In this paper, we focus on describing the oscillation period and index of fuzzy tensor. The definition of the induced third-order fuzzy tensor is proposed. By using this notion, firstly, the oscillation period and index of fuzzy tensor are obtained on the basis of Power Method with max-min operation. Secondly, we rely on Minimal Strong Component to find the oscillation period of fuzzy tensor. It is a more practical graph theory method that the number of nonzero elements is less than half of the sum of fuzzy tensor elements. Furthermore, numerical results demonstrate the Power Method and the Minimal Strong Component two algorithms for solving the period and index of fuzzy tensor which are effective and promising.