• 대한수학회보
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• 제47권5호
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• pp.933-950
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• 2010

We study a relationship between sets of uniqueness, weakly sufficient sets and sampling sets in the space $A^{-{\infty}}(\mathbb{B})$ of holomorphic functions with polynomial growth on the unit ball of $\mathbb{C}^n$ ($n\;{\geq}\;1$).

• 충청수학회지
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• 제24권2호
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• pp.253-266
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• 2011

We would like to generalize about trapezoidal fuzzy set and to calculate four operations based on the Zadeh's extension principle for two generalized trapezoidal fuzzy sets. And we roll up triangular fuzzy numbers and generalized triangular fuzzy sets into it. Since triangular fuzzy numbers and generalized triangular fuzzy sets are generalized trapezoidal fuzzy sets, we need no more the separate painstaking calculations of addition, subtraction, multiplication and division for two such kinds once the operations are done for generalized trapezoidal fuzzy sets.

• Kyungpook Mathematical Journal
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• 제52권4호
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• pp.405-412
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• 2012

The purpose of the present paper is towards working out a unified version of the study of certain weak forms of generalized open sets and their neighbouring forms, as are already available in the literature. In terms of an operation, as initiated by $\acute{A}$. Cs$\acute{a}$sz$\acute{a}$r, we introduce unified definitions of ${\wedge}_{\psi}$-sets, ${\vee}_{\psi}$-sets, $g{\cdot}{\wedge}_{\psi}$-sets and $g{\cdot}{\vee}_{\psi}$-sets and derive results concerning them.

• 한국컴퓨터정보학회논문지
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• 제1권1호
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• pp.183-188
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• 1996

Zadeh에 의하여 소개된 퍼지 집합은 소속 함수를 이용하여 애매한 정보처리 및 추론을 가능토록 한 개념이다 Rough 집합의 개념은 Pawlak에 의하여 소개 되었으며.식별 곤란한 데이터의 분류, 축소 및 근사추론을 가능토록 한다. Pawlakl은 퍼지 집합과 Hough 집합을 서로 다른 개념으로 비교하여 서로 결합할 수 없는 것으로 정의하였다. 본 논문의 목적은 Pawlak의 정의와는 달리 퍼지 집합의 소속 함수를 Rough 집합에 적용함으로써 퍼지 집합과 Rough집합을 결합한 퍼지-rough집합의 개념을 정립하기 위한 것이다.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2001년도 춘계학술대회 학술발표 논문집
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• pp.34-37
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• 2001

Park et al. [Proc. KFIS Fall Conf. 10(2) (2000), 59-62] defined fuzzy ${\gamma}$-open sets by using an operation ${\gamma}$ on a fts (X, $\tau$) and investigated the related fuzzy topological properties of the associated fuzzy topology $\tau$/seb ${\gamma}$/ and $\tau$. As generalizations of the notion of fuzzy ${\gamma}$-closed sets, we define gf. ${\gamma}$-closed sets and g*f. ${\gamma}$-closed sets and study basic properties of these sets relative to union and intersection. Also, we introduce and study two classes of ftss called fuzzy ${\gamma}$-T* and fuzzy ${\gamma}$-T$_{1}$2/ spaces by using the notions of gf. ${\gamma}$-closed and g*f. ${\gamma}$-closed sets.

• 한국수학교육학회지시리즈A:수학교육
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• 제4권1호
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• pp.16-28
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• 1966

According to the modernization of mathematics education, new abstract concepts such as the concept of sets are introduced in many fields of it. The purpose of this thesis is to adopt the concept of sets to 'probability' which is included in the curriculum of high school matematics education. The considerations of the preceding chapter III, and their obvious generalizations to more complicated experiments, justify the conclusion that probability theory consists of the study of sets. An event is a set, its opposite event is the complementary set; mutually exclusive events are disjoint sets, and an event consisting of the simultaneous occurrence of two other events is a sets obtained by intersecting two other sets it is clear how this glossary, translating physical terminology into set theoretic terminology, may be continued. Furthermore, the important theorems of probability; Additional theorem, multiplication theorem, their applications and so on, are proved by the technical operations of sets. Thinking of the mathematics education introduced by the concept of sets is very important in future.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.413-437
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• 2023

