• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.587-591
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• 2009

The structure of a TL-subgroup can be understood from the representations of the TL-sub group as meets of TL-subgroups containing the TL-subgroup. Indeed, the structure of the meet of TL-subgroups can easily be obtained from the structures of the TL-subgroups and the structures of the TL-subgroups may be more simple than the structure of the meet. In this paper, we discuss meet-reducibility of TL-subgroups.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.105-116
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• 2021

Information systems and decision rules with imprecision and uncertainty in data analysis are studied in complete residuated lattices. In this paper, we introduce the notions of distance spaces, Alexandrov pretopology (precotopology) and join-meet (meet-join) operators in complete co-residuated lattices. We investigate their relations and properties. Moreover, we give their examples.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.401-409
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• 2007

This paper is sequel to [3]. In this paper, we discuss some properties of an algebraic meet-continuous lattice and study a complete lattice which can be embedded into an algebraic meet-continuous lattice.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.553-565
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• 2014

In this paper, we investigate the properties of Alexandrov fuzzy topologies and join-meet approximation operators. We study fuzzy preorder, Alexandrov topologies join-meet approximation operators induced by Alexandrov fuzzy topologies.We give their examples.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.499-510
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• 2024

We introduce the concepts of right join-dense, right meet-dense, left join-dense and left meet-dense induced by bi-partially ordered sets on complete generalized residuated lattices. We investigate properties of these concepts and give an example related to them.

• East Asian mathematical journal
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• v.16 no.1
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• pp.33-48
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• 2000

In this paper, for any ring R with an identity, in order to study prime ideals of the endomorphism ring $End_R$(M) of left R-module $_RM$, meet-prime submodules, prime radical, sum-prime submodules and the prime socle of a module are defined. Some relations of the prime radical, the prime socle of a module and the prime radical of the endomorphism ring of a module are investigated. It is revealed that meet-prime(or sum-prime) modules and semi-meet-prime(or semi-sum-prime) modules have their prime, semi-prime endomorphism rings, respectively.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.79-89
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• 2020

We introduce the concepts of fuzzy join-complete lattices and Alexandrov L-pre-topologies in complete residuated lattices. We investigate the properties of fuzzy join-complete lattices on Alexandrov L-pre-topologies and fuzzy meet-complete lattices on Alexandrov L-pre-cotopologies. Moreover, we give their examples.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.1
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• pp.133-138
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• 2009

We investigate the properties of meet preserving maps on strictly two-sided, commutative biquantales. Using the properties of meet preserving maps, we induce the Zadeh image and pre image operators.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.19-29
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• 2022

Information systems and decision rules with imprecision and uncertainty in data analysis are studied in complete residuated lattices. In this paper, we introduce the notions of Alexandrov pretopology (precotopology) and join-meet (meet-join) operators in complete co-residuated lattices. Moreover, their properties and examples are investigated.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.33 no.5
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• pp.709-719
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• 2023

Recently, Post-Quantum Cryptography (PQC), which is secure against attacks using quantum computers, has been actively studied. In 2022, the KpqC competition, a competition for domestic PQC standardization, was launched, and a total of 16 candidate algorithms were received, and the first round is underway. In this paper, we apply Alexander May's Meet-LWE attack to TiGER, a lattice-based key encapsulation mechanism that is a candidate for the first round of the KpqC competition, and analyze its concrete attack complexity. The computational results of applying the Meet-LWE attack to each of the proposed parameters of TiGER show that the proposed TiGER192 parameter, which targets 192-bit quantum security, actually achieves 170-bit classical security. In addition, we propose a parameter setting to increase the attack complexity against the Meet-LWE attack.