基于Z-数信息的多属性群决策方法及其应用研究

Z-number is an efficient type of information for realizing high-quality evaluations and decision making. Taking the energy safety assessment decision as an example, not only the attribute-values of alternatives are needed, but also the credibility level of such attribute-values should be considered. How to construct new multiple attributes group decision making models and approaches based on Z-number information comes to be a key scientific problem with theoretical and practical meaning in the field of evaluations and decision making. The development of Z-number information stays in an early stage, the underlying basic core framework of such information including the algebra operations, order relations and information fusion has not been completely built. With the above background, this project aims to study on multiple attributes group decision making with Z-number information and its applications. Firstly, new algebra operational laws of linguistic variables that satisfy additive idempotency and multiplication asymmetry are developed, based on which a more logical algebra structure of Z-numbers is built. Besides, other underlying contents including the normalization, incomplete Z-number information processing, and distance and similarity measures of Z-numbers are considered, their mathematical properties are also studied. Secondly, by introducing the games theory and Takag-Sugeno-Kang (TSK) fuzzy reasoning rules to multiple attributes group decision making with Z-number information, the weighting method and logical reasoning structure based Z-number information fusion under new decision principles are considered. By the case study of energy security assessment and optimization in the central 6 provinces, feedback the theoretical analysis and providing decision-making reference for regional economic construction are realized.

Z-数信息是实现高质量评价和决策的一种有效信息形式。以能源安全评估决策为例，不仅需要提供方案的指标属性值，而且要提供该属性值的可信性程度。如何构建新的基于Z-数信息的多属性群决策模型和方法成为决策和评价领域既有理论又有实践意义的关键科学问题。Z-数信息的概念刚提出不久，其代数运算、序关系和信息融合方法等底层基础性核心框架尚未完全建立。本项目拟开展基于Z-数信息的多属性群决策模型和应用研究。首先构建语言变量满足加法幂等和乘法非对称性的新代数运算体系，并由此建立Z-数更具逻辑性的基本代数结构，同时探究Z-数规范化、缺省数据插值方法、距离和熵测度理论，论证其数理性质；其次将博弈原理和TSK模糊推理规则引入Z-数多属性群决策问题中，探讨新的决策准则下的赋权方法和逻辑推理结构的Z数信息融合。通过中部6省能源安全评估与优化的案例研究，反馈理论模型的可行性和有效性，从而为区域经济建设提供决策参考。

实际的经济和管理决策问题中，决策和预测信息往往蕴含不同程度的不确定性。无论是客观观测的数据亦或是主观给出的评价结果，其可信性一直未引起足够的重视。Z数的提出为此类考虑决策和预测数据可信性的信息提供了新的概念和表达形式。Z数通过给出观测或者评估数据的概率分布表达数据的可信性。以Z数为基础，包括仅应用一个[0, 1]中的固定数值表达观测或者评估数据可信性程度的基本不确定信息以及应用概率值表达可信性的不同类型概率语言等为蕴含可信性数据的问题建模和分析提供了多样化的技术和工具。本项目对新型信息表达形式的代数运算规则、集合运算规则、信息测度和信息融合方式等基础框架和原理进行了系统研究。Z数信息环境下，提出语言型Z数的集合运算规则和多模态Z数排序规则。同时，对与Z数同质的基本不确定信息进行了相应研究。对所提出运算满足的数学性质给出了相应的证明，在此基础上提出语言Z数软集和基本不确定信息软集以及对应的多属性群决策模型，给出了一类处理此类决策信息的非参数数学工具。基于排序集成提出一类基于排序集成的混合Z数多属性决策原理和方法，其仅依赖于序关系即可以得到方案的最终排序。针对不确定信息已有代数运算的不足，基于阿基米德copula、co-copula、最小公倍数原理和近世代数加法幂等性等规则提出直觉模糊数、犹豫语言术语集和犹豫模糊信息等新的代数运算体系和信息测度等。所提出的代数运算规则或者可以综合考虑模糊信息之间的联系或者可以降低运算结果的维数以免造成维数灾难。拓展了已有的多属性决策原理，如ORESTE、ELECTRE-TRI、VIKOR和前景理论等到不同类型模糊决策信息情境下。针对不同模糊情境下的偏好关系矩阵的一致性结合局部反馈机制和DEA交叉效率等给出一致性调整和优化算法。针对决策的预测前提，探讨了一系列组合预测和基于数值分解和最优组合预测的人工智能预测算法，并将其应用到空气质量指数、PM2.5、电力负荷和原油价格等预测实践。本项目的研究结果可为相关部门的预测和决策分析提供理论依据和技术支持。