The purpose of this paper is to put forward the basics results of complex fuzzy sets (CFSs) such ... more The purpose of this paper is to put forward the basics results of complex fuzzy sets (CFSs) such as union, intersection, complement, product into complex neutrosophic sets because as the CFSs and complex intuitionistics sets does give the erroneous and inconvenient information about uncertainty and periodicity and also there are results related to different norms. Moreover we give some results about the distance measures of complex neutrosophic sets and define some notions.
The notion of a uni-soft commutative ideal with thresholds is introduced, and related properties ... more The notion of a uni-soft commutative ideal with thresholds is introduced, and related properties are investigated. Relations between a uni-soft ideal with thresholds and a uni-soft commutative ideal with thresholds are discussed. Conditions for a uni- soft ideal with thresholds to be a uni-soft commutative ideal with the same thresholds are provided. Characterizations of a uni-soft commutative ideal with thresholds are established
Journal of applied mathematics & informatics, 2008
We construct the sets of Boolean matrix pairs, which are naturally occurred at the extreme cases ... more We construct the sets of Boolean matrix pairs, which are naturally occurred at the extreme cases for the Boolean rank inequalities relative to the sums and difference of two Boolean matrices or compared between their Boolean ranks and their real ranks. For these sets, we consider the linear operators that preserve them. We characterize those linear operators as T(X) = PXQ or with appropriate invertible Boolean matrices P and Q.
Let $\Omega_n$ be the polyhedron of $n \times n$ doubly stochastic matrices, that is, nonnegative... more Let $\Omega_n$ be the polyhedron of $n \times n$ doubly stochastic matrices, that is, nonnegative matrices whose row and column sums are all equal to 1. The permanent of a $n \times n$ matrix $A = [a_{ij}]$ is defined by $$ per(A) = \sum_{\sigma}^ a_{1\sigma(a)} \cdots a_{n\sigma(n)} $$ where $\sigma$ runs over all permutations of ${1, 2, \ldots, n}$.
The permanent function on certain faces of the polytope of doubly stochastic matrices are studied... more The permanent function on certain faces of the polytope of doubly stochastic matrices are studied. These faces are shown to be barycentric, and the minimum values of permanent are determined.
Let $M_{m,n}$ be the set of all $m \times n$ real matrices. For a matrix $A = [a_{ij}] \in M_{m,n... more Let $M_{m,n}$ be the set of all $m \times n$ real matrices. For a matrix $A = [a_{ij}] \in M_{m,n}$, the sign of $a_{ij}$ is defined by $$ sgn a_{ij} = { 0 if a_{ij} = 0, { +1 if a_{ij} > 0, { -1 if a_{ij}
Let S be an antinegative semiring. The rank of an m × n matrix B over S is the minimal integer r ... more Let S be an antinegative semiring. The rank of an m × n matrix B over S is the minimal integer r such that B is a product of an m × r matrix and an r × n matrix. The isolation number of B is the maximal number of nonzero entries in the matrix such that no two entries are in the same column, in the same row, and in a submatrix of B of the form b i , j b i , l b k , j b k , l with nonzero entries. We know that the isolation number of B is not greater than the rank of it. Thus, we investigate the upper bound of the rank of B and the rank of its support for the given matrix B with isolation number h over antinegative semirings.
Abstract Let M n ( B ) denote the set of n × n ( 0 , 1 ) -matrices with Boolean arithmetic. The s... more Abstract Let M n ( B ) denote the set of n × n ( 0 , 1 ) -matrices with Boolean arithmetic. The set of primitive matrices of exponent k, denoted E k , is the set of matrices such that A k has all nonzero entries and A j has zero entries for all j k . For 3 ≤ k ≤ n , we characterize those linear operators that map E k to E k and E k − 1 to E k − 1 . We also characterize those linear operators that strongly preserve E k for 3 ≤ k ≤ n , that is, that map E k to E k and the complement of E k to the complement of E k .
