Abstract
As one of the burgeoning decision-making instruments, the integrity of dual probabilistic linguistic term sets (DPLTSs) is to express the decision information in terms of cognitive certainty and uncertainty. The superiority of correlation coefficient is to demonstrate the interrelationship of the variables. This paper aims to give full play to the advantages of the above two. Firstly, it defines the dual probabilistic linguistic correlation coefficient. Then, it is based on the proposed entropy for DPLTSs calculates the comprehensive weight vector. Moreover, combined with the proposed correlation coefficient, it further defines the weighted correlation coefficient as a measure for the application about artificial intelligence. Besides, it uses the dual probabilistic linguistic closeness coefficient as the reference to compare the pros and cons. Finally, a specific numeric simulation is utilized to demonstrate the feasibility of the two different measures.

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Acknowledgements
This work was supported by the Scientific Research Foundation of Graduate School of Southeast University (No. YBJJ1832), the FEDER financial support from the Project TIN2016-75850-R, and the Postgraduate Research and Practice Innovation Program of Jiangsu Province (No. KYCX18_0199).
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Xie, W., Xu, Z., Ren, Z. et al. The probe for the weighted dual probabilistic linguistic correlation coefficient to invest an artificial intelligence project. Soft Comput 24, 15389–15408 (2020). https://doi.org/10.1007/s00500-020-04873-0
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DOI: https://doi.org/10.1007/s00500-020-04873-0