混合型概率犹豫模糊熵和交叉熵测度  

Hybrid entropy and cross-entropy measures of probabilistic hesitant fuzzy information

作　　者：方冰 韩冰 FANG Bing;HAN Bing(Army Command College of PLA,Nanjing 210045,China)

机构地区：[1]陆军指挥学院,南京210045

出　　处：《控制与决策》2023年第2期546-554,共9页Control and Decision

摘　　要：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,提出一种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,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,能够克服已有交叉熵测度的设计缺陷,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,进一步设计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.数值和理论分析结果表明,所提出的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.The paper aims at solving the shortcomings of existing entropy measures of probabilistic hesitant fuzzy elements(PHFEs), which are either too complex in structure or too weak in discriminating ability, and proposes some hybrid entropy measures of PHFEs. The hybrid entropy measures of 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 normalized PHFEs, some hybrid cross-entropy measures of 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 discrimination degrees between PHFEs, and possess natural symmetry. Based on proposed entropy and cross-entropy measures, a multi-attribute decision-making(MADM) method with PHFEs is further developed and applied to evaluate the combat effectiveness of UAV clusters. Numerical and theoretical results show that hybrid entropy and cross-entropy measures of PHFEs, which can be designed in pairs and supportive to each other, have a wide range of applications.

关 键 词：概率犹豫模糊集 概率犹豫模糊元 熵测度 交叉熵测度 作战效能评估 

分 类 号：C934[经济管理—管理学]