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The meta-synthesis method has achieved good results in China's aerospace engineering and population economic regulation. This theoretical achievement obtained from engineering practice becomes an effective way to solve complex decision-making problems. The meta-synthesis method obtains the final decision-making result by comprehensively considering qualitative and quantitative criteria and gathering multivariate heterogeneous attribute information. In view of the broad application of entropy theory in quantitative evaluation and fuzzy decision-making, this paper proposes a meta-synthesis decision-making method based on probabilistic linguistic cross-entropy and priority relations for multicriteria decision-making problems including qualitative and quantitative multivariate heterogeneous attribute information. First, the quantitative attribute weight is calculated based on the entropy weight method, and the qualitative attribute weight is calculated by considering the individual effects and interactions of the probabilistic linguistic term sets under qualitative attributes comprehensively through probabilistic linguistic entropy and cross-entropy. Then, the weight preference coefficient is used to integrate the qualitative and quantitative heterogeneous attribute weights to obtain standardized processing weight information, and, on the basis of the 0-1 priority relation matrix, we compare and analyze the advantages and disadvantages of alternatives under all criteria and obtain an overall ranking result of the alternatives. Finally, the effectiveness and superiority of the proposed method are verified by a comparative analysis of a numerical example and the decision-making method.

Integrated Decision-Making Method for Heterogeneous Attributes Based on Probabilistic Linguistic Cross-Entropy and Priority Relations