• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.619-627
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• 2014

Let $\mathcal{M}(S)$ denote the set of all $m{\times}n$ matrices over a semiring S. For $A{\in}\mathcal{M}(S)$, zero-term rank of A is the minimal number of lines (rows or columns) needed to cover all zero entries in A. In [5], the authors obtained that a linear operator on $\mathcal{M}(S)$ preserves zero-term rank if and only if it preserves zero-term ranks 0 and 1. In this paper, we obtain new characterizations of linear operators on $\mathcal{M}(S)$ that preserve zero-term rank. Consequently we obtain that a linear operator on $\mathcal{M}(S)$ preserves zero-term rank if and only if it preserves two consecutive zero-term ranks k and k + 1, where $0{\leq}k{\leq}min\{m,n\}-1$ if and only if it strongly preserves zero-term rank h, where $1{\leq}h{\leq}min\{m,n\}$.

• 대한수학회지
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• 제50권1호
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• pp.127-136
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• 2013

The term rank of a matrix A is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we obtain a characterization of linear transformations that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear transformation T from a matrix space into another matrix space over antinegative semirings preserves term rank if and only if T preserves any two term ranks $k$ and $l$.

• 대한수학회지
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• 제42권2호
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• pp.223-241
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• 2005

Inequalities on the rank of the sum and the product of two matrices over semirings are surveyed. Preferences are given to the factor rank, row and column ranks, term rank, and zero-term rank of matrices over antinegative semirings.

• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.465-472
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• 2010

In this paper, we consider two extreme sets of zero-term rank sum of fuzzy matrix pairs: $$\cal{z}_1(\cal{F})=\{(X,Y){\in}\cal{M}_{m,n}(\cal{F})^2{\mid}z(X+Y)=min\{z(X),z(Y)\}\};$$ $$\cal{z}_2(\cal{F})=\{(X,Y){\in}\cal{M}_{m,n}(\cal{F})^2{\mid}z(X+Y)=0\}$$. We characterize the linear operators that preserve these two extreme sets of zero-term rank sum of fuzzy matrix pairs.

• 대한수학회지
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• 제51권1호
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• pp.113-123
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• 2014

The term rank of a matrix A over a semiring $\mathcal{S}$ is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.

• 대한수학회지
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• 제36권6호
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• pp.1181-1190
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• 1999

Zero-term rank of a matrix is the minimum number of lines (rows or columns) needed to cover all the zero entries of the given matrix. We characterized the linear operators that preserve zero-term rank of the m×n matrices over binary Boolean algebra.

• 호남수학학술지
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• 제33권3호
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• pp.301-310
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• 2011

In this paper, we construct the sets of fuzzy matrix pairs. These sets are naturally occurred at the extreme cases for the zero-term rank inequalities derived from the multiplication of fuzzy matrix pairs. We characterize the linear operators that preserve these extreme sets of fuzzy matrix pairs.

• 대한수학회보
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• 제45권2호
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• pp.355-363
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• 2008

For a Boolean rank 1 matrix $A=ab^t$, we define the perimeter of A as the number of nonzero entries in both a and b. The perimeter of an $m{\times}n$ Boolean matrix A is the minimum of the perimeters of the rank-1 decompositions of A. In this article we characterize the linear operators that preserve the perimeters of Boolean matrices.

• 정보관리학회지
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• 제16권1호
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• pp.7-30
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• 1999

본 연구의 목적은 문헌의 구조에 근거한 비통계적 용어 가중치 기법을 사용함으로써 기존의 불 논리 검색 시스템에 용이하게 적용될 수 있는 P-norm 검색의 효과적인 문헌 순위화 기법을 찾아내는 데 있다. 또한 용어 가중치를 사용하여 검색 된 문헌들을 대상으로 상위문헌 몇 개와 유사도가 높은 문헌의 순위를 높여주는 순위 조정 과정을 추가하여 검색성능을 더욱 향상시킬 수 있도록 하였다. 비통계적 가중치 기법으로는 필드 가중치와 근접거리 가중치를 사용하였고, 통계적 기법을 이용한 검색도 실시하여 검색성능을 비교하였다. 순위 조정 실험에서는 문헌간의 유사도 측정의 기준에 되는 상위문헌수를 1건으로 사용하는 경우부터 5건으로 사용하는 경우까지 5번에 걸친 실험을 실시하였다. 실험결과 비통계적 가중치 기법은 통계적 기법보다 더욱 효과가 있었고, 순위 조정 과정은 전반적으로 검색효율이 크게 향상되는 것으로 밝혀졌다.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.627-634
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• 2001

Under contamination, Bahadur representations with a strong remainder term are derived for random central order statistics with a prescribed limiting rank, and asymptotic normalities for these statistics of truncated and contaminated data are proved, with a suitable limiting rank. From these results, an application to the fixed-width confidence interval problem is available.