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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Rank and perimeter preserver of rank-1 matrices over max algebra

100%
Song S.-Z., Kang K.-T.
Discussiones Mathematicae - General Algebra and Applications
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2003
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tom 23
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nr 2
125-137
EN
For a rank-1 matrix $A = a ⊗ b^{t}$ over max algebra, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over max algebra. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices if and only if it has the form T(A) = U ⊗ A ⊗ V, or $T(A) = U ⊗ A^{t} ⊗ V$ with some monomial matrices U and V.
2
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Zero-term rank preservers of integer matrices

100%
Song S.-Z., Jun Y.-B.
Discussiones Mathematicae - General Algebra and Applications
|
2006
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tom 26
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nr 2
155-161
EN
The zero-term rank of a matrix is the minimum number of lines (row or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve the zero-term rank of the m × n integer matrices. That is, a linear operator T preserves the zero-term rank if and only if it has the form T(A)=P(A ∘ B)Q, where P, Q are permutation matrices and A ∘ B is the Schur product with B whose entries are all nonzero integers.
3
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Maximal column rank preservers of fuzzy matrices

100%
Song S.-Z., Park S.-R.
Discussiones Mathematicae - General Algebra and Applications
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2001
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tom 21
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nr 2
207-218
EN
This paper concerns two notions of rank of fuzzy matrices: maximal column rank and column rank. We investigate the difference of them. We also characterize the linear operators which preserve the maximal column rank of fuzzy matrices. That is, a linear operator T preserves maximal column rank if and only if it has the form T(X) = UXV with some invertible fuzzy matrices U and V.
4
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Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras

100%
Jun Y. B., Song S.-Z.
Bulletin of the Section of Logic
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2020
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tom 49
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nr 1
EN
Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are discussed. Using the notion of Inf-hesitant fuzzy (p-) ideals, a characterization of a p-semisimple BCI-algebra is provided. Extension properties for an Inf-hesitant fuzzy p-ideal is established.
5
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Int-Soft Ideals of Pseudo MV-Algebras

81%
Jun Y. B., Song S.-Z., Bordbar H.
Bulletin of the Section of Logic
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2018
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tom 47
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nr 1
EN
The notion of (implicative) int-soft ideal in a pseudo MV -algebra is introduced, and related properties are investigated. Conditions for a soft set to be an int-soft ideal are provided. Characterizations of (implicative) int-soft ideal are considered. The extension property for implicative int-soft ideal is established.
6
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Length Neutrosophic Subalgebras of BCK=BCI-Algebras

81%
Jun Y. B., Khan M., Smarandache F., Song S.-Z.
Bulletin of the Section of Logic
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2020
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tom 49
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nr 4
377-400
EN
Given i, j, k ∈ {1,2,3,4}, the notion of (i, j, k)-length neutrosophic subalgebras in BCK=BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided.
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Linear operators preserving maximal column ranks of nonbinary boolean matrices

71%
Song S.-Z., Yang S.-D., Hong S.-M., Jun Y.-B., Kim S.-J.
Discussiones Mathematicae - General Algebra and Applications
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2000
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tom 20
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nr 2
255-265
EN
The maximal column rank of an m by n matrix is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over a nonbinary Boolean algebra. We also characterize the linear operators which preserve the maximal column ranks of matrices over nonbinary Boolean algebra.
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