Simultaneously controllable fuzzy matrices

Let F be a set of n x n fuzzy matrices. F is called simultaneously controllable if there exists a permutation matrix P such that for each A @e F, C = [c"i"j] = P @? A @? P^T satisfies c"i"j >= c"j"i for i > j, where @? is the max-min composition. In this paper, the necessary and sufficient conditions for a set of n x n fuzzy matrices to be simultaneously controllable will be established. A constructive algorithm which can determine a simultaneously controllable set of n x n fuzzy matrices is presented as well.

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