Information quality (IQ) is a significant index in information processing, e.g. multiple information fusion. An extended method considering the IQ has been investigated using the multi-complex-valued information. However, how to fuse the multiple complex-valued distributions (CvDs) with correlation and preference of decision-maker may be a fantastic issue. In this paper, we propose a new method using the power ordered weighted average (POWA) operator to integrate multi-complex-valued distributions considering the information correlation and preference of decision-maker. The proposed method is an extension of the previous work. Some examples and applications are used to illustrate the effectiveness of the proposed method.