• Korean Journal of Mathematics
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• v.32 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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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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• v.27 no.5_6
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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.

• Korean Journal of Veterinary Research
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• v.37 no.2
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.3
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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.

• Honam Mathematical Journal
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• v.40 no.3
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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.

• Korean Journal of Materials Research
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• v.3 no.6
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• pp.678-683
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• 1993

Atomic arral1gement of ordered phase in $GaAs_{0.5}Sb_{0.5}$ epilayer was studied by observation of selected area diffraction patterns and high resolution images. The epilayer was grown on untilted (001) GaAs substrate at $580^{\circ}C$ by molecular beam epitaxy(MBE). A 1/2(111) type long-range ordered phase is formed in the epilayer. Atomic arrangement of the ordered phase is described as an alternative stacking of As-rich and Sb-rich {111} planes in group V sublattice. Space group of the ordred structure belongs to R3m, and unit cell of the ordered structure is rhombohedral.

• Journal of Korean Society of Transportation
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• v.30 no.4
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• pp.61-70
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• 2012

This research explores different non-work trip characteristics between the elderly group (65+) and the working age group (20-64) using heteroscadastic ordered logit model. The analysis is based on travel survey data of Seoul Metropolitan area in 2006. The results show that age induces heteroscadasticity and the model provides a better fit than ordered logit model. The factors increasing the number of non-work trip of the elderly were driver's license and household income. Conversely, the number of non-work trips decreased in those groups that were male, with a job, in aging, and with the number of preschool children. The factors having opposite effects (increased the number of non-work trips in the working age groups and decreased in the elderly group) between the elderly group and working age group were age and job.

• Honam Mathematical Journal
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• v.35 no.4
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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.