• 한국IT서비스학회지
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• 제5권1호
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• pp.191-198
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• 2006

Boolean matrices have been successfully used in various areas, and many researches have been performed on them. However, almost all the researches focus on the efficient multiplication of two boolean matrices and no research has been shown to deal with the multiplication of all boolean matrices and their consecutive multiplications. The paper suggests a mathematical theory that enables the efficient consecutive multiplications of all $l{\times}n,\;n{\times}m,\;and\;m{\times}k$ boolean matrices, and discusses its computational complexity and the execution results of the consecutive multiplication algorithm based on the theory.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.531-543
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• 2022

The article proposed a new type of data relationship: Positive Boolean dependencies by groups on block and slice in the database model of block form, where instead of considering value pairs, we consider a group of p values (p ≥ 2). From this new concept, the article stated and demonstrated the equivalence of the three types of deduction, namely: deduction by logic, deduction by block with groups, deduction by block has no more than p elements with groups. Operations on blocks or slices performed for index attributes on blocks, the properties related to this new concept as theorem the equivalen of the three types of deduction, closure of set positive Boolean dependencies by groups and representation and tight representation set of positive Boolean dependencies by groups when the block degenerated into relation are true in the relational database model and also stated and proven in this paper.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.349-356
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• 1998

We give the new formulas counting the total number of all lines planes and tetrahedrons in the n-dimensional Boolean space.

• 대한수학회보
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• 제42권3호
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• pp.501-507
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• 2005

A Boolean matrix with rank 1 is factored as a left factor and a right factor. The perimeter of a rank-1 Boolean matrix is defined as the number of nonzero entries in the left factor and the right factor of the given matrix. We obtain new characterizations of rank preservers, in terms of perimeter, of Boolean matrices.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권2호
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• pp.71-78
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• 2000

Any Hausdoroff space on a set which has at least two points a regular closed Boolean algebra different from the indiscrete regular closed Boolean algebra as indiscrete space. The Sierpinski space and the space with finite complement topology on any infinite set etc. do the same. However, there is $T_{0}$ space which does the same with Hausdorpff space as above. The regular closed Boolean algebra in a topological space is isomorphic to that algebra in the space with its open extension topology.

• 호남수학학술지
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• 제36권4호
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• pp.813-830
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• 2014

The notions of a (Boolean, prime, ultra, good) hesitant fuzzy filter and a hesitant fuzzy MV -filter of an MTL-algebras are introduced, and their relations are investigated. Characterizations of a (Boolean, ultra) hesitant fuzzy filter are discussed. Conditions for a hesitant fuzzy set to be a hesitant fuzzy filter, and for a hesitant fuzzy filter to be a Boolean hesitant fuzzy filter are provided.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.475-484
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• 2004

In general, a matrix A is idempotent if $A^2$ = A. The idempotent matrices play an important role in the matrix theory and some properties of the Boolean matrices are examined. Using the upper diagonal completion process, we give the characterization of the Boolean idempotent matrices in modified Frobenius normal form.

• 대한수학회지
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• 제43권1호
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• pp.77-86
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• 2006

We consider the set of commuting pairs of matrices and their preservers over binary Boolean algebra, chain semiring and general Boolean algebra. We characterize those linear operators that preserve the set of commuting pairs of matrices over a general Boolean algebra and a chain semiring.

• 대한수학회지
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• 제6권2호
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• pp.75-80
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• 1969

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권1호
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• pp.19-26
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• 2000

The purpose of the paper is to show that in the Fraenkel-Mostowski topos, the category of the Boolean algebras has enough injectives.