On simultaneously nilpotent fuzzy matrices Original Research Article

Nilpotent fuzzy matrices play a crucial role in the study of fuzzy matrices. In this paper, we shall extend the nilpotence to the notion of simultaneous nilpotence for a finite set of fuzzy matrices. The notion of simultaneous nilpotence relates to the infinite products of a finite number of fuzzy matrices which converge to the zero matrix. Properties of the simultaneous nilpotence will be established. In the study of consecutive powers of a fuzzy matrix, a controllable fuzzy matrix can be characterized by an associated nilpotent fuzzy matrix. In this paper, we propose the notion of simultaneously controllable fuzzy matrices which can be thought of as a generalization of the notion of controllable fuzzy matrices. Similar to the nilpotent characterization for a controllable fuzzy matrix, the simultaneously controllable fuzzy matrices can be characterized by a finite set of associated simultaneously nilpotent fuzzy matrices.