基于不确定性测度的犹豫模糊决策模型

针对已有犹豫模糊熵测度计算复杂、区分能力弱等问题，在综合衡量犹豫模糊元自身不确定性及其所表达信息不确定性的基础上，以凸组合的形式设计了混合型犹豫模糊熵和交叉熵测度。混合型犹豫模糊交叉熵测度用于度量两个犹豫模糊元之间的区分程度，它和混合型犹豫模糊熵测度一起统一于犹豫模糊元的不确定性测度。与已有的犹豫模糊不确定性测度相比，混合型熵测度具有结构简单、物理意义明确、区分能力强等优势；而混合型交叉熵测度则具有自然的对称性。然后，基于混合型犹豫模糊熵和交叉熵测度构建了属性权重未知条件下的多属性决策模型，并将其应用于无人机作战效能评估。

Hesitant Fuzzy Decision-Making Model Based on Uncertainty Measures

To address the problems of complicated calculations and weak discriminating ability for some existing hesitant fuzzy entropy measures, the hybrid entropy and cross-entropy measures for hesitant fuzzy elements (HFEs) are designed in the form of convex combinations on the basis of comprehensively evaluating the uncertainty of HFEs themselves and the information they express. The hybrid cross-entropy measures for HFEs are used to measure the differentiated degree between two HFEs and can be unified together with the hybrid entropy measures as the uncertainty measures for HFEs.Compared with the existing uncertainty measures for HFEs, the hybrid entropy measures show the advantages of simple structure, clear physical meaning, and strong discriminating ability, with the hybrid cross-entropy measure being naturally symmetrical. Then, based on the proposed entropy and cross-entropy measures for HFEs, a multi-attribute decision-making (MADM) model, under the condition of unknown attribute weights, is established and further applied to the evaluation of UAVs'' combat effectiveness.