A note on the power sequence of a fuzzy matrix
The author examines the min-max product of matrices over the semiring ([0, 1], min, max) [cf. \textit{M. Z. Ragab} and \textit{F. G. Emam}, Fuzzy Sets Syst. 75, No. 1, 83-92 (1995; Zbl 0860.15013)] as a dual of the usually used max-min product. This provides dual versions of known results. Next, the convergence of the matrix powers sequence under sup-t-norm composition is characterized. However, the author changes the well-known definition of triangular norms [Definition 1; cf. \textit{B. Schweizer} and \textit{A. Sklar}, Probabilistic metric spaces (North-Holland, Amsterdam) (1983; Zbl 0546.60010), Definition 5.5.1] which can generate misunderstandings in applications of his results. Similarly, in Definition 6 the Archimedean triangular norm is called a zero-t-norm. Remark: In general the S-T composition from Definition 4 is not associative (e.g. for \[ S(x,y) = x + y - xy,\;T(x,y) = xy,\;x, y \in [0,1]), \] which is necessary for the unique definition of matrix powers in Definition 5.
scientific article; zbMATH DE number 1339537