On simultaneously nilpotent fuzzy matrices
The theory of nilpotent fuzzy matrices is developed [cf. \textit{H. Hashimoto}, Fuzzy Sets Syst. 10, 101-108 (1983; Zbl 0512.15014); \textit{J.-X. Li}, ibid. 45, 313-319 (1992; Zbl 0749.15014); ibid. 62, 83-88 (1994; Zbl 0826.15020); \textit{Y.-Y. Lur}, \textit{S.-M. Guu} and \textit{C. S. Pang}, On the eigenvalues of fuzzy matrices. Working paper, Department of Information Management, Yuan Ze Univ. (2001)]. As a generalization, the notions of the simultaneous nilpotence and of the simultaneously controllable fuzzy matrices are introduced. The properties of the simultaneous nilpotence, related to the infinite products of a finite number of fuzzy matrices which converge to the zero matrix, are established. It is also taken into account that in the study on consecutive powers of fuzzy matrices, a controllable fuzzy matrix can be characterized by an associated nilpotent fuzzy matrix. As an analogue, it is shown that the simultaneously controllable fuzzy matrices can be characterized by a finite set of the associated simultaneously nilpotent fuzzy matrices.
scientific article; zbMATH DE number 1917802