• 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.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.341-355
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• 2003

The fuzzification of ${\bigotimes}-closed$ set is considered, and its basic properties we investigated. Characterizations of fuazzy ${\bigotimes}-closed$ set we given. Using a collection of ${\bigotimes}-closed$ sets with additional conditions, a fuzzy ${\bigotimes}-closed$ set is stated. The theory of fuzzy topological ${\bigotimes}-closed$ sets is discussed.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.227-233
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• 2006

A condition for a lattice filter to be a filter is given. Using the prime filter theorem which is discussed in [2], topological aspects on filters are discussed.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.137-155
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• 2004

Fuzzification of a fantastic filter in a lattice implication algebra is considered. Relations among a fuzzy filter, a fuzzy fantastic filter, and fuzzy positive implicative filter are stated. Conditions for a fuzzy filter to be a fuzzy fantastic filter are given. Using the notion of level set, a characterization of a fuzzy fantastic filter is considered. Extension property for fuzzy fantastic filters is established. The notion of normal/maximal fuzzy fantastic filters and complete fuzzy fantastic filters is introduced, and some related properties are investigated.

• Journal of Convergence for Information Technology
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• v.7 no.3
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• pp.65-71
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• 2017

The quantum logic was introduced by G. Birkhoff and 1. von Neumann in order to study projections of a Hilbert space for a formulation of quantum mechanics, and Husimi proposed orthomodular law and orthomodular lattices to complement the quantum logic. Abott introduced orthoimplication algebras and its properties to investigate an implication of orthomodular lattice. The commuting relation is an important property on orthomodular lattice which is related with the distributive law and the modular law, etc. In this paper, we define a binary operation on orthoimplication algebra and the greatest lower bound by using this operation and research some properties of this operation. Also we define a homomorphism and characterize the commuting relation of orthoimplication algebra by the homomorphism.