• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1301-1316
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• 2017

It is well known that every $x{\in}(0,1]$ can be expanded to an infinite $L{\ddot{u}}roth$ series with the form of $$x={\frac{1}{d_1(x)}}+{\cdots}+{\frac{1}{d_1(x)(d_1(x)-1){\cdots}d_{n-1}(x)(d_{n-1}(x)-1)d_n(x)}}+{{\cdots}}$$, where $d_n(x){\geq}2$ for all $n{\geq}1$. In this paper, the set of points with some restrictions on the digits in $L{\ddot{u}}roth$ series expansions are considered. Namely, the Hausdorff dimension of following the set $$F_{\phi}=\{x{\in}(0,1]\;:\;d_n(x){\geq}{\phi}(n),\;i.o.n}$$ is determined, where ${\phi}$ is an integer-valued function defined on ${\mathbb{N}}$, and ${\phi}(n){\rightarrow}{\infty}$ as $n{\rightarrow}{\infty}$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.867-871
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• 2009

A module M over a ring R is said to satisfy (P) if every generating set of M contains an independent generating set. The following results are proved; (1) Let $\tau$ = ($\mathbb{T}_\tau,\;\mathbb{F}_\tau$) be a hereditary torsion theory such that $\mathbb{T}_\tau$ $\neq$ Mod-R. Then every $\tau$-torsionfree R-module satisfies (P) if and only if S = R/$\tau$(R) is a division ring. (2) Let $\mathcal{K}$ be a hereditary pre-torsion class of modules. Then every module in $\mathcal{K}$ satisfies (P) if and only if either $\mathcal{K}$ = {0} or S = R/$Soc_\mathcal{K}$(R) is a division ring, where $Soc_\mathcal{K}$(R) = $\cap${I 4\leq$ $R_R$ : R/I$\in\mathcal{K}$}.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.2
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• pp.183-190
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• 2007

We present a new decision tree classification algorithm using rough set theory that can induce classification rules, the construction of which is based on core attributes and relationship between objects. Although decision trees have been widely used in machine learning and artificial intelligence, little research has focused on improving classification quality. We propose a new decision tree construction algorithm that can be simplified and provides an improved classification quality. We also compare the new algorithm with the ID3 algorithm in terms of the number of rules.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.524-528
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• 1996

Quality information is known to have the characteristic of continuous distribution in many manufacturing processes. It is difficult to describe the process condition by classifying the distribution into discrete ranges which is based on the set concept. Fuzzy control chart has been developed for the control of linguistic data but it still utilizes the dichotomous notion of classical set theory. In this paper, the fuzzy sampling method is studied in order to manage the ambiguous data properly and incorporated for generating fuzzy control chart. The method is based on the fuzzy set concept and considered to be appropriate for the realization of a complete fuzzy control chart. The fuzzy control chart was compared with the conventional generalized p-chart in the sensitivity for quality distribution and robustiness against the noise. The fuzzy control chart with the fuzzy sampling method showed better characteristics.

• Proceedings of the Korea Society for Energy Engineering kosee Conference
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• 1998.10a
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• pp.64-68
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• 1998

This paper discusses the potential application of fuzzy set theory to the decision-making in the area of radioactive waste management. the approach proposed in this study is based on the concepts of fuzzy set theory and the hierarchical structure analysis. The linguistic variables and fuzzy numbers are used to aggregate the decision maker's subjective assessments of the decision criteria and of the decision alternatives with respect to these criteria. For each alternative, the fuzzy appropriateness index is evaluated to obtain the final score. Using total integral value method, one of methods for ranking fuzzy numbers, the fuzzy appropriateness indices are ranked. As a case problem, selection of the most suitable option for spent fuel storage is illustrated.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.59-76
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• 2011

Starting from a collection V as a model which satisfies the axioms of NBG, we call the elements of V as sets and the subcollections of V as classes. We reconstruct the G$\ddot{o}$del's proof of the consistency of GCH and AC with the axioms of Zermelo-Fraenkel set theory by using Mostowski-Shepherdson mapping theorem, reflection principles in Tarski-Vaught theorem and Montague-Levy theorem and the fact that NBG is a conservative extension of ZF.

• Bulletin of the Korean Chemical Society
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• v.30 no.4
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• pp.794-796
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• 2009

We have studied the structures and stabilities of Au6 to explore the origin of the large discrepancy between relative energies obtained from the density functional theory (DFT) and ab initio correlated levels of theory. The MP2 methods significantly overestimate the stability of the non-planar isomer when the double-$\zeta$ polarization quality of basis sets, such as LANL2DZ+1f and CEP31G+1f, are used. However, we show that such preference for the non-planar structure at the MP2 level mainly originates from the large basis set superposition error.

• The Korean Journal of Food And Nutrition
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• v.13 no.4
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• pp.353-359
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• 2000

This study was carried out to introduce the fuzzy theory to standardize recipe of Korean foods, such as Pibimbab, Deonjang chigae (soybean stew), and Kimchi chigae (Kimchi stew). That is recipe of Pibimbab using fuzzy theory. Before this recipe was introduced, it thoroughly analyzed a number of data on Korean food such as materials used by cook book, commercial food, restaurants, food service operation recipes, and home recipes. And then the recipe of Korean food, Pibimbab will be possible to be standardized by fuzzy theory. The theory of fuzzy set is a theory of graded concept. The theory has matured into a wide ranging collection of concepts and techniques for dealing with complex phenomena. It defined a Membership function of fuzzy set by analyzed four sorts of data on Korean food, Pibimbab, and it established the fuzzy model using the quantity of materials as input and sensory test scores as output. This study will contribute to develop standard recipe for Korean foods and expert system of recipes using computer system.

• The Mathematical Education
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• v.18 no.1
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• pp.21-23
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• 1980

In [3], an extension of B. Brosowski s T-invariant Point Theorem is given where the linearity of the function and the convexity of the set are relaxed. In this paper, our main purpose is to generalize S. P. Singh's T-invariant Point Theorem to Approximation Theory.

• Journal for History of Mathematics
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• v.14 no.2
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• pp.93-100
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• 2001

The problem of vagueness has been investigated for a long time by philosophers and mathematicians. There are there approaches in mathematics to the problem, which are probability theory, fuzzy logic, and rough set theory. In this paper I introduce these theories and their meanings.