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Zero-term rank preservers of integer matrices

Seok-Zun SongYoung-Bae Jun — 2006

Discussiones Mathematicae - General Algebra and Applications

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.

Maximal column rank preservers of fuzzy matrices

Seok-Zun SongSoo-Roh Park — 2001

Discussiones Mathematicae - General Algebra and Applications

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.

Rank and perimeter preserver of rank-1 matrices over max algebra

Seok-Zun SongKyung-Tae Kang — 2003

Discussiones Mathematicae - General Algebra and Applications

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.

Linear maps that strongly preserve regular matrices over the Boolean algebra

Kyung-Tae KangSeok-Zun Song — 2011

Czechoslovak Mathematical Journal

The set of all m × n Boolean matrices is denoted by 𝕄 m , n . We call a matrix A 𝕄 m , n regular if there is a matrix G 𝕄 n , m such that A G A = A . In this paper, we study the problem of characterizing linear operators on 𝕄 m , n that strongly preserve regular matrices. Consequently, we obtain that if min { m , n } 2 , then all operators on 𝕄 m , n strongly preserve regular matrices, and if min { m , n } 3 , then an operator T on 𝕄 m , n strongly preserves regular matrices if and only if there are invertible matrices U and V such that T ( X ) = U X V for all X 𝕄 m , n , or m = n and T ( X ) = U X T V for all X 𝕄 n .

Linear operators that preserve Boolean rank of Boolean matrices

LeRoy B. BeasleySeok-Zun Song — 2013

Czechoslovak Mathematical Journal

The Boolean rank of a nonzero m × n Boolean matrix A is the minimum number k such that there exist an m × k Boolean matrix B and a k × n Boolean matrix C such that A = B C . In the previous research L. B. Beasley and N. J. Pullman obtained that a linear operator preserves Boolean rank if and only if it preserves Boolean ranks 1 and 2 . In this paper we extend this characterizations of linear operators that preserve the Boolean ranks of Boolean matrices. That is, we obtain that a linear operator preserves Boolean rank...

Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras

Young Bae JunSeok-Zun Song — 2020

Bulletin of the Section of Logic

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...

Perimeter preserver of matrices over semifields

Seok-Zun SongKyung-Tae KangYoung Bae Jun — 2006

Czechoslovak Mathematical Journal

For a rank- 1 matrix A = 𝐚 𝐛 t , 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 semifields. That is, a linear operator T preserves the rank and perimeter of rank- 1 matrices over semifields if and only if it has the form T ( A ) = U A V , or T ( A ) = U A t V with some invertible matrices U and V.

Linear operators that preserve graphical properties of matrices: isolation numbers

LeRoy B. BeasleySeok-Zun SongYoung Bae Jun — 2014

Czechoslovak Mathematical Journal

Let A be a Boolean { 0 , 1 } matrix. The isolation number of A is the maximum number of ones in A such that no two are in any row or any column (that is they are independent), and no two are in a 2 × 2 submatrix of all ones. The isolation number of A is a lower bound on the Boolean rank of A . A linear operator on the set of m × n Boolean matrices is a mapping which is additive and maps the zero matrix, O , to itself. A mapping strongly preserves a set, S , if it maps the set S into the set S and the complement of...

Possible isolation number of a matrix over nonnegative integers

LeRoy B. BeasleyYoung Bae JunSeok-Zun Song — 2018

Czechoslovak Mathematical Journal

Let + be the semiring of all nonnegative integers and A an m × n matrix over + . The rank of A is the smallest k such that A can be factored as an m × k matrix times a k × n matrix. The isolation number of A is the maximum number of nonzero entries in A such that no two are in any row or any column, and no two are in a 2 × 2 submatrix of all nonzero entries. We have that the isolation number of A is a lower bound of the rank of A . For A with isolation number k , we investigate the possible values of the rank of A ...

Perimeter preservers of nonnegative integer matrices

Seok-Zun SongKyung-Tae KangSucheol Yi — 2004

Commentationes Mathematicae Universitatis Carolinae

We investigate the perimeter of nonnegative integer matrices. We also characterize the linear operators which preserve the rank and perimeter of nonnegative integer matrices. 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 ) = P ( A B ) Q , or T ( A ) = P ( A t B ) Q with appropriate permutation matrices P and Q and positive integer matrix B , where denotes Hadamard product.

Int-Soft Ideals of Pseudo MV-Algebras

Young Bae JunSeok-Zun SongHashem Bordbar — 2018

Bulletin of the Section of Logic

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.

Length Neutrosophic Subalgebras of BCK=BCI-Algebras

Young Bae JunMadad KhanFlorentin SmarandacheSeok-Zun Song — 2020

Bulletin of the Section of Logic

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.

Commutative Energetic Subsets of BCK-Algebras

Young Bae JunEun Hwan RohSeok Zun Song — 2016

Bulletin of the Section of Logic

The notions of a C-energetic subset and (anti) permeable C-value in BCK-algebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an (anti) permeable C-value are provided. Also conditions for a subset to be a C-energetic subset are discussed. We decompose BCK-algebra by a partition which consists of a C-energetic subset and a commutative ideal.

Linear operators preserving maximal column ranks of nonbinary boolean matrices

Seok-Zun SongSung-Dae YangSung-Min HongYoung-Bae JunSeon-Jeong Kim — 2000

Discussiones Mathematicae - General Algebra and Applications

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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