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Arithmetic mean as a linear combination of two quasi-arithmetic means
Publicationes Mathematicae Debrecen, 2002Under twice continuous differentiability assumptions on the generator functions \(f\) and \(g\), the authors determine all two variable quasi-arithmetic means \(M^{[f]}\), \(M^{[g]}\) and all real numbers \(\lambda\) and \(\mu\) such that \[ \lambda M^{[f]}+\mu M^{[g]}=A, \] where \(A\) denotes the two variable arithmetic mean.
Głazowska, Dorota +2 more
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The Arithmetic-Geometric Mean of Gauss
1997This paper is an expository account of the arithmetic-geometric mean M(a,b) of two numbers a,b. For \(a,b>0\) define \(a_ 0=a\), \(b_ 0=b\) and \(a_{n+1}=(a_ n+b_ n)/2,\quad b_{n+1}=(a_ nb_ n)^{1/2},\quad n=0,1,2,\ldots.\) It follows by elementary methods that the two sequences \(a_ n\), \(b_ n\) have a common limit M(a,b).
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Arithmetic Facts without Meaning
Cortex, 1997The paper presents a single-case study of patient J.G. showing severe calculation problems (and also agraphia, finger agnosia, right-left disorientation and apraxia) after the surgery of a left parietal tumor. Although the patient completely lost conceptual knowledge of arithmetic, she preserved part of memorised fact knowledge (multiplications and ...
M, Delazer, T, Benke
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