基于综合犹豫模糊熵的多属性决策研究  

Multi-attribute decision making based on comprehensive hesitation fuzz entropy

作　　者：刘赢 关欣 李易城 LIU Ying;GUAN Xin;LI Yi-cheng(Naval Aviation University,Yantai 264001,China;93116 Troop of PLA,Shenyang 110000,China)

机构地区：[1]海军航空大学,山东烟台264001 [2]93116部队,沈阳110000

出　　处：《控制与决策》2024年第6期2022-2030,共9页Control and Decision

基　　金：国防科技卓越青年人才基金项目(2017-JCJQ-ZQ-003);泰山学者工程专项经费项目(ts201712072)。

摘　　要：针对犹豫模糊集现有熵测度存在的计算过程复杂以及反直觉等现象,提出一种综合犹豫模糊熵,并基于累积前景理论,改进传统的TOPSIS决策方法,构建属性权重未知下的多属性决策模型.首先,在模糊度和非明确度的基础上,给出犹豫模糊熵新的公理化定义;然后,定义综合犹豫模糊熵,并证明其满足新的公理化定义,与现有犹豫模糊熵的对比分析表明,综合犹豫模糊熵在更为合理表征犹豫模糊元模糊性的同时,也解决了反直觉的问题;最后应用改进TOPSIS方法对所提出的综合性熵测度进行仿真分析,通过实例分析验证所提出的犹豫模糊熵的有效性.相比现有熵测度,综合犹豫模糊熵还具有计算简单和易于理解等优点,改进TOPSIS方法能够考虑决策者的心理偏好,相比传统决策手段,其决策效果更为合理.In view of the complex calculation process and counter-intuitive phenomena of the existing entropy measures of hesitant fuzzy sets,a comprehensive hesitant fuzzy entropy is proposed.At the same time,the traditional TOPSIS method is improved based on the cumulative prospect theory,and a multi-attribute decision-making model with unknown attribute weights is constructed.First,a new definition of hesitation fuzzy entropy is offered based on fuzziness and uncertainty.Then,the comprehensive hesitation fuzzy entropy of the hesitation fuzzy element is provided,and it is shown that it fulflls the new axiomatic definition.Additionally,the results compared with the existing entropys demonstrate that the proposed entropy not only more accurately captures the fuzziness of hesitant fuzzy elements,but also resolves the paradoxical phenomena.Finally,the comprehensive entropy measure is applied and analyzed using the improved TOPSIS method.The case study serves as evidence for the success of the proposed approach.In addition,when compared to the existing entropies,the comprehensive hesitant fuzzy entropy offers the benefits of straightforward calculation and simple comprehension,at the same time,the improved TOPSIS method can take into account the psychological preferences of decision makers,and the effect is more reasonable than traditional methods.

关 键 词：犹豫模糊集 犹豫模糊熵 模糊度 非明确度 累积前景理论 改进TOPSIS方法 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]