• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.13-16
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• 2002

Recently, Szmidt and Kacprzyk[Fuzzy Sets and Systems 118(2001) 467-477] Proposed a non-probabilistic-type entropy measure for intuitionistic fuzzy sets. It is a result of a geometric interpretation of intuitionistic fuzzy sets and uses a ratio of distances between them. They showed that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of F∩F$\^$c/ and F∪F$\^$c/, while applying the Hamming distances. In this note, while applying the Euclidean distances, it is also shown that the proposed measure can be defined in terms of the ratio of some function of intuitionistic fuzzy cardinalities: of F∩F$\^$c/ and F∪F$\^$c/.

• Journal of Integrative Natural Science
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• v.11 no.3
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• pp.161-164
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• 2018

Over the past decade, mass spectrometry-based metabolomics, especially two dimensional gas chromatography mass spectrometry (GCxGC/TOF-MS), has become a key analytical tool for metabolomics data because of its sensitivity and ability to analyze complex biological or biochemical sample. However, the need to reduce variations within/between experiments has been reported and methodological developments to overcome such problem has long been a critical issue. Along with methodological developments, developing reasonable performance measure has also been studied. Following four numerical measures have been typically used for comparison: sensitivity, specificity, receiver operating characteristic (ROC) curves, and positive predictive value (PPV). However, more recently, such measures are replaced with F1 score in many fields including metabolomics area without any carefulness of its validity. Thus, we want to investigate the validity of F1 score on two examples, with the goal of raising the awareness in choosing appropriate performance comparison measure. We noticed that F1 score itself, as a performance measure, was not good enough. Accordingly, we suggest that F1 score be supplemented with other performance measure such as specificity to improve its validity.

• The Journal of the Korea Contents Association
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• v.2 no.4
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• pp.99-103
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• 2002

In this paper, we investigate for how to define a fuzzy measure by using the semi-normed fuzzy integral of a given measurable function with respect to another given fuzzy measure when t-seminorm is continuous. Let (X, F, g) be a fuzzy measure space, h$\in$L$^\circ$(X), and $\top$ be a continuous t-seminorm.. Then the set function $\nu$ defined by $\nu$(A)=$\int _A$h$\top$g for any $A\in$F is a fuzzy measure on (X, F).

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.89-99
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• 2009

Let $\mu$ be a finite positive Borel measure on the unit ball $B{\subset}\mathbb{C}^n$ and $\nu$ be the Euclidean volume measure such that ${\nu}(B)=1$. For the unit sphere $S=\{z:{\mid}z{\mid}=1\}$, $\sigma$ is the rotation-invariant measure on S such that ${\sigma}(S)=1$. Let $\mathcal{P}[f]$ be the invariant Poisson integral of f. We will show that there is a constant M > 0 such that $\int_B{\mid}{\mathcal{P}}[f](z){\mid}^{p}d{\mu}(z){\leq}M\;{\int}_B{\mid}{\mathcal{P}}[f](z)^pd{\nu}(z)$ for all $f{\in}L^p({\sigma})$ if and only if ${\parallel}{\mu}{\parallel_r}\;=\;sup_{z{\in}B}\;\frac{\mu(E(z,r))}{\nu(E(z,r))}\;<\;\infty$.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2007.11a
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• pp.457-462
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• 2007

시멘틱 웹에서의 온톨로지는 특정 영역의 설명을 위해 공유할 개념화된 명세란 정의로 널리 알려져 있으며, 시멘틱웹의 중요한 요소기술이다. 온톨로지는 특정 도메인에 대한 정보를 기술하는데, 이러한 온톨로지를 매핑할 경우 많은 양의 정보를 통합관리하거나, 상호호환성을 이룰 수 있다. 여러 온톨로지 매핑 방법론의 성능을 평가하는 수단 중 f-measure란 것이 있는다. f-measure의 값은 정확도(precision)과 응답률(recall)에 의해서 결정된다. 정확도와 응답률이 변화함에 따라 f-measure 값도 자연히 변하기 때문에, 높은 f-measure 값을 구하기 위해서는 정확도와 응답률의 밸런스를 조정할 필요가 있다. 본 논문에서는 높은 f-measure값을 얻을 수 있는 정확도와 재현률을 구하는 방법을 휴리스틱적 방법을 통하여 알아보고자 한다.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.63-72
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• 1999

