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-1is equal to the adjoint matrix of A if the matrix A satisfies A≥In. © 2003 Elsevier B.V. All rights reserved.
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