The Period Index Of Lattice Matrices

In this paper, an exact upper bound of period for fuzzy matrices is given and conditions that the lattice satisfied when the period for lattice matrices is [n] are studied.At first, concepts of fuzzy matrices are given, and then the paper briefly reviews the previous researches in relative fields. On these bases, we study the period for fuzzy matrices using the decomposition theorem and graph-theoretical approach, so the upper bound is given. As the composition is max? min and the interval is [0, 1] of the previous researches, we extend to Algebra System-lattice, on the divisibility lattice, lattice matrix can be constructed of which period is [n].In order to study this kind of lattice, the definition of dimension of lattice is given. we discuss the constructor of the lattice when the period for lattice matrix is [n].The results presented could be regarded as development of the previous research on fuzzy matrices. And these problems are basically resolved for fuzzy matrices applying to the fields of nerve network.