We introduce a concept of fuzzy linearity: A function $F:L^0(X){\rightarrow}\mathbb{R}$ is fuzzy linear if $F[({\alpha}{\wedge}f){\vee}(b{\wedge}g)]=[a{\wedge}F(f)]{\vee}[b{\wedge}F(g)]$ for $f,g{\in}L^0(X)$ and a, b > 0. We show that a fuzzy integral is fuzzy linear if the measure is fuzzy c-additive.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.2
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• pp.562-574
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• 2012

Simulation validation techniques which have been employed in most studies are statistical analysis, which validate a model with mean or variance of throughput and resource utilization as an evaluation object. However, these methods have not been able to ensure the reliability of individual elements of the model well. To overcome the problem, the weighted F-measure method was proposed, but this technique also had some limitations. First, it is difficult to apply the technique to complex system environment with numerous values of interarrival time because it assigns a class to an individual value of interarrival time. In addition, due to unbounded weights, the value of weighted F-measure has no lower bound, so it is difficult to determine its threshold. Therefore, this paper propose weighted F-measure technique with cluster analysis to solve these problems. The classes for the technique are defined by each cluster, which reduces considerable number of classes and enables to apply the technique to various systems. Moreover, we improved the validation technique in the way of assigning minimum bounded weights without any lack of objectivity.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1085-1100
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• 2023

For any given function f, we focus on the so-called prescribed mean curvature problem for the measure e^-f(|x|2)dx provided thate^-f(|x|2) ∈ L¹(ℝⁿ⁺¹). More precisely, we prove that there exists a smooth hypersurface M whose metric is ds² = dρ² + ρ²d𝜉² and whose mean curvature function is ${\frac{1}{n}}(\frac{u^p}{{\rho}^{\beta}})e^{f({\rho}^2)}{\psi}(\xi)$ for any given real constants p, β and functions f and ψ where u and ρ are the support function and radial function of M, respectively. Equivalently, we get the existence of a smooth solution to the following quasilinear equation on the unit sphere 𝕊ⁿ, $${\sum_{i,j}}({{\delta}_{ij}-{\frac{{\rho}_i{\rho}_j}{{\rho}^2+|{\nabla}{\rho}|^2}})(-{\rho}ji+{\frac{2}{{\rho}}}{\rho}j{\rho}i+{\rho}{\delta}_{ji})={\psi}{\frac{{\rho}^{2p+2-n-{\beta}}e^{f({\rho}^2)}}{({\rho}^2+|{\nabla}{\rho}|^2)^{\frac{p}{2}}}}$$ under some conditions. Our proof is based on the powerful method of continuity. In particular, if we take $f(t)={\frac{t}{2}}$, this may be prescribed mean curvature problem in Gauss measure space and it can be seen as an embedded result in Gauss measure space which will be needed in our forthcoming papers on the differential geometric analysis in Gauss measure space, such as Gauss-Bonnet-Chern theorem and its application on positive mass theorem and the Steiner-Weyl type formula, the Plateau problem and so on.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.779-789
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• 2011

In this paper we study the Banach space $L^1$(G) of real valued measurable functions which are integrable with respect to a vector measure G in the sense of D. R. Lewis. First, we investigate conditions for a scalarly integrable function f which guarantee $f{\in}L^1$(G). Next, we give a sufficient condition for a sequence to converge in $L^1$(G). Moreover, for two vector measures F and G with values in the same Banach space, when F can be written as the integral of a function $f{\in}L^1$(G), we show that certain properties of G are inherited to F; for instance, relative compactness or convexity of the range of vector measure. Finally, we give some examples of $L^1$(G) related to the approximation property.

• Journal of the Korean Statistical Society
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• v.18 no.1
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• pp.62-71
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• 1989

We consider a Markov proces ${X_n} on [0,\infty)^k$ which is generated by $X_{n+1} = f(X_n) + \varepsilon_{n+1}$ where f is a continuous, nondecreasing concave function. Sufficient conditions for the existence of a unique invariant probability measure for ${X_n}$ are obtained.