Generalized fuzzy matrices are considered as matrices over a special type of semiring which is called an incline, and their transitive closure, powers, determinant and adjoint matrices are studied. An expression for the transitive closure of a matrix A as a sum of its powers and some sufficient conditions for powers of a matrix to converge are given. If the incline is commutative, a sufficient condition for nilpotency of a matrix is obtained, namely the determinants of the principal submatrices of the matrix are all equal to zero element. In addition, it is proved that An-1 is equal to the adjoint matrix of A if the matrix A satisfies A≥In. © 2003 Elsevier B.V. All rights reserved.
CITATION STYLE
Duan, J. S. (2004). The transitive closure, convergence of powers and adjoint of generalized fuzzy matrices. Fuzzy Sets and Systems, 145(2), 301–311. https://doi.org/10.1016/S0165-0114(03)00165-9
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