• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.971-983
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• 2016

A partially ordered set P is ideal-homogeneous provided that for any ideals I and J, if $$I{\sim_=}_{\sigma}J$$, then there exists an automorphism ${\sigma}^*$ such that ${\sigma}^*{\mid}_I={\sigma}$. Behrendt [1] characterizes the ideal-homogeneous partially ordered sets of height 1. In this paper, we characterize the ideal-homogeneous partially ordered sets of height 2 and nd some families of ideal-homogeneous partially ordered sets.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.161-169
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• 2024

A semi-well ordered set is a partially ordered set in which every non-empty subset of it contains a least element or a greatest element. It is defined as an extension of the concept of well ordered sets. An attempt is made to identify the properties of a semi-well ordered set equipped with the order topology.

• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.243-254
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• 1991

For a given function f.mem.F and a set of functions J.subeq.F, the problem of isotonic optimization is to determine an element in the set nearest to f in some sense. Specifically, let X be a partially ordered finite set with a partial order << and, let F"=F(X) be the linear space of all bounded real valued functions on X. A function g.mem.F is said to be an isotonic function if g(x).leq.g(y) whenever x,y.mem.X and x << y.<< y.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.1-11
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• 2019

In this paper we prove certain coupled coincidence point and coupled common fixed point results in partially ordered metric spaces for a pair of compatible mappings which satisfy certain rational inequality. The results are supported with two examples.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.525-535
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• 2016

We define a fuzzy lattice as a fuzzy relation, prove the distributive inequalities and the modular inequality of fuzzy lattices, and show that the fuzzy totally ordered set is a distributive fuzzy lattice and that the distributive fuzzy lattice is modular.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.105-113
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• 2012

Generalizing modular lattices, a concept of modular ordered sets was introduced by Chajda and Rachunek. In this paper, we characterize modular ordered sets as those partially ordered set P satisfying that for $a,\;b,\;c\;{\in}\;P\;with\;b\;{\leq}\;c,\;l(a,\;b)\;=\;l(a,\;c)\;and\;u(a,\;b)\;=\;u(a,\;c)$ imply $b\;=\;c$. Using this, we obtain a sufficient condition for them. We also discuss the modularity of the Dedekind-MacNeille completions of ordered sets.

• East Asian mathematical journal
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• v.31 no.1
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• pp.65-75
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• 2015

In modern times, coupled fixed point theorems have been rigorously studied by many researchers in the milieu of partially ordered G-metric spaces using different contractive conditions. In this note, some coupled fixed point theorems using mixed monotone property in partially ordered G-metric spaces are obtained. Furthermore some theorems by omitting the completeness on the space and continuity conditions on function, are obtained. Our results partially generalize some existing results in the present literature. To exemplify our results and to distinguish them from the existing ones, we equip the article with suitable examples.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.751-757
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• 1998

Using idempotents in quasi-lattices, we show that the category Latt of lattices is both reflective and coreflective in the category qLatt of quasi-lattices and homomorphisms. It is also shown that a quasi-ordered set is a quasi-lattice iff its partially ordered reflection is a lattice.

• Kyungpook Mathematical Journal
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• v.2 no.1
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• pp.17-22
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• 1959

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.557-569
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• 2015

We dene a fuzzy lattice as a fuzzy relation, develop some basic properties of the fuzzy lattice, show that the operations of join and meet in fuzzy lattices are isotone and associative, characterize a fuzzy lattice by its level set, and show that the direct product of two fuzzy lattices is a fuzzy lattice.