The Convergence Of Two Kinds Of Fuzzy Transitive Matrices And The Solution Sets Of Max-algebraic Linear Equation Systems

This paper tries to investigate the convergence of two kinds of fuzzy transitive matrices and the representations of solutions of max-algebraic linear systems. Firstly, we define sz-fuzzy transitive matrix and prove that An=A2n=A3n=…. Secondly, we define za-fuzzy transitive matrix and proved all the elements of A(n-1)2+1 are nonzero. Next, we gave some sufficient conditions for za-fuzzy transitive matrix to be convergent or oscillatory. Then we deals with the max-algebraic linear equation system A(?)x=b. As in the conventional linear algebra such a linear system may have none, exactly one or infinitely many solutions. If the max-algebraic linear equation system has only one solution,then the Cramer's rule is given as an analogue of the classical linear algebra. When the number of solutions is infinite, the existence of a minimal solution is shown and the formulas of minimal solutions are given. Furthermore, it is proved that every solution can be expressed as a linear combination of a respective minimal solution and some special vectors.