Army command college of PLA
论文针对已有概率犹豫模糊熵测度构造复杂、区分能力弱等缺点, 提出了混合型概率犹豫模糊熵测度. 混合型熵测度能够综合反映概率犹豫模糊元所具有的个体不确定性和整体不确定性, 具有结构简单、物理意义明确、区分能力强等优势. 在概率犹豫模糊元规范化的基础上, 论文基于混合型熵测度的构造理念所设计的混合型交叉熵测度, 克服了已有交叉熵测度的设计缺陷, 能够综合反映两个概率犹豫模糊元之间的个体区分度和整体区分度, 且具有自然的对称性. 基于混合型熵测度和交叉熵测度, 论文进一步设计了概率犹豫模糊环境下的多属性决策方法, 并将其应用于无人机集群作战效能评估. 数值和理论结果表明, 论文所提混合型概率犹豫模糊熵和交叉熵测度能够成对设计, 互为印证, 具有广泛的应用前景.
Aiming at solving the shortcomings of existing entropy measures of the probabilistic hesitant fuzzy elements (PHFEs), which are too complex in structure and too weak in discriminating ability, some hybrid entropy measures of the PHFEs are proposed in this work. The hybrid entropy measures of the PHFEs can comprehensively reflect their individual and collective uncertainties, and possess some advantages of simple structure, clear physical meaning and strong discriminating ability. Based on the normalized PHFEs, some hybrid cross-entropy measures of the PHFEs are designed with the construction method of hybrid entropy measures, which can overcome the design flaws of existing cross-entropy measures, comprehensively reflect the individual and collective discriminations between the PHFEs, and possess natural symmetry. Based on the proposed entropy and cross-entropy measures, we further develop a multi-attribute decision-making (MADM) method with the PHFEs and apply it to evaluate the combat effectiveness of UAV clusters. Numerical and theoretical results show that the hybrid entropy and cross-entropy measures of the PHFEs can be designed in pairs, be supportive to each other and have a wide range of applications.