The periodicity of square fuzzy matrices based on minimal strong components (Q1602908)

The index and period of square matrices over the lattice \(([0,1],\max,\min)\) were intensively examined [cf. e.g. \textit{K. Cechlárová}, Linear Algebra Appl. 128, 35-50 (1990; Zbl 0704.15003); \textit{J. Li}, Fuzzy Sets Syst. 48, No. 3, 365-369 (1992; Zbl 0760.15012); \textit{K. Nachtigall}, Math. Methods Oper. Res. 46, No. 1, 87-102 (1997; Zbl 0885.90111); \textit{Z. Fan} and \textit{D. Liu}, Fuzzy Sets Syst. 93, No. 1, 75-85 (1998; Zbl 0918.15005); \textit{M. Molnárová}, Tatra Mt. Math. Publ. 16, No. 1, 135-141 (1999; Zbl 0949.05053)]. Here known results on the dependence between indices of a fuzzy relation and indices of its level sets are reproved [cf. \textit{M. Gavalec}, Tatra Mt. Math. Publ. 6, 35-46 (1995; Zbl 0860.15012); ibid. 16, No. 1, 47-60 (1999; Zbl 0949.15022); Discrete Appl. Math. 75, No. 1, 63-70 (1997; Zbl 0876.05070); ibid. 100, No. 1-2, 49-65 (2000; Zbl 0954.65093); \textit{M. Gavalec} and \textit{G. Rote}, Tatra Mt. Math. Publ. 16, No. 1, 61-79 (1999; Zbl 0952.15009)]. The authors present an algorithm for the computation of the matrix period based on a determination of strongly connected graphs.