基于Z数的决策方法及应用研究

The reliability of information can directly affect the accuracy of decision-making. Z-numbers contain fuzzy information and stochastic information, and consider both reliability and uncertainty of information. Thus, using Z-numbers to depict decision information can effectively improve the accuracy and validity of decision-making results. Therefore, based on the theories of fuzzy decision-making and stochastic decision-making, this project intends to make a systematic study on Z-number-based decision-making methods. Considering the existing problems and shortcomings in the research outcomes about Z-numbers, this project will propose new transformation methods of discrete Z-numbers, explore reasonable operation methods of continuous Z-numbers regarding the integrability of functions involved in continuous Z-numbers, and define different forms of extended Z-numbers from distinctive perspectives, including two parts of Z-numbers being expressed by different fuzzy numbers, the introduction of time factor and so on. Subsequently, we are going to improve or define the operation rules, comparison rules, and measures for discrete Z-number, continuous Z-numbers and extended Z-numbers. On this basis of the aforementioned research, a series of multi-criteria decision methods for different Z-numbers will be proposed. Finally, to verify the feasibility and effectiveness of the proposed methods, all the methods will be respectively applied to handle different practical decision-making problems related to this project, such as service evaluation of modern logistics, chronic disease early-warning under big data environment, E-commerce product recommendation, etc. In summary, the research achievements of this project will enrich the uncertain decision theory and will provide a series of new ideas and methods for scientific decision-making.

信息的可靠性直接影响决策结果的准确性。Z数包含模糊信息和随机信息，且综合考虑了信息的可靠程度和不确定性，使用Z数刻画决策信息可充分提高决策结果的准确性和有效性。为此，在模糊决策和随机决策理论的基础上，本项目拟对基于Z数的决策方法进行系统研究。针对Z数现有研究存在的问题和不足，本项目提出新的离散Z数转换方法，考虑连续Z数所涉函数是否可积，探究合理的连续Z数运算方法，以及从Z数两部分由不同模糊数表示和引入时间因素等方面定义不同形式的扩展Z数；改进或定义离散Z数、连续Z数和扩展Z数的运算规则、比较规则和测度等。在此基础上，提出一系列基于不同形式Z数的多准则决策方法。最后，将所提出的方法应用于解决现代物流服务评价、大数据环境下慢性疾病预警和电商产品推荐等与本项目相关的实际决策问题，以验证方法的可行性和有效性。本项目成果将丰富不确定决策理论，为科学决策提供一系列新的思路和方法。

信息的可靠性直接影响决策结果的准确性。Z数包含模糊信息和随机信息，且综合考虑了信息的可靠程度和不确定性，使用Z数刻画决策信息可充分提高决策结果的准确性和有效性。本项目针对Z数现有研究存在的问题和不足，主要对Z数的相关理论基础和基于Z数的多准则决策方法展开研究。利用模糊集理论、多准则决策理论和有限理性行为决策理论（前景理论、后悔理论、有限理性行为测度的相关模型等），定义了一系列Z数的扩展形式、运算规则、聚合算子、测度方法和优序关系模型，提出了一系列基于Z数测度的多准则决策方法和基于Z数优序关系的多准则决策方法。此外，探讨了概率语言术语集、图片模糊集和中智集的基本性质，并提出了大数据驱动的管理与决策方法。本项目的成果丰富了不确定决策理论的内容，为科学决策提供了新方法，可用于解决现代物流服务评价、电商产品推荐以及大数据环境下风险评估等相关实际问题。经过4年的努力工作，本项目全面完成了预定的研究内容。在国内外重要期刊及国际学术会议上发表了论文39篇和完成博士学位论文2篇，其中SCI/SSCI期刊论文39篇，ESI高被引论文2篇。