Big data is changing our lives and the way we understand the world, as well as the operational patterns of business and social organizations. Fully understanding the value of data and knowing how to use big data to provide a basis for business decision-making has gradually become the most basic thinking that business organizations should possess in the era of big data. Under the thinking mode of data-driven decision-making, many information science researchers have discussed the model, architecture, operation mechanism and other aspects of big data competitive intelligence system. At the same time, more and more enterprises, such as IBM, Amazon, Google, Microsoft, Wal Mart, etc., have begun to attach importance to the development and construction of big data competitive intelligence software systems, and have achieved certain results. The enterprise competitive intelligence system evaluation in the context of big data is regarded as multi-attribute decision-making (MADM). In this paper, the Hamy mean (HM) and the power average (PA) are connected with 2-tuple linguistic neutrosophic sets (2TLNSs) to propose the 2-tuple linguistic neutrosophic numbers power HM (2TLNPHM) operator. Then, use the 2TLNPHM operator to handle MADM with 2TLNS. Finally, taking the enterprise competitive intelligence system evaluation in the context of big data as an example, the proposed method is explained. The main contributions of this study are summarized: the establishment of the 2TLNPHM operator; (2) The 2TLNPHM operator was developed to handle MADM with 2TLNS; (3) Through the empirical application of the enterprise competitive intelligence system evaluation, the proposed method is validated; (4) Some comparative studies have shown the rationality of the 2TLNPHM operator.