• 산업경영시스템학회지
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• 제35권4호
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• pp.244-248
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• 2012

F-Measure is one of the external measures for evaluating the validity of clustering results. Though it has clear advantages over other widely used external measures such as Purity and Entropy, F-Measure has inherently been less sensitive than other validity measures. This insensitivity owes to the definition of F-Measure that counts only most influential portions. In this research, we present $F_n$-Measure, an external cluster evaluation measure based on F-Measure. $F_n$-Measure is so sensitive that it can detect their difference in the cases that F-Measure cannot detect the difference in clustering results. We compare $F_n$-Measure to F-Measure for a few clustering results and show which measure draws better result based upon homogeneity and completeness.

• 대한수학회보
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• 제57권3호
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• pp.569-581
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• 2020

In this paper, we introduce the new general concept of usual expansiveness which is called "positively weak measure expansiveness" and study the basic properties of positively weak measure expansive C¹-differentiable maps on a compact smooth manifold M. And we prove that the following theorems. (1) Let 𝓟𝓦𝓔 be the set of all positively weak measure expansive differentiable maps of M. Denote by int(𝓟𝓦𝓔) is a C¹-interior of 𝓟𝓦𝓔. f ∈ int(𝓟𝓦𝓔) if and only if f is expanding. (2) For C¹-generic f ∈ C¹ (M), f is positively weak measure-expansive if and only if f is expanding.

• 호남수학학술지
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• 제8권1호
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• pp.51-74
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• 1986

The thery of measure is significant in that we extend from it to the theory of integration. AS specific metric outer measures we can take Hausdorff outer measure and Lebesgue-Stieltjes outer measure connecting measure with monotone functions.([12]) The purpose of this paper is to find some properties of Lebesgue-Stieltjes measure by extending it from $R^1$ to $R^n(n{\geq}1)$ $({\S}3)$ and differentiation of the integral defined by Borel measure $({\S}4)$. If in detail, as follows. We proved that if $_n{\lambda}_{f}^{\ast}$ is Lebesgue-Stieltjes outer measure defined on a finite monotone increasing function $f:R{\rightarrow}R$ with the right continuity, then $$_n{\lambda}_{f}^{\ast}(I)=\prod_{j=1}^{n}(f(b_j)-f(a_j))$$, where $I={(x_1,...,x_n){\mid}a_j$<$x_j{\leq}b_j,\;j=1,...,n}$. (Theorem 3.6). We've reached the conclusion of an extension of Lebesgue Differentiation Theorem in the course of proving that the class of continuous function on $R^n$ with compact support is dense in $L^p(d{\mu})$ ($1{\leq$}p<$\infty$) (Proposition 2.4). That is, if f is locally $\mu$-integrable on $R^n$, then $\lim_{h\to\0}\left(\frac{1}{{\mu}(Q_x(h))}\right)\int_{Qx(h)}f\;d{\mu}=f(x)\;a.e.(\mu)$.

• 한국화재소방학회논문지
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• 제10권3호
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• pp.19-28
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• 1996

본 논문은 Fuzzy Measure를 이용한 화재감지기의 사고판정을 결정하는 방법을 제시한 것으로 Belief measere를 기본으로하여 Dempster의 결합 Rule을 사용하였다. 감지기에서의 화재 판정 결정은 화재(F), 비화재(N)의 2가지로 하였으며, 이를 판정하기 위해 현재 사용되고있는 열, 연기감지기에 대한 정정값에 대해 Fuzzy Rule을 적용하여 시뮬레이션 하였다. 그 결과 Fuzzy Rule의 수를 많이 적용할수록, 최종동작은 Bel(F)의 값을 높게 할수록 확실한 화재 판별이 가능함을 입증하였다.

• 한국콘텐츠학회논문지
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• 제2권2호
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• pp.91-97
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• 2002

Let (X, F, g) be a fuzzy measure space. Then for any h$\in$ $L^{0}$ (X) , a$\in$[0 , 1] , and $A\in$F ∫$_{A}$aㆍh($\chi$)┬g＝aㆍ∫$_{A}$h($\chi$)┬g with the t-seminorm ┬(x, y)= xy. And we prove that the Seminormed fuzzy integral has some linearity properties only for ｛0,1｝-classes of fuzzy measure as follow, For any f, h$\in$ $L^{0}$ ($\chi$), any a, b$\in$R+: af＋bh$\in$ $L^{0}$ ($\chi$)⇒ ∫$_{A}$(af＋bh)┬g＝a∫$_{A}$f┬g＋b∫$_{A}$h┬g; if and only if g is a probability measure fulfilling g(A) $\in$｛0, 1｝ for all $A\in$F.n$F.

• 대한수학회지
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• 제57권4호
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• pp.935-955
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• 2020

In this paper we present a measurable version of the Smale's spectral decomposition theorem for homeomorphisms on compact metric spaces. More precisely, we prove that if a homeomorphism f on a compact metric space X is invariantly measure expanding on its chain recurrent set CR(f) and has the eventually shadowing property on CR(f), then f has the spectral decomposition. Moreover we show that f is invariantly measure expanding on X if and only if its restriction on CR(f) is invariantly measure expanding. Using this, we characterize the measure expanding diffeomorphisms on compact smooth manifolds via the notion of Ω-stability.

• 대한수학회지
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• 제55권5호
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• pp.1131-1142
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• 2018

A notion of measure expansivity for homeomorphisms was introduced by Morales recently as a generalization of expansivity, and he obtained many interesting dynamic results of measure expansive homeomorphisms in [8]. In this paper, we introduce a concept of weak measure expansivity for homeomorphisms which is really weaker than that of measure expansivity, and show that a diffeomorphism f on a compact smooth manifold is $C^1$-stably weak measure expansive if and only if it is ${\Omega}$-stable. Moreover we show that $C^1$-generically, if f is weak measure expansive, then f satisfies both Axiom A and the no cycle condition.

• 충청수학회지
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• 제22권3호
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• pp.579-586
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• 2009

Let $\varphi$ be a complete probability measure on $\mathbb{R}$, let $m_{\varphi}$ be the analogue of Wiener measure over paths on [0, T] and let f(t) be continuously differentiable on [0, T]. In this note, we give the analogue of Wiener measure $m_{\varphi}$ of {x in C[0, T]$\mid$x(0) < f(0) and $x(s_0){\geq}f(s_{0})$ for some $s_{0}$ in [0, T]} by use of integral equation techniques. This result is a generalization of Park and Paranjape's 1974 result[1].

• 충청수학회지
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• 제36권3호
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• pp.171-180
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• 2023

Investigating local dynamics requires precise control to effectively manage the subtle differences that distinguish it from global dynamics. This paper aims to study the localized perspective of the recently proposed continuum-wise expansive measures [13]. Let f : M → M be a diffeomorphism on a closed smooth manifold M and let p be a hyperbolic periodic point of f. We prove that if the homoclinic class H_f (p) of f associated to p is C¹-robustly measure continuum-wise expansive then it is hyperbolic.

• 한국지능시스템학회논문지
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• 제12권6호
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• pp.583-588
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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. Tt 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 $F\bigcapF^c and F\bigcupF^c$, 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 $F\bigcapF^c and F\bigcupF^c$.