Fuzzy ideals in BE-algebras.
Linear preservers of regular matrices over general Boolean algebras.
Zero-term rank preservers of integer matrices
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
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
For a rank-1 matrix 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 with some monomial matrices U and V.
Superior subalgebras and ideals of BCK/BCI-algebras
The notions of superior subalgebras and (commutative) superior ideals are introduced, and their relations and related properties are investigated. Conditions for a superior ideal to be commutative are provided.
Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras
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...
Linear operators that preserve Boolean rank of Boolean matrices
The Boolean rank of a nonzero Boolean matrix is the minimum number such that there exist an Boolean matrix and a Boolean matrix such that . 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 and . 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...
Linear maps that strongly preserve regular matrices over the Boolean algebra
The set of all Boolean matrices is denoted by . We call a matrix regular if there is a matrix such that . In this paper, we study the problem of characterizing linear operators on that strongly preserve regular matrices. Consequently, we obtain that if , then all operators on strongly preserve regular matrices, and if , then an operator on strongly preserves regular matrices if and only if there are invertible matrices and such that for all , or and for all .
Extreme preservers of maximal column rank inequalities of matrix sums over semirings
We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme properties with respect to maximal column rank inequalities of matrix sums over semirings.
A conjecture on minimum permanents
We consider the permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square -matrices containing the identity submatrix. We show that a conjecture in K. Pula, S. Z. Song, I. M. Wanless (2011), is true for some cases by determining the minimum permanent on some faces of the polytope of doubly stochastic matrices.
Linear operators that preserve graphical properties of matrices: isolation numbers
Let be a Boolean matrix. The isolation number of is the maximum number of ones in such that no two are in any row or any column (that is they are independent), and no two are in a submatrix of all ones. The isolation number of is a lower bound on the Boolean rank of . A linear operator on the set of Boolean matrices is a mapping which is additive and maps the zero matrix, , to itself. A mapping strongly preserves a set, , if it maps the set into the set and the complement of...
Int-Soft Ideals of Pseudo MV-Algebras
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
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
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.
Perimeter preserver of matrices over semifields
For a rank- matrix , we define the perimeter of as the number of nonzero entries in both and . We characterize the linear operators which preserve the rank and perimeter of rank- matrices over semifields. That is, a linear operator preserves the rank and perimeter of rank- matrices over semifields if and only if it has the form , or with some invertible matrices U and V.
Invertible commutativity preservers of matrices over max algebra
The max algebra consists of the nonnegative real numbers equipped with two binary operations, maximization and multiplication. We characterize the invertible linear operators that preserve the set of commuting pairs of matrices over a subalgebra of max algebra.
Perimeter preservers of nonnegative integer matrices
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 preserves the rank and perimeter of rank- matrices if and only if it has the form , or with appropriate permutation matrices and and positive integer matrix , where denotes Hadamard product.
Possible isolation number of a matrix over nonnegative integers
Let be the semiring of all nonnegative integers and an matrix over . The rank of is the smallest such that can be factored as an matrix times a matrix. The isolation number of is the maximum number of nonzero entries in such that no two are in any row or any column, and no two are in a submatrix of all nonzero entries. We have that the isolation number of is a lower bound of the rank of . For with isolation number , we investigate the possible values of the rank of ...
Zero-term ranks of real matrices and their preservers
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 characterize the linear operators that preserve zero-term rank of the real matrices. We also obtain combinatorial equivalent condition for the zero-term rank of a real matrix.
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