Decomposition theorem of fuzzy tensors and its applications.

In this paper, we focus on investigating decomposition theorem of fuzzy tensors. We first propose definitions of cutting tensor and anti-fuzzy cutting tensor. Scalar product and anti-fuzzy scalar product of number and fuzzy tensor are put forth, and some properties of scalar product are discussed. Then, we propose and prove decomposition theorem of fuzzy tensor. Our numerical examples and applications show that the feasibility of the presented decomposition methods.