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On the sequence of consecutive powers of a fuzzy matrix with max-Archimedean-t-norms. (English) Zbl 1087.15023

The paper deals with matrices over the lattice \(([0,1],max,min,T)\) (fuzzy matrices), where \(T\) is an Archimedean triangular norm [for triangular norms cf. E. P. Klement, R. Mesiar, and E. Pap, Triangular norms. Trends in Logic–Studia Logica Library. 8. (Dordrecht: Kluwer Academic Publishers) (2000; Zbl 0972.03002)]. Mixed max-min powers of such matrices were examined by S.-M. Guu, H.-H. Chen, and C.-T. Pang [Fuzzy Sets Syst. 121, 203–207 (2001; Zbl 0994.15017)].
The author examines \(\max\)-\(T\) product and \(\max\)-\(T\) powers of such matrices, generalizing previous results on max-min powers. Another generalization concerns results on max-product powers of matrices [cf. M. M. Bourke and D. G. Fisher, Fuzzy Sets Syst. 81, 227–234 (1996; Zbl 0885.93038) and L. Elsner and P. van den Driessche [Lin. Alg. Appl. 302–303, 17-32 (1999; Zbl 0949.65032)]. In particular, convergence and asymptotic periodicity of matrix powers are characterized [cf. also Z.-T. Fan, Fuzzy Sets Syst. 102, 281–286 (1999; Zbl 0939.15011)].

MSC:

15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A30 Algebraic systems of matrices
03E72 Theory of fuzzy sets, etc.
06F05 Ordered semigroups and monoids
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