In this paper, we introduce the concepts of (inf, sup)-hesitant fuzzy subsemigroups and (inf, sup)-hesitant fuzzy (generalized) bi-ideals of semigroups, and investigate their properties. The concepts are established in terms of sets, fuzzy sets, negative fuzzy sets, interval-valued fuzzy sets, Pythagorean fuzzy sets, hesitant fuzzy sets, and bipolar fuzzy sets. Moreover, some characterizations of bi-ideals, fuzzy bi-ideals, anti-fuzzy bi-ideals, negative fuzzy bi-ideals, Pythagorean fuzzy bi-ideals, and bipolar fuzzy bi-ideals of semigroups are given in terms of the (inf, sup)-type of hesitant fuzzy sets. Also, we characterize a semigroup which is completely regular, a group and a semilattice of groups by (inf, sup)-hesitant fuzzy bi-ideals.

• Nuclear Engineering and Technology
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• 제52권6호
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• pp.1137-1147
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• 2020

The discrete ordinates method (S_N) is one of the major shielding calculation method, which is suitable for solving deep-penetration transport problems. Our objective is to explore the available quadrature sets and to improve the accuracy in shielding problems involving strong anisotropy. The linear discontinuous finite-element (LDFE) quadrature sets based on the icosahedron (in short, ICLDFE quadrature sets) are developed by defining projected points on the surfaces of the icosahedron. Weights are then introduced in the integration of the discontinuous finite-element basis functions in the relevant angular regions. The multivariate secant method is used to optimize the discrete directions and their corresponding weights. The numerical integration of polynomials in the direction cosines and the Kobayashi benchmark are used to analyze and verify the properties of these new quadrature sets. Results show that the ICLDFE quadrature sets can exactly integrate the zero-order and first-order of the spherical harmonic functions over one-twentieth of the spherical surface. As for the Kobayashi benchmark problem, the maximum relative error between the fifth-order ICLDFE quadrature sets and references is only -0.55%. The ICLDFE quadrature sets provide better integration precision of the spherical harmonic functions in local discrete angle domains and higher accuracy for simple shielding problems.

• 대한수학회논문집
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• 제33권4호
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• pp.1341-1356
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• 2018

The author devotes this paper to defining a new class of generalized soft open sets, namely soft somewhere dense sets and to investigating its main features. With the help of examples, we illustrate the relationships between soft somewhere dense sets and some celebrated generalizations of soft open sets, and point out that the soft somewhere dense subsets of a soft hyperconnected space coincide with the non-null soft ${\beta}$-open sets. Also, we give an equivalent condition for the soft csdense sets and verify that every soft set is soft somewhere dense or soft cs-dense. We show that a collection of all soft somewhere dense subsets of a strongly soft hyperconnected space forms a soft filter on the universe set, and this collection with a non-null soft set form a soft topology on the universe set as well. Moreover, we derive some important results such as the property of being a soft somewhere dense set is a soft topological property and the finite product of soft somewhere dense sets is soft somewhere dense. In the end, we point out that the number of soft somewhere dense subsets of infinite soft topological space is infinite, and we present some results which associate soft somewhere dense sets with some soft topological concepts such as soft compact spaces and soft subspaces.

• Journal of Communications and Networks
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• 제14권3호
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• pp.230-236
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• 2012

Based on the known binary sequence sets and Gray mapping, a new method for constructing quaternary sequence sets is presented and the resulting sequence sets' properties are investigated. As three direct applications of the proposed method, when we choose the binary aperiodic, periodic, and Z-complementary sequence sets as the known binary sequence sets, the resultant quaternary sequence sets are the quaternary aperiodic, periodic, and Z-complementary sequence sets, respectively. In comparison with themethod proposed by Jang et al., the new method can cope with either both the aperiodic and periodic cases or both even and odd lengths of sub-sequences, whereas the former is only fit for the periodic case with even length of sub-sequences. As a consequence, by both our and Jang et al.'s methods, an arbitrary binary aperiodic, periodic, or Z-complementary sequence set can be transformed into a quaternary one no matter its length of sub-sequences is odd or even. Finally, a table on the existing quaternary periodic complementary sequence sets is given as well.