On convergence of the min-max compositions of fuzzy matrices (Q5929895)

The authors examine matrices over the lattice \(([0,1],\max,\min)\). Properties of max-min powers of such matrices are well known [cf. e.g. \textit{Z. Fan} and \textit{D. Liu}, Fuzzy Sets Syst. 88, No. 3, 363-372 (1997; Zbl 0915.15016)]. Dual properties of min-max powers can be simply derived by de Morgan laws [cf. Theorem 2 in \textit{Z. Fan}, Fuzzy Sets Syst. 102, No. 2, 281-286 (1999; Zbl 0939.15011)]. The authors describe a convergence of a min-max power sequence with a complete dual proof. The paper contains also some remarks about the min-max product of triangular matrices (not connected with the main problem).