Abstract: Based on the definition of fuzzy matrix and λ Cutting matrix, a production operation of number and fuzzy matrix is put forth, through which the decomposition theorem of fuzzy matrix is thus established, and the transformation relationship between fuzzy matrix and 〖WTBX〗λ〖WTBZ〗-Cutting matrix, the transformation relationship between a category of classic set matrix and fuzzy matrix are also acquired. The properties of the product operation concerning numbers and fuzzy matrices are put under discussion as well.