On the powers of matrices in bottleneck/fuzzy algebra
The author examines max-min powers of square matrices over the semiring (\([0,1]\),max,min) [cf. \textit{M. G. Thomason}, J. Math. Analysis Appl. 57, 476-480 (1977; Zbl 0345.15007)]. She characterizes stable matrices (with convergent power sequence) by properties of the associated graph and by properties of iterative sequences of the induced quasilinear transformation \(y=Ax\). As special cases, upper-triangular and circulant matrices are considered. Results of the paper are generalized by \textit{M. Gavalec} [Periodicity of matrices and orbits in fuzzy algebra, Tatra Mt. Math. Publ. 6, 35-46 (1995; Zbl 0860.15012)].
scientific article; zbMATH DE number 951793