The generalized intuitionistic fuzzy weighted interaction average operators are proposed based on the interactions between the membership function and the non-membership function of different intuitionistic fuzzy sets. The concrete expressions of these operators are obtained by derivation and some properties of these operators are investigated. A multi-attribute decision making method based on the proposed operators is investigated. An example shows the feasibility and validity of the proposed operator in the application of decision making problems and the influence of different parameters lambda on decision making is analyzed. The influences of interactions on decision results are interpreted and the stability of the proposed generalized operators are illustrated by sensitivity and other corresponding analysis.