“…In particular, for the description of the behaviour of fuzzy systems, whose states are expressed using fuzzy values taken from the real interval 0; 1 or an arbitrary distributive lattice, the powers of lattice matrices are of special importance. Among the structures, over which the powers of matrices are computed, are max-addition (linear systems with synchronization [3,11,24,39,45]) max-multiplication [12,13], max-min (fuzzy systems, [9,16,17,18,20,35,36,53]), and their generalizations to max-t-norm [14,15] and to general sup-inf in a distributive lattice [52]. Results include proving convergence for special types of matrices [16,29,53], proving upper bounds [36] or computing the length of the oscillation period of the matrix power sequence [20], estimating its exponent, investigating connections between power sequence and eigenvectors [8,51], etc.…”