The purpose of this paper is to put forward the basics results of complex fuzzy sets (CFSs) such ... more The purpose of this paper is to put forward the basics results of complex fuzzy sets (CFSs) such as union, intersection, complement, product into complex neutrosophic sets because as the CFSs and complex intuitionistics sets does give the erroneous and inconvenient information about uncertainty and periodicity and also there are results related to different norms. Moreover we give some results about the distance measures of complex neutrosophic sets and define some notions.
The notion of a uni-soft commutative ideal with thresholds is introduced, and related properties ... more The notion of a uni-soft commutative ideal with thresholds is introduced, and related properties are investigated. Relations between a uni-soft ideal with thresholds and a uni-soft commutative ideal with thresholds are discussed. Conditions for a uni- soft ideal with thresholds to be a uni-soft commutative ideal with the same thresholds are provided. Characterizations of a uni-soft commutative ideal with thresholds are established
Journal of applied mathematics & informatics, 2008
We construct the sets of Boolean matrix pairs, which are naturally occurred at the extreme cases ... more We construct the sets of Boolean matrix pairs, which are naturally occurred at the extreme cases for the Boolean rank inequalities relative to the sums and difference of two Boolean matrices or compared between their Boolean ranks and their real ranks. For these sets, we consider the linear operators that preserve them. We characterize those linear operators as T(X) = PXQ or with appropriate invertible Boolean matrices P and Q.
Let $\Omega_n$ be the polyhedron of $n \times n$ doubly stochastic matrices, that is, nonnegative... more Let $\Omega_n$ be the polyhedron of $n \times n$ doubly stochastic matrices, that is, nonnegative matrices whose row and column sums are all equal to 1. The permanent of a $n \times n$ matrix $A = [a_{ij}]$ is defined by $$ per(A) = \sum_{\sigma}^ a_{1\sigma(a)} \cdots a_{n\sigma(n)} $$ where $\sigma$ runs over all permutations of ${1, 2, \ldots, n}$.
The permanent function on certain faces of the polytope of doubly stochastic matrices are studied... more The permanent function on certain faces of the polytope of doubly stochastic matrices are studied. These faces are shown to be barycentric, and the minimum values of permanent are determined.
Let $M_{m,n}$ be the set of all $m \times n$ real matrices. For a matrix $A = [a_{ij}] \in M_{m,n... more Let $M_{m,n}$ be the set of all $m \times n$ real matrices. For a matrix $A = [a_{ij}] \in M_{m,n}$, the sign of $a_{ij}$ is defined by $$ sgn a_{ij} = { 0 if a_{ij} = 0, { +1 if a_{ij} > 0, { -1 if a_{ij}
Let S be an antinegative semiring. The rank of an m × n matrix B over S is the minimal integer r ... more Let S be an antinegative semiring. The rank of an m × n matrix B over S is the minimal integer r such that B is a product of an m × r matrix and an r × n matrix. The isolation number of B is the maximal number of nonzero entries in the matrix such that no two entries are in the same column, in the same row, and in a submatrix of B of the form b i , j b i , l b k , j b k , l with nonzero entries. We know that the isolation number of B is not greater than the rank of it. Thus, we investigate the upper bound of the rank of B and the rank of its support for the given matrix B with isolation number h over antinegative semirings.
Abstract Let M n ( B ) denote the set of n × n ( 0 , 1 ) -matrices with Boolean arithmetic. The s... more Abstract Let M n ( B ) denote the set of n × n ( 0 , 1 ) -matrices with Boolean arithmetic. The set of primitive matrices of exponent k, denoted E k , is the set of matrices such that A k has all nonzero entries and A j has zero entries for all j k . For 3 ≤ k ≤ n , we characterize those linear operators that map E k to E k and E k − 1 to E k − 1 . We also characterize those linear operators that strongly preserve E k for 3 ≤ k ≤ n , that is, that map E k to E k and the complement of E k to the complement of E k .
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