• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.11-21
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• 2004

We discuss the n-fold implicative/fantastic filters in lattice implication algebras, which are extended notions of implicative/fantastic filters. Characterizations of n-fold implicative/fantastic filters are given. Conditions for a filter to be n-fold implicative are provided. Extension property for an n-fold fantastic filter is established.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.323-330
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• 2014

The notion of transitive filters is introduced in lattice implication algebras. A necessary and sufficient condition is derived for every filter to become a transitive filter. Some sufficient conditions are also derived for a filter to become a transitive filter. The concept of absorbent filters is introduced and their properties are studied. A set of equivalent conditions is obtained for a filter to become an absorbent filter.

• Journal of Convergence for Information Technology
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• v.9 no.5
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• pp.7-13
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• 2019

Role-based access or attribute-based access control in cloud environment or big data environment need requires a suitable mathematical structure to represent a hierarchical model. This paper define the notion of multipliers and simple multipliers of lattice implication algebras that can implement a hierarchical model of role-based or attribute-based access control, and prove every multiplier is simple multiplier. Also we research the relationship between multipliers and homomorphisms of a lattice implication algebra L, and prove that the lattice [0, u] is isomorphic to a lattice $[u^{\prime},1]$ for each $u{\in}L$ and that L is isomorphic to $[u,1]{\times}[u^{\prime},1]$ as lattice implication algebras for each $u{\in}L$ satisfying $u{\vee}u^{\prime}=1$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1483-1495
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• 2016

The notion of int-soft (implicative) filters in lattice implication algebras is introduced, and related properties are investigated. Characterizations of int-soft (implicative) filters are discussed. Conditions for an int-soft filter to be an int-soft implicative filter are provided. Extension property for int-soft implicative filters is established.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.153-163
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• 2003

The fuzzification of a positive implicative filter is considered, and some of properties are investigated. The relation among fussy filter, fuzzy n-fold implicative filter, and fuzzy n-fold positive implication filter is discussed.

• Proceedings of the Korea Contents Association Conference
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• 2018.05a
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• pp.381-382
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• 2018

격자함의 대수와 헤이팅 대수는 부울 대수를 일반화한 논리체계이며 논리적 함의(${\rightarrow}$)를 이항연사자로 갖는 대수적 체계를 갖는다. 본 논문에서는 격자함의 대수와 헤이팅 대수가 서로 다른 대수체계를 갖는다는 것을 예로 보이고, 이들의 차이점을 조사한다. 또한 격자함의 대수, 헤이팅 대수, 그리고 부울 대수의 관계를 알아본다.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.635-641
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• 2003

The notion of negative difference on a poset is introduced, and the interrelations between FI-algebras and posets with negative difference are discussed.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.207-213
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• 2002

We discuss the filter generated by an arbitrary set in fuzzy implication algebra, and consider the uniformity of a fuzzy implication algebra by using filters.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.957-967
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• 2022

Recently, Brešar's Jordan {g, h}-derivations have been investigated on triangular algebras. As a first aim of this paper, we extend this study to an interesting general context. Namely, we introduce the notion of Jordan 𝒢_n-derivations, with n ≥ 2, which is a natural generalization of Jordan {g, h}-derivations. Then, we study this notion on path algebras. We prove that, when n > 2, every Jordan 𝒢_n-derivation on a path algebra is a {g, h}-derivation. However, when n = 2, we give an example showing that this implication does not hold true in general. So, we characterize when it holds. As a second aim, we give a positive answer to a variant of Lvov-Kaplansky conjecture on path algebras. Namely, we show that the set of values of a multi-linear polynomial on a path algebra KE is either {0}, KE or the space spanned by paths of a length greater than or equal to 1.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1119-1131
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• 2019

In this paper, we introduce the notion of generalized f-derivation of lattice implication algebra and investigate some related properties. Also, we prove that if D is a generalized f-derivation associated with an f-derivation d of L, then D(x → y) = f(x) → D(y) for all x, y ∈ L.