Wang Lei, Xue Huifeng
China Academy of Aerospace Systems Science and Engineering, Beijing 100035, China.
Entropy (Basel). 2020 Sep 9;22(9):1009. doi: 10.3390/e22091009.
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.
综合集成方法在中国航天工程和人口经济调控中取得了良好效果。这一源于工程实践的理论成果成为解决复杂决策问题的有效途径。综合集成方法通过综合考虑定性和定量标准并收集多源异构属性信息来获得最终决策结果。鉴于熵理论在定量评价和模糊决策中的广泛应用，本文针对包含定性和定量多源异构属性信息的多准则决策问题，提出一种基于概率语言交叉熵和优先关系的综合集成决策方法。首先，基于熵权法计算定量属性权重，通过概率语言熵和交叉熵综合考虑定性属性下概率语言术语集的个体效应和交互作用来计算定性属性权重。然后，利用权重偏好系数对定性和定量异构属性权重进行集成，得到标准化处理后的权重信息，并基于0-1优先关系矩阵，比较分析各方案在所有准则下的优劣，获得方案的总体排序结果。最后，通过数值算例与决策方法的对比分析，验证了所提方法的有效性和优越性。
