The DTRS is based on strict indiscernibility relation， therefore, it can only be applied to discretized data. In consequence, a fuzzy decision-theoretic rough set(FDTRS) model and a forward greedy attribute reduction algorithm were proposed based on the FDTRS model. The FDTRS model generalizes the indiscernibility relation to fuzzy T-equivalence relations based on Gaussian kernel and defines the conditional probability from the perspective of degree of fuzzy membership. The FDTRS can deal with numerical data directly. Four UCI data sets were used to compare the performance of the FDTRS with Pawlak rough set and decision-theoretic rough set on attribute reduction. Experimental results help quantify the performance of the FDTRS.