On Infinite Products of Fuzzy Matrices

In this paper, we study the convergence of infinite products of a finite number of fuzzy matrices, where the operations involved are max-min algebra. Two types of convergences in this context will be discussed: the weak convergence and strong convergence. Since any given fuzzy matrix can be "decomposed" of the sum of its associated Boolean matrices, we shall show that the weak convergence of infinite products of a finite number of fuzzy matrices is equivalent to the weak convergence of infinite products of a finite number of the associated Boolean matrices. Further characterizations regarding the strong convergence will be established. On the other hand, sufficient conditions for the weak convergence of infinite products of fuzzy matrices are proposed. A necessary condition for the weak convergence of infinite products of fuzzy matrices is presented as well.

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