The conventional intuitionistic fuzzy multi-attribute decision making method has following drawbacks: The fixed weight system is difficult to reflect effectively the nonlinear combination mechanism among factors for complex systems; the intrinsic relevancy of alternatives is ignored; the heterogeneous risk attitude of decision-makers is not considered sufficiently. To overcome abovementioned drawbacks, based on the thinking perspective of nonlinear complex systems, an intuitionistic fuzzy multi-attribute decision making method with variable weights is proposed, which integrates well of the three aspects: the varying weights of attribute factors, the correlation of alternatives and the reasonable introduction of risk attitude of decision-maker. It should be noted that, varying attribute weights are determined by applying decision making trial and evaluation lab(DEMATEL) method. Furthermore, a new score function is constructed by combining the set pair potential theory with the risk attitude parameter, and its relevant properties are also proved. Finally, a real example study and corresponding comparative analysis verify the scientificity and feasibility of the proposed method.