• Korean Journal of Mathematics
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• 제32권2호
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• pp.195-211
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• 2024

In this paper, we introduce the concept of a fuzzy lattice ordered group, which is based on a fuzzy lattice that Chon developed in his paper "Fuzzy Partial Order Relations and Fuzzy Lattice". We will also discuss fuzzy lattice-ordered groups in detail, provide several results that are analogous to the classical theory of lattice-ordered groups, and characterize the relationship between a fuzzy lattice-ordered group using its level set and support. Moreover, we define the concepts of fl-subgroups, quotients, and cosets of fl-groups and obtain some fundamental results for these fuzzy algebraic structures.

• 대한수학회지
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• 제40권2호
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• pp.225-239
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• 2003

(G, <) is an ordered group if'<'is a total order relation on G in which f < g implies that xfy < xgy for all f, g, x, y $\in$ G. We say that (G, <) is centrally ordered if (G, <) is ordered and ［G,D］ $\subseteq$ C for every convex jump C $\prec$ D in G. Equivalently, if $f^{-1}g f{\leq} g^2$ for all f, g $\in$ G with g > 1. Every order on a torsion-free locally nilpotent group is central. We prove that if every order on every two-generator subgroup of a locally soluble orderable group G is central, then G is locally nilpotent. We also provide an example of a non-nilpotent two-generator metabelian orderable group in which all orders are central.

• 대한수학회보
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• 제60권2호
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• pp.529-539
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• 2023

In this paper, we study nuclearity of semigroup crossed products for quasi-lattice ordered groups. We show the relationships among nuclearity of the semigroup crossed product, amenability of the quasi-lattice ordered group and nuclearity of the underlying C^*-algebra.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1447-1457
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• 2009

In this paper we define intuitionistic fuzzy interior ideals in ordered semigroups. We prove that in regular(resp. intra-regular and semisimple) ordered semigroups the concepts of intuitionistic fuzzy interior ideals and intuitionistic fuzzy ideals coincide. We prove that an ordered semi group is intuitionistic fuzzy simple if and only if every intutionistic fuzzy interior ideal is a constant function. We characterize intra-regular ordered semi groups in terms of interior (resp. intuitionistic fuzzy interior) ideals.

• 대한수의학회지
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• 제37권2호
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• pp.281-289
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• 1997

The study was designed to investigate the effects of progesterone and estrogen on the uterus of rats by immunohistochemical methods using Proliferating Cell Nuclear Antigen (PCNA) antibody. Eighteen female rats(Wistar), weighing initially about 300g, were ovariectomized. These rats were divided into four groups, progesterone-treated group, estrogen-treated group, estrogen+progesterone-treated group, and control group, progesterone-treated group was injected with 1mg of progesterone per rat per day for 2 days and estrogen-treated group with $20{\mu}g$ of $17{\beta}-estradiol$ for 3 days and estrogen+progesterone-treated group with $17{\beta}-estrdiol$ for 3 days and then with progesterone for 2 days as above. In gross findings, the uteri were markedly hypertrophied by estrogen treatment but were not affect in size by progesterone treatment. Immunohistochemical investigation was performed on the cell types with higher appearance of PCNA positive reaction cells in four groups. The groups with higher appearance of the stromal cells were ordered as estrogen-treated group, progesterone-treated group, estrogen+progesterone-treated group, and control group. The muscle cells were ordered as progesterone-treated group, estrogen-treated group, estrogen+progesterone-treated group, and control group. Positive reaction cells of the stromal cells were total 4.6 times higher than those of muscle cells. Therefore, the affect of the hypertrophy on the uterus by estrogen was larger than those of progesterone and affect on the uterus by stromal cells were larger than those of muscle cells. The group with more PCNA positive reaction cells of luminal epithelial cells were ordered as control group, progesterone-treated group, estrogen+progesterone-treated group, and estrogen-treated group, and glandular epithelial cells were ordered as estrogen+progesterone-treated group, progesterone-treated group, control group, and estrogen-treated group. It was suggested that estrogen and progesterone did not affect on the proliferating cells of luminal epithelial cells and affection of progesterone on the development of glandular epithelial cell was larger than that of estrogen.

• 한국지능시스템학회논문지
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• 제20권3호
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• pp.434-440
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• 2010

In this paper, we define generalized induced linguistic aggregation operator called generalized induced linguistic ordered weighted harmonic mean(GILOWHM) operator. Each object processed by this operator consists of three components, where the first component represents the importance degree or character of the second component, and the second component isused to induce an ordering, through the first component, over the third components which are linguistic variables and then aggregated. It is shown that the induced linguistic ordered weighted harmonic mean(ILOWHM) operator and linguistic ordered weighted harmonic mean(LOWHM) operator are the special cases of the GILOWHM operator. Based on the GILOWHM and LWHM operators, we develop an approach to group decision making with linguistic preference relations. Finally, a numerical example is used to illustrate the applicability of the proposed approach.

• 호남수학학술지
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• 제40권3호
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• pp.457-486
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• 2018

In several fields the soft set theory has a very vast range uses and applications. A soft group is a proper family of subgroups and a fuzzy soft group is a proper family of fuzzy subgroups. Here in this paper the concept of lattice ordered fuzzy soft groups is introduced. Also its some properties are studied and discussed. In addition, the defintion of lattice order fuzzy soft right (left) cosets and lattice order soft product of fuzzy soft subgroups and some related results are discussed to clear these ideas.

• 한국재료학회지
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• 제3권6호
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• pp.678-683
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• 1993

MBE법으로 $580^{\circ}C$에서 성장한 $GaAs_{0.5}Sb_{0.5}$/(001)GaAs 에피층의 원자 배열을 TEM을 이용하여 분석하였다. 1/2(111) 형의 장범위 규칙상이 $GaAs_{0.5}Sb_{0.5}$/(001)GaAs 에피층에서 발견되었다. 이 규칙상의 원자 배열은 As의 농도가 높은 {111}As 면과 Sb의 농도가 높은 {l1l}Sb 면이 V족 소격자에 교대로 나열된 구조이며, 주기는 {111} 면간 거리의 2배이다. 이 구조는 R3m 의 공간군에 속하며, 단위포는 능면체정이다.

• 대한교통학회지
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• 제30권4호
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• pp.61-70
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• 2012

본 연구에서는 2006년 수도권 가구통행실태조사 자료를 활용하여 비업무통행빈도에 대한 고령자의 통행특성을 분석하였다. 분석결과 비업무통행빈도에 대한 고령자의 통행특성은 타 연령층과 상이한 것으로 나타났으며, 분석모형은 특정 변수에 이분산성을 가정한 이분산 서열로짓모형의 설명력이 우수한 것으로 나타났다. 모형추정 결과 고령자는 연령층이 낮을수록, 여성일수록, 운전면허를 가지고 있을수록, 직업 및 가구내 미취학 아동이 없을수록, 그리고 가구내 특정수준 이상의 월평균소득이 있을 경우 비업무통행빈도가 증가하는 것으로 나타났다. 본 연구의 분석결과에 대한 정책적 시사점으로 모든 고령자에 대하여 획일적인 교통정책을 수립하는 것 보다 고령자의 개인적 특성차이(연령대별 건강상태 등)를 고려한 교통정책이 수립되어야 할 것으로 판단된다.

• 호남수학학술지
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• 제35권4호
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• pp.583-606
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• 2013

We generalize the idea of (${\in}$, ${\in}{\vee}q_k$)-fuzzy ordered semi-group and give the concept of (${\in}$, ${\in}{\vee}q_k$)-fuzzy ordered $\mathcal{LA}$-semigroup. We show that (${\in}$, ${\in}{\vee}q_k$)-fuzzy left (right, two-sided) ideals, (${\in}$, ${\in}{\vee}q_k$)-fuzzy (generalized) bi-ideals, (${\in}$, ${\in}{\vee}q_k$)-fuzzy interior ideals and (${\in}$, ${\in}{\vee}q_k$)-fuzzy (1, 2)-ideals need not to be coincide in an ordered $\mathcal{LA}$-semigroup but on the other hand, we prove that all these (${\in}$, ${\in}{\vee}q_k$)-fuzzy ideals coincide in a left regular class of an ordered $\mathcal{LA}$-semigroup. Further we investigate some useful conditions for an ordered $\mathcal{LA}$-semigroup to become a left regular ordered $\mathcal{LA}$-semigroup and characterize a left regular ordered $\mathcal{LA}$-semigroup in terms of (${\in}$, ${\in}{\vee}q_k$)-fuzzy one-sided ideals. Finally we connect an ideal theory with an (${\in}$, ${\in}{\vee}q_k$)-fuzzy ideal theory by using the notions of duo and (${\in}{\vee}q_k$)-fuzzy duo.