To solve the problem that the traditional grey correlation degree can not effectively deal with the interaction between attributes, the grey fuzzy integral correlation degree is defined. At the same time, a calculation method of fuzzy measures is given. In the method, weights of attributes and the interaction degree between attributes are transformed into lambda fuzzy measure with φ_s  transformation function. A calculation method of weights based on Mahalanobis-Taguchi Gram-
Schmidt is proposed, which can not only consider the subjective preference of decision makers, also can eliminate the overlap information between attributes, so that the weights of attributes the method calculated is more reasonable. A decision making model based on grey fuzzy integral correlation degree is presented, and an application example is analyzed. Finally, the example verifies the feasibility of the decision making model, and the sensitivity of the decision result is analyzed based on different interaction